Frege's Rationalist Epistemology

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced withwith permission permission of of the the copyright copyright owner. owner. Further Further reproduction reproduction prohibited prohibited without without permission. permission. FREGE’S RATIONALIST EPISTEMOLOGY

Dennis Dale Burke

submitted to the

Faculty of the College of Arts and Sciences

of The American University

in Partial Fulfillment of

the Requirements for the Degree of

Master of Arts

Philosophy

Chain David F. T. Rodier, Ph.D.

Rom Harr6, Ph. D.

Dean of the College of Arts and Sciences

The American University

Washington, D.C. 20016

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UMI 300 North Zeeb Road Ann Arbor, MI 48103

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DENNIS DALE BURKE

1999

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TO ANN BURKE

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FREGE’S RATIONALIST EPISTEMOLOGY

Dennis D. Burke

ABSTRACT

This thesis examines the rationalist epistemology of the German logicist mathematician

Gottlob Frege (1868-1925), whose principal contribution to mathematical logic was the

invention of the logical quantifier and application of mathematical functions to

propositional functions of logic. Frege is revered for his seminal investigations into

semantics. His work is credited by some as having inaugurated the 'linguistic turn.’ It

has been held that Frege's interests were primarily semantic and not epistemological.

The extreme realistic views attributed to him make it seem that he was interested in

ontology and an ally of Russell and Moore in the revolt against idealism. He rejected

formalism, empiricism and psychologism in logic and mathematics. I argue

controversially that Frege was indeed a psychologistic and rationalist philosopher with

strong ties to Neo-Kantianism and was concerned with the epistemology of

mathematical truth.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS

This thesis was written over a period of approximately two years affording me the

opportunity of receiving valuable comments and criticism of my advisors David Rodier,

Rom Harr6 and John Shosky. I am especially grateful to John Shosky for introducing me

to the philosophy of language in his course during the spring term in 1991, and to the

many other forays into analytical philosophy since then. This thesis would never have

been completed without the encouragement and guidance John Shosky. To David

Rodier I am most grateful for first introducing me to Gottlob Frege's writings in an

independent reading course on twentieth century philosophy in the summer of 1991. I

am privileged to have received invaluable criticism and advice from Rom Harr6 in

preparation of this thesis, especially concerning the philosophy of Leibniz and its

connection to Frege. I have also benefited immeasurably from visiting lecturers at The

American University, particularly Antony Flew, Paul Benacerraf and Nicholas Griffin.

Finally, I am indebted to ideas and insightful discussions with fellow students, especially

Robert Bernard, Jeff Cothran, and Sylvia Rolloff.

iii

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ABSTRACT...... ii

ACKNOWLEDGEMENTS...... iii

Chapter

1. INTRODUCTION...... 1

2. DISTORTIONS OF THE STANDARD INTERPRETATION...... 13

Contemporary View of Frege’s Place in Philosophy

Rational and Historical Reconstruction of Frege

Frege, as Philosopher of Language

Frege, as Philosophical Revolutionary

Frege's Cartesian Perspective

3. HISTORIC PHILOSOPHICAL AND SCIENTIFIC SETTING...... 51

Modem Philosophy and Scientific World View

Post-Kantian Idealism

Naturalism, Materialism, and Positivism

Psychologism and Anti-Psychologism

Neo-Kantianism

Neo-Hegelianism

Movement Toward Objectivity

Mathematical setting

4. FREGE’S INTELLECTUAL DEVELOPMENT...... 101

Frege’s Enigmatic Background

Philosophical and Mathematical Education

Neo-Kantian Influences

Lotzian Influences

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Leibnizian Influences

5. FREGE'S RATIONALIST EPISTEMOLOGY...... 124

Frege's Epistemological Motivations

Self-Evidence in Frege’s Thought

Epistemological Foundationalism

Metaphysical and Epistemological Dualism

Mathematical-Deductive Methodology

Axiomatization of Knowledge

Objectivity of Knowledge and Anti-Psychologism

Frege's Theory of Judgment

The Context Principle

Subjectivism and Objectivism

6. REALISM OR IDEALISM...... 186

Introduction

Realism

Idealism

7. CONCLUSION...... 203

BIBLIOGRAPHY...... 205

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1

INTRODUCTION

In this thesis I will challenge what has become in recent years the

standard interpretation of Frege. I follow Hans Sluga in referring to Michael Dummett’s

exegesis of Frege as the 'standard interpretation'.1 It is only fair however to point out that

Dummett rejected this appellation. In fact, Dummett claims “[tjhere is no received

interpretation [of Frege]."2 The standard interpretation of Frege stems as much from the

intense interest during this century in the philosophy of language, as it does from

Dummett’s exegesis of Frege.

Dummett is the most visible, authoritative and prolific of the interpreters

who have advanced the view of Frege as philosopher of language. He is by far the most

widely read and influential commentator on Frege today, and the interpreter who has

most vigorously advanced the standard interpretation. Michael Beaney has observed

that Dummett has written more about Frege than Frege himself wrote during his

lifetime.3 A complete list of Dummett’s works to which I will refer are included in the

Bibliography of this paper. The greater part of Dummett’s views on Frege are set forth

in three books: Frege: Philosophy of Language (1973,1981), The Interpretation of

Frege's Philosophy (1981), and Frege's Philosophy of Mathematics (1991 ).4 Any

alternative interpretation of Frege must necessarily confront Dummett’s

1 Hans Sluga, “Frege’s Alleged Realism” inInquiry, 20 (1977): 227. 2 Michael Dummett, The Interpretation of Frege's Philosophy (Cambridge: Harvard University Press), xiv. 3 Michael Beaney, ed.,The Frege Reader (Oxford: Blackwell, 1997), 386. 4 See Bibliography for other articles cited by Michael Dummett. 1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 substantial and highly influential exegesis. However, it is not my purpose in this paper to

indulge in analysis of the polemics between Dummett and Sluga, or to analyze his

dispute with Hacker and Baker, or others. Rather, it is my purpose to advance an

alternative interpretation that is at odds with the generally accepted view of Frege as a

philosopher of language. In the following presentation, some of Dummett’s views serve

as a convenient foil, against which the plausibility of my alternative interpretation can be

demonstrated. I will begin by summarizing some of what I believe to be the inaccuracies

in Dummett’s interpretation of Frege. Dummett emphasizes the semantic and ontological

elements while placing too little emphasis on the epistemological elements in Frege’s

thought. He gives central place to language in Frege's philosophy by equating Frege’s

’theory of meaning’, as “a theory of the practice of using language.”5 According to

Dummett, “Frege’s fundamental achievement was to alter our perspective in philosophy,

to replace epistemology, as the starting point of the subject, by what he called ‘logic’.”6

Dummett has claimed, “Much that traditionally belonged to metaphysics becomes part of

the theory of meaning as practiced by Frege: in particular, ontological questions.”7 He

attributes to Frege an extreme realistic view, referring to Frege’s work as representing “a

classic statement both of a realistic theory of meaning and of the realistic interpretation

of mathematics that goes under the name of ‘platonism’.”8 Dummett’s interpretation of

Frege minimizes the traditional philosophical standpoint of Frege’s work, and gives in

sufficient weight to the Kantian, the idealist, and the rationalist elements in Frege’s

thought. In contrast to the standard interpretation of Frege, I intend to advance an

5 Michael Dummett,Frege: Philosophy of Language, 2n ed., (Cambridge: Harvard University Press, 1981), 682. 8 Michael Dummett, Truth and Other Enigmas (Cambridge: Harvard University Press, 1978), 441. 7 Dummett, Frege: Philosophy of Language, 671. 8 Dummett, Frege: Philosophy of Language, 683.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 alternative interpretation in this paper intended to correct these deficiencies and

emphasize the rationalist and idealist elements in Frege’s thought.

The standard interpretation of Frege owes its genesis to the early

references to Frege by Bertrand Russell, who, in the Appendix to his Principles of

Mathematics (1903), provided a summary of “The Logical and Arithmetical doctrines of

Frege." In it, Russell emphasizes the semantic elements in Frege’s work. Notably,

Russell translates Frege’s technical term ‘Sinn’, into English as ‘meaning’.9 Anyone

unfamiliar with Frege’s actual works would easily assume that Frege was primarily

interested in semantics and logical analysis of expressions in ordinary language.

Wittgenstein and his followers also contributed to this view of Frege. Wittgenstein

emphasized the importance of language, as the totality of propositions constituting the

limits of reality10, equated philosophy with the critique of language11, and assimilated the

theory of knowledge with psychology.12

Those who followed Wittgenstein, who were not directly familiar with

Frege’s works, erroneously attributed to Frege similar views. This became the canonical

view of Frege, which received additional support from Rudolph Camap, a former student

of Frege. Carnap’s series of works on the semantics and their relations to syntactical

concepts, Introduction of Semantics (1942), Formalization of Logic (1943), and Meaning

and Necessity (1947) stresse the semantic aspects of in Frege’s works. Under the

influence of Tarski, Camap was motivated to develop a formal method of semantics - an

analysis of the signifying function of language to supplement the syntactic methods of

9 Russell,The Principles of Mathematics, 2n ed., (reprint, New York: Norton, 1938), 501ff. 10 Ludwig Wittgenstein, Tractatus Logico-Philosophicus, (reprint, London: Routledge, 1922). 4.001. Hereafter, I will refer to this work as simply,Tractatus. 11 Wittgenstein, Tractatus, 4.0031. 12 Wittgenstein, Tractatus, 4.1121.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 formal logic.13 Camap and Wittgenstein, by placing emphasis upon Frege’s work in

semantics, encouraged their readers to view Frege as a logician primarily interested in

the semantic workings of natural and formal languages.

Those English-speaking philosophers coming after Wittgenstein and

Camap, and thus under their influence, were naturally more interested in what then

became the contemporary problems in the philosophy of language. Frege’s works were

not available in English translation until the mid-twentieth century. Frege’s essay “Clber

Sinn und Bedeutung" was the first of Frege's works to be translated in English as “On

sense and reference" in 1948.14 This essay became the most widely published of

Frege’s works in the English language. Herbert Feigel translated it the next year.15

Eventually it was published in 1950 in a collection of essays edited by Peter Geach and

Max Black, entitled Translations from the Philosophical Writings of Gottlob Frege.'6

Wittgenstein initially suggested this collection.17 J.L. Austin, most noted as the an

Oxford 'ordinary language' philosopher who sought solutions to problems in philosophy

in linguistic usage, translated into English Frege’s Die Grundlagen der Arithmetik, as

The Foundations of Arithmetic in 1950. Alonzo Church first published his highly

influential Introduction to Mathematical Logic, Part in I, 1944, with an enlarged and

revised edition in 1956, which adapts a modified form of Frege’s the theory as advanced

in “Clber Sinn und Bedeutung", as its semantic base.

13 Camap, Introduction to Semantics and Formalization of Logic in Studies in Semantics, (Cambridge: Harvard University Press, 1961), x. 14 Gottlob Frege, ‘On Sense and Reference", trans. Max Black,Philosophical Review 57 (1948), 207-230. 15 H. Feigel and W. Sellars,Readings in Philosophical Analysis, New York: Appleton-Century- Crofts, 1949, 85-102. 16 Gottlob Frege, “On Sense and Reference", trans. Max Black,Translations in from the Philosophical Works of Gottlob Frege, ed. Max Black and Peter Geach, 2n ed., (Oxford: Blackwell, 1960). 17 Hans Sluga, “Frege on meaning" inThe Rise of Analytic Philosophy, ed. Hans-Johann Glock, (Oxford: Blackwell, 1997), 17-34.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 By 1950 the influence of Frege upon analytic philosophy was great, but it

was largely second hand, known only through a few philosophers who had studied him

directly, such as Russell, Camap, Wittgenstein, Black, Geach, Austin and Feigl. A

canonical picture of Frege, as primarily a philosopher of language, emerged in the 1940s

and 1950s. It found further elaboration in Peter Geach's (with Anscombe) Three

Philosophers (1961), and also in Geach’s Reference and Generality (1962). It has now

found its contemporary and most vigorous elaboration in Dummett, and close followers

of the canon, like Anthony Kenny in his Frege (1995).

There are a number of recent works, which emphasize various elements

of Frege's work, but which do not challenge in any significant respect the canonical

interpretation of Frege. Michael Resnick18 has written on the mathematical aspects of

Frege's thought, while paying passing tribute to Frege’s contributions to the philosophy

of language. David Bell's Frege’s Theory of Judgment (1979) explicates and expounds

Frege’s views concerning the problem of the unity of the proposition. Crispin Wright’s

Frege's Conception of Numbers as Objects defends Frege’s Platonism. Gilead Bar-Elli

explored intentionality in Frege’s thought in his The Sense of Reference (1996).

There have been, nevertheless, several recent ‘revisionist’ interpretations

of Frege. Philip Kitcher has written on Frege’s epistemological motivations, while

acknowledging Frege’s influence by Kant, in his “Frege’s Epistemology" (1979).19 The

epistemological aspects of Frege’s thought have been emphasized by Gregory Currie in

his book Frege: An Introduction to His Philosophy (1982), and by Wolfgang Carl in his

Frege's Theory of Sense and Reference (1994). Carl also rightly emphasizes the

historical influences on Frege, but unjustly separates Frege's mathematical interests

18 Michael Resnick,Frege and the Philosophy of Mathematics (Ithaca: Cornell University Press, 1980).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 from his interests in semantics. Hans Sluga in his Gottlob Frege (1980 has emphasized

the Kantian influences in Frege’s thought. Sluga has also emphasized both the

rationalist and idealist elements in Frege’s thought, respectively, in his articles “Frege as

Rationalist" (1976) and “Frege’s Alleged Realism" (1977). He presented an alternative

view as to Frege’s place in the history of analytic philosophy in his “Frege and the Rise

of Analytic Philosophy" (1975). More recently, Joan Weiner has also presented an

alternative interpretation, acknowledging the Kantian influences on his thought, in her

book Frege in Perspective (1990). Clair Ortiz Hill, in her Word and Object in Husserl,

Frege and Russell (1991), has examined the historical situation and some close

connections in the work of the three philosophers. J. N. Mohanty, in Husserl and Frege

(1982), explores the historical connections between Husserl and Frege and similarities

in their respective works, and has called into question commonly held beliefs concerning

the impact of Frege on Husserl. Gordon P. Baker and P.M.S. Hacker, in Frege: Logical

Excavations (1984), have presented perhaps the most critical view challenging the

preeminence given by other commentators to the importance of Frege’s thought to

analytical philosophy.

Sometimes the philosophical outlook of the interpreters themselves must

call into question the correctness of an exegesis. It is ironic that Dummett, who is

Frege’s most prolific interpreter and has revered Frege as the father of analytical

philosophy and the rightful originator of the ‘linguistic turn’, tirelessly points out how

Frege never really got things right. It is interesting that Dummett is also a dedicated

antirealist and intuitionist Frege would have rejected both Dummett’s antirealism and

intuitionism. The main thesis of the anti-semantic realism advocated by Dummett is that

we do not have to regard every declarative statement as determinably true or false

19 Kitcher, “Frege’s Epistemology" inPhilosophical Review 88 (1979) 235-262.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 independently of our means of coming to know what its truth value is; that is, anti-

semantic realism rejects the principle of bivalence. Intuitionism derives from Kant’s

account of temporal intuition. It regards logic as properly part of mathematics, and the

vehicle and ground of knowledge is mathematical proof. Mathematics is concerned with

the construction of proofs, not their discovery.

For an intuitionist, the truth of a mathematical statement depends on

whether there exists a proof for it. Thus, the law of the excluded middle fails since it is

not possible to admit its universal validity, as mathematical truth depends upon the

construction of a proof for it. Obviously, Frege would have rejected both antirealism and

intuitionism. He would have rejected antirealism because he held that every proposition

expressed by a declarative sentence must refer to the true or the false. He held logic to

be grounded in reason, and thus analytic, and not, as the intutitionists believe, grounded

in the faculty of pure intuition, or synthetic a priori knowledge.

It seems that beneath Dummett’s deconstruction of Frege lie antirealist

and intuitionist motivations. It seems, for Dummett, that Frege must be shown to be a

realist, as a foil for Dummett’s claims for anti-realism and intuitionism. Dummett’s

motivations are outside the scope of this paper; but my reading of Dummett suggests

that he is more interested in exploring modem philosophical problems connected with

his theories involving realism and antirealism and questions related to intuitionist logic

and mathematics than in understanding Frege’s thought within its historical problem-

situation.

The background and interests of Frege’s interpreters often color their

reading of him. It is necessary to take into account their standpoint and possible

motivations in considering their interpretation of Frege. Russell, who with Moore led the

revolt in England against the monistic Neo-Hegelian idealism at the turn of the century,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 saw in Frege an ally in his drive toward a pluralistic realism. Russell he'd a Platonist

view of universal truths. Thus, any attributions by him of Frege’s leanings toward

Platonism ought to be carefully weighed against other possible interpretations that would

be consistent with Frege’s actual writings. Philip Kitcher, who recognizes the apriorist

epistemological motives and psychological tendencies and the Kantian influence on

Frege’s thought, is himself an advocate of an empiricist epistemology of mathematics.20

We may wish to ask ourselves when reading Kitchens interpretation of Frege’s position:

how might Kitcher’s interpretation, as opposed to alternate interpretations, support his

own views concerning the foundations of mathematics? Baker and Hacker, who are

ardent interpreters and defenders of Wittgenstein, are defenders of his preeminent place

in twentieth-century analytic philosophy. They are severe critics of Frege and defenders

of Wittgenstein’s legacy. I believe Baker and Hacker21 rightly reject many of Dummett’s

claims for the preeminence of Frege’s works. However, we may legitimately ask whether

their substantial scholarship and research into interpreting Wittgenstein’s works motivate

Baker and Hacker’s interpretation of Frege. Sluga, who written extensively on the

idealist and rationalist elements in Frege, is equally at home with topics in the history of

Continental philosophy, as evidenced by his recent publication of a historical and

philosophical work on Heidegger.22 In considering his interpretation of Frege’s

philosophical outlook it is justifiable to examine Sluga’s own presuppositions and

leanings. However, there is no assurance that any interpreter will provide a perfectly

balanced interpretation. We have to grant each a degree of latitude and interpretive

20 Philip Kitcher, The Nature of Mathematical Knowledge (New York: Oxford University Press, 1984). 21G. P. Baker and P. M. S. Hacker,Wittgenstein: Understanding and Meaning (Chicago: University of Chicago Press, 1980), and P. M. S. Hacker,Wittgenstein’s Place in Twentieth Century Analytic Philosophy (Oxford: Blackwell, 1996). 22 Sluga, Hans, Heidegger’s Crisis: Philosophy and Politics in Nazi Germany (Cambridge: Harvard University Press, 1995).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 freedom, and assess their reconstruction in light of historic circumstances and the

consistency of the textural evidence of the body of work that is examined.

I will present an alternative interpretation of Frege’s philosophy, as an

epistemological rationalist, a mathematician whose concern in developing a theory of

sense and reference was ancillary to his primary interests in the nature and sources of

mathematical knowledge. His motivations were primarily, indeed overtly,

epistemological. Though he was particularly concerned with the nature and foundations

of mathematical knowledge, his interests extended to the validity of claims to scientific

knowledge in general. In contrast to the extreme realist picture of Frege, who is often

presented as a Platonist, I will present an alternative view of him as a conceptualist

whose metaphysical beliefs may be more closely linked to transcendental idealism than

to realism.

In developing my alternative interpretation of Frege, I will explore some

supporting arguments made by Sluga, Weiner, Baker and Hacker, Currie, Carl, Burge,

and others, and, in contrast, some of Dummett’s counter arguments to the revisionists. I

will examine also some of the views of Russell, Wittgenstein and Camap, who were

among the earliest interpreters of Frege, and whose miscontruels in some respects gave

impetus to the rise of the standard interpretation. Some views of David Bell, Paul

Benacerraf, Tyler Burge, Ray Monk, Philip Kitcher, Michael Resnick, Thomas Ricketts,

Howard Wettstein, and Crispin Wright will also be considered. All of the commentators

mentioned, including Dummett, and others to whom I will have occasion to refer later in

this paper, whether in agreement or not with my thesis, have all contributed in profound

respects to my understanding of Frege’s work.

Though my interpretation of Frege is in agreement with some of these

commentators in certain respects, none of them have presented an interpretation wholly

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 consistent with my own views. The methodological principles, which will guide my

exposition of Frege’s thought, will be both philosophical and historical. I intend to first

examine Frege’s thought within the context of his times rather than the problem-situation

of later twentieth century analytic philosophy. In this respect I will follow Sluga in

developing the historic-philosophical background and the intellectual developments in

which Frege found himself. Only within the context of temporal historic philosophical

developments and the problem-situation of the late nineteenth century and early

twentieth century, is it possible to understand Frege's work accurately. For if it is our

purpose is to understand Frege, and not the philosophical problems, which occupy

present day philosophers, then we must take into account an accurate historic

reconstruction. It is the failure to consider the historic problem-situation that has led to

the misinterpretation of Frege by present-day philosophers of language.

Second, though direct evidence in Frege’s work for his influence by other

philosophers is slender, some evidence linking him to those who influenced him

philosophically does, nevertheless, exist. It is possible to establish that Frege was in an

historic position to have been influenced by certain figures and events even if there is no

explicit confirmation by Frege himself. Though perhaps not sufficient to establish their

positive influence on him with certitude, it is nevertheless reasonable to assume that he

was aware of these figures and events and not ignorant of their relevance to his work.

Third, there is ample evidence for Frege's influence by certain key ideas

central to the philosophical tradition and framework to which Frege was unavoidably an

intellectual heir. By examining the evidence linking Frege to the main philosophical

tradition I expect to achieve a more balanced representation of Frege’s ideas as

contributions to the mainstream. There is no reason to suppose that Frege was not part

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 of the main philosophical tradition unless our purpose is to mythologize him, as Dummett

has done, as some sort of intellectual maverick outside the philosophical mainstream.

Fourth, the only way to assess Frege’s work is to take him at his word.

The accuracy of any interpretation rests upon what Frege actually said concerning a

topic in a given context. I will follow Weiner in examining the structure, overall content

and key elements in Frege’s thought as laid down by Frege in his hand and in his

principal published works. After taking these principles into account, if it is possible to

develop a consistent interpretation of Frege’s thought, it would be more reasonable to

assume the correctness of such an interpretation than to accept Dummett’s dogmatic

claims for a privileged interpretation of Frege, especially, if the privileged interpretation

makes contemporary problems in latter-day theories of meaning and the philosophy of

language Frege’s primary concerns.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2

DISTORTIONS OF THE STANDARD INTERPRETATION

Contemporary View of Frege’s Place In Philosophy

It is not surprising that Frege's interests in epistemology have gone

largely unnoticed. Most of Frege's writings remained obscure, and unavailable in

English translation until the mid-twentieth century, at a time when the concerns of Anglo-

American philosophy centered on linguistic philosophy. Max Black's translation of “Ober

Sinn und Bedeutung", as “On Sense and Reference", was published in Philosophical

Review in 1948. This was later reprinted in Translations from the Philosophical Writings

of Gottlob Frege in 1952. J.L. Austin's English translation of Die Grundlagen der

Arithmetik, as The Foundations of Arithmetic, was published in 1950.

Frege's basic works were known to only a handful of English speaking

philosophers before the 1948-50 era. Wittgenstein, Russell and Camap made his ideas

known, in the beginning, to the wider philosophical community in Britain and America,

principally by references to them. Wittgenstein proclaims his indebtedness to Frege in

the Preface of Tractatus Logico-Philosophicus, which first appeared in English in 1922.

Russell was the first to make reference to Frege in Principles of Mathematics in 1903,

and later in his essay “On Denoting" in 1905. Russell and Whitehead express their

indebtedness to Frege “in all questions of logical analysis" in the Preface to Principia

Mathematica published in 1910.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 Our knowledge of his ideas was shaped initially by the interests of just a

few early interpreters who were predominantly empiricists and realists. Frege first came

to the notice of Bertrand Russell while he was writing Principles of Mathematics, which

was published in 1903. Through Russell’s references to Frege in that work, other

philosophers became familiar with Frege. Russell’s followers were sympathetic to his

metaphysical pluralism, rejected the monistic idealism of Bradley (1846-1924),

McTaggart (1866-1925) and Bernard Bosanquet (1848-1923), and embraced realism.

Bradley and Bosanquet were leading English Neo-Hegelian philosophers at Oxford,

while McTaggart held a similar influential position at Cambridge. After Russell's and

Moore’s revolt against Neo-Hegelianism, Frege's work became associated with the

extreme realism of Russell's mathematical philosophy and common sense realism of

Moore, and their followers, principally at Cambridge. Frege’s avowed anti-psychologistic

conception of logic was attractive to Russell and Moore and their followers because it

seemed to reject the psychologism, which they associated with the idealism then current

at Cambridge and Oxford. They overlooked the close linkage of psychologism and

empiricism. Moore and Russell also rejected idealism because of its inability to account

for the pluralistic and objective nature of reality.

The rationalist elements in Frege’s thought were consequently simply

played down or ignored by the early British analytic philosophers. Russell’s empiricism

rejected the psychologists tendencies of idealism, and replaced it with an extreme

realism. Russell, like Frege, believed that all of mathematics could be reduced to

principles of logic. For Russell logical relations were mind-independent, and thus

atemporal and aspatial. Logical relations were universal, or Platonistic entities, to which

the mind somehow has privileged access.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 It was only natural that Russell's Platonistic tendencies would be also

attributed to Frege. After all, Russell made favorable mention of Frege in his

mathematical and logical works, suggesting to anyone unfamiliar with Frege's original

work that Frege too shared with Russell a penchant for extreme realism. In fact, as I

shall argue, Frege was not a realist, but rather an idealist in the neo-Kantian tradition.

As such, Frege’s notion of logic, and despite his avowed anti-psychologism, was

nevertheless grounded in a psychologistic epistemology based on self-evidence.

Despite evidence in Frege’s writings to the contrary, the tendency has been for most

analytic philosophers in the twentieth century, to associate Frege with the Platonism of

Russell and Moore, and to reject rationalism in favor of an empiricist epistemology.

The break with rationalism by analytic philosophers is obscured in part by

Russell's apriorism, which grounds a priori knowledge in seeming non-psychologistic,

other worldly and mind-independent objective truths. Though Russell officially rejected

psychologism, his rejection was disingenuous. He advanced a theory of knowledge by

acquaintance or description that was psychologistic in origin.23 Wittgenstein was

unconvinced, and called Russell’s epistemology psychologistic.

in the Tractatus, Wittgenstein tried to make the break from the dictatorial

control over the rest of philosophy that had long been exercised by the theory of

knowledge, i.e. by the philosophy of sensation, perception, imagination, and, generally

of experience.24 According to Wittgenstein, “Psychology is no more akin to philosophy

than any other natural science. Theory of knowledge is the philosophy of psychology."25

In contrast to Frege, Wittgenstein conflated psychology with epistemology, and avoiding

23 Russell, Problems of Philosophy (Home University Library, 1912; reprint, Indianapolis, Hackett, n.d.). 24 Anscombe, An Introduction to Wittgenstein's Tractatus, 152. 25 Wittgenstein, Tractatus, §4.1121.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 epistemology altogether, concentrated instead on the logic of language, making it the

starting-point of philosophy. He termed logical propositions ‘tautologies’, and relegated

philosophical propositions to the realm of meaningless expressions. As analytic

philosophy developed, it gradually made more and more concessions to empiricism, and

the center of focus became semantics and philosophy of language.

Wittgenstein's Tractatus was highly influential on the logical positivists

who, in the 1920s and 1930s, continuing the trend way from psychologism and

rationalism. The logical positivists maintained that kinds of sentences would differentiate

epistemological questions by separating of scientific propositions from metaphysical

propositions. Rationalism was associated with speculative metaphysics, and thus, non-

scientific. They were concerned with developing a theory of meaning adequate for

understanding science, as the repository of all human knowledge. The emphasis

centered on empirical questions of verification. They sought to analyze the meanings of

scientific statements in terms of observation statements of human experience. They

wanted to show that all human experience could be expressed in sentences that are true

or false.

Ironically, it was a former student of Frege, Rudolph Camap, who was

most instrumental in furthering the empiricist outlook of logical positivism. Camap credits

Frege for his pioneer work in logic and semantics in Der Logische Aufbau da Welt

(1928), first English translation published in 1967. He refers to Frege in his Introduction

to Semantics, his Formalization of Logic (1942), and Meaning and Necessity (1947).

Carnap’s works emphasize only the semantic relevance of Frege’s work for formal

languages.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 Wittgenstein, Russell and Camap shared with Frege several common

concerns: (i) They rejected of psychologism in logic and mathematics because it could

not account for the objectivity, necessity and universality of the truths belonging to these

disciplines, (ii) They rejected of radical empiricism, (iii) They embraced moderate

empiricism and acceptance of apriorism in the field of logic and mathematics, (iv) They

held a logicist view of the foundations of mathematics (v) Interest in theories of sense

and reference for its useful application in analyzing the logical form of otherwise

misleading linguistic expressions.

In keeping with the empiricist outlook, Carnap adopted a verifiability

criterion of meaning. His views concerning analyticity are relevant for our understanding

of contemporary distortions of Frege. Frege claimed that analytic propositions are

provable from logical laws.26 For Frege, this meant they were grounded in reason; and

thus they were not empirical. In trying to ‘correct’ a defect in Frege's explication of

analytic propositions, which seemed to him to rest unnecessarily upon some extra-

logical principle of definition, Camap introduced what he called ‘meaning postulates'.27

Meaning postulates were intended to remove definitions from having anything at all to do

with meaning, or what might be considered to be psychological in nature. According to

Camap, statements such as ‘Ail bachelors are males’, which may be expressed in

logical terminology by: (Vx)(x is a bachelor -> x is male), express nothing more than the

logical constraints with respect to which such statements can be evaluated for truth an

validity. Thus, a statement such as ‘All bachelors are males’ is deemed a necessary

truth because it is true in virtue of the linguistic meanings of the terms ‘bachelors' and

‘males’.

28 Frege, Foundations of Arithmetic, §88.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 For Camap, and the logical positivists, the puzzling sentences of

traditional philosophy, or 'metaphysics’, could be seen to differ from the sentences of the

empirical science in that the later, but not the former, were verifiable. On this doctrine

sentences are meaningful if and only if they are true or false. If the sentences of science

were verifiable, their truth or falsity would rest upon empirical principles. Under

Wittgenstein's influence, sentences of mathematics and logic were considered

tautologies.28 The logical positivists reformulated sentences of logic or mathematics

linguistically; such sentences were considered to be true in virtue of the meanings of the

words contained in them. Thus, sentences expressing analytic truths are trivially true in

virtue of the conventional meanings the words contained in them.

On the other hand, a sentence is a synthetic truth, if it is true in virtue of

the way the world is. Kant’s third distinction, the synthetic a priori, was totally rejected.

The presupposition of the ‘linguiscism’ underlying logical positivism was that once the

relation between logic and language is exposed, the nature of a priori knowledge would

also be exposed. The importance of reformulating a priori knowledge was that it had

been traditionally linked to the speculative metaphysics and introspective psychologistic

epistemology, which were associated with rationalism and idealism. Under the new

formulation, the propositions of logic and mathematics would be seen as rules

determining the use of language. Thus, under the new formulation their absolute truth

cannot be denied because they are true in virtue of the meanings of the terms

comprising them; so they are a priori true. Since they do deal with facts but only with

linguistic expressions, they are analytic and not synthetic.

27 Camap, Meaning and Necessity (Chicago: University of Chicago Press, 1988), 222-229. 28 Wittgenstein, Tractatus, §§4.46-4.4611, §5.142, especially, §6.1 and §6.22.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 After the 1940s English philosophy moved toward a linguistic conception

of philosophy. This is the view that philosophical problems could be illuminated,

transformed or solved by study of the way language is actually used, taught and

developed in ordinary discourse. Traditional philosophical problems were seen as being

caused by superficial grammatical similarities. Philosophy is viewed as analysis of

language. At Cambridge, under the influence of the later Wittgenstein, the philosophical

dictum of linguistic philosophers became ‘meaning as use'. Wittgenstein, continuing the

anti-psychologistic tradition, argued that meaning and understanding should not be

construed as species of mental acts. According to Wittgenstein, “when I think in

language, there aren’t ‘meanings’ going through my mind in addition to the verbal

expressions: the language is itself the vehicle of thought."29 Pondering rhetorically,

Wittgenstein asked: “But what did his understanding, and the meaning, consist in? He

uttered the sounds in a cheerful voice perhaps, pointing to the sky, while it was still

raining but was already beginning to clear up; later he made a connexion between his

words and the English words.”30

During this period J. L. Austin, the originator of ordinary language

philosophy at Oxford advocated a detailed examination of linguistic expression. It was

during this period that the first English translations of some of Frege’s principal writings

became available to the wider audience of Anglo-American philosophers. Austin was

led to translate the Foundations of Arithmetic31 because he was keenly aware of the

semantic relevance of Frege’s work for the analysis of ordinary language. Ironically, the

Foundations of Arithmetic did not concern semantics at all. Frege wrote it to promote his

29 Wittgenstein, Philosophical Investigations, trans. G.E.M. Anscombe (New York: Macmillan, 1968), §329. 30 Ibid., §541; also, 175-6. 31 Gottlob Frege, Foundations of Arithmetic (Oxford: Blackwell, 1950).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 philosophical views concerning the source of mathematical knowledge. Undoubtedly,

Austin realized the significance of the context principle to explain how words acquire

meaning in natural language. The context principle was one of the three methodological

principles that Frege used in formulating his ideas concerning the nature of the meaning

of the mathematical term ‘number’.

Several translations of Frege’s “On Sense and Reference" became

available in English. Wittgenstein urged the publication of several of Frege’s works

dealing primarily with language in what became the Translations of the Wn'tings of

Gottlob Frege (1952).32 So scare were Frege’s works, the collection would not have

been possible had it not been for Russell and Gilbert Ryle who lent copies of certain

works, which would not otherwise been available to the editors.33 Frege’s influence was

greatly enlarged with the appearance of these translations. Today, Frege is widely

acknowledged, as the father of semantic analysis; and his work recognized by

philosophers of language for its contribution to linguistic philosophy.

Analytic philosophy moved toward extreme empiricism and psychologism

in the later twentieth century. Latter-day empiricists, like Quine, have called into

question the sense of such notions as ’true by definition’, ’true by convention’ and

‘analytic truth’. Quine’s attack34 on the analytic-synthetic distinction challenges the

Fregean definition of analyticity as either (i) logical truth, or (ii) reducibility to logical truth

by substitution of synonyms for synonyms. Synonymy consists simply in the

interchangeability of terms in all contexts without change of truth-value, in Leibniz’s

32 Gottlob Frege, Translations from the Philosophical Works of Gottlob Frege, ed. Max Black and Peter Geach, (Oxford: Blackwell, 1952). 33 Preface, ibid. 34 W. V. O. Quine, “Two Dogmas of Empiricism” in From a Logical Point of View (Cambridge: Harvard University Press, 1953)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 phase, salva veritate.35 The distinction between analytic statements, such as ‘all

bachelors are male’, which are considered true by virtue of the meaning of he lot ms, and

other truths, which are grounded in ‘fact’, are rejected in favor of monatomic

epistemological model consisting of degrees of truth in a ‘web of belief.36

Now, under the influence of Quine, there is a growing tendency of among

analytic philosophers, if they accept the importance of epistemology at all, to embrace a

'naturalized epistemology.'37 Physics and the natural sciences are the considered the

starting point for what exists. Knowledge and the acquisition of Knowledge are thought of

in terms of behaviorist psychology. Thus, epistemology is relegated to cognitive science,

and made a part of the physical sciences. Traditional questions of epistemology having

to do with justification are no longer asked. The questions now are about how

knowledge is to be explained physiologically.

In the new naturalized epistemology, skeptical questions arise entirely

within empirical science. Thus, epistemology becomes a branch of natural science

studying the relationship between humans and the environment. Scientific theories take

on an evolutionary character; and the tendency is to embrace psychology and sociology

anew. The trend is moving toward the reversal of Frege’s anti-psychologistic initiative,

and is seen as giving way to a new version of extreme empiricism and new form

psychologism. These developments would have been anathema to Frege.

In the classical epistemological outlook stemming from Descartes,

epistemological theories were developed independently of, and prior to, any scientific

theorizing. Proper scientific theorizing had to await the prior development of an

35 Ibid., 27. 36 W. V. O. Quine, The Web of Belief (Hew York: McGraw-Hill, 1978) 37 W. V. O. Quine, “Epistemology Naturalized" in Ontological Relativity and Other Essays (New York: Columbia University Press, 1969).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 epistemological theory. This is the tradition to which Frege properly belongs. In order to

thwart the skeptical challenge, all beliefs that might be in doubt are rejected, and new

beliefs are built on a secure footing. The traditional foundational view of human

knowledge secures all true beliefs as inferentially derived from self-evident truths. In the

traditional view such truths are either a priori justified by reason alone, or they are a

posteriori and justified empirically through knowledge derived from the senses.

Under the influence of contemporary philosophy of language and the

widespread advances of empiricism, the interest in Frege’s work among contemporary

philosophers has centered on how it has contributed to the contemporary philosophical

debate. Influential modern interpreters of Frege, like Benacerraf, Dummett, Geach,

Kenny and Anscombe, whose own interests are shaped by contemporary debates in

philosophy and mathematics, or under the influence of Wittgenstein reject epistemology,

have largely ignored the evidence in Frege’s writings for his epistemological interests,

particularly, rationalist elements in his thought. They consider Frege a failed theorist in

the foundations of mathematics but pay homage to him as the father of modem logic.

They mainly view Frege as an ally in the contemporary debate in matters concerning

semantic theory, and the significance of his work related more to the interpretation of

formal languages or mathematical logic, and truth conditions for natural languages.

Their interpretations of Frege have centered on the linguistic and

ontological elements related to theories of meaning; and thus they are led to reject the

notion that Frege was concerned with epistemology at all. Geach, for example, has said

that Frege “wholly rejected an epistemological approach to philosophical problems.”38

Likewise, Dummett has remarked that “Frege’s contributions to epistemology are sparse:

38 Peter Geach and G. E. M. Anscombe, Three Philosophers (Oxford: Blackwell, 1961), 137.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 in particular, he expressed no views concerning the character of the knowledge that is

not arrived at by inference and is not apriori.”39 According to Kenny, “For most of his life,

Frege gave priority to logic simply by ignoring epistemology."40 Benacerraf claims that

Frege was only interested in revealing the “metaphysical relations of dependence"

among mathematical propositions, thus implying that Frege was not pursuing an

epistemological investigation into the sources of mathematical knowledge at all.41

One reason why some interpreters are led to believe that Frege had no

interest in epistemology is evidently due to Wittgenstein himself, who was one of Frege’s

earliest and most important interpreters and notably one of the few who had actually

read any of Frege's work at the time. Wittgenstein expressed almost total lack of

interest in epistemology. Yet he was known to have been deeply influenced by Frege,

and to whom, in part, he had dedicated the Tractatus. According to Anscombe, an

important interpreter of Wittgenstein presumably well acquainted with Frege, “At the time

he wrote the Tractatus Wittgenstein pretended that epistemology had nothing to do with

the foundations of logic and the theory of meaning.”42 Twentieth-century interpreters of

Wittgenstein in their haste to explain the genesis of Wittgenstein’s thought have

imparted Wittgenstein’s lack of concern with epistemology to Frege. Anscombe adds to

this myth by claiming that Frege “was not a general philosopher and had no concern with

either ethics or theory of knowledge."43

39 Dummett, The Interpretation of Frege’s Philosophy, 452. 40 Anthony Kenny, Frege: An Introduction to the Founder of Analytic Philosophy (London: Penguin, 1995), 212. 41 Benacerraf, “The Last Logiscist" in Midwest Studies in Philosophy, vol. vi., eds. Peter A. Finch, theodore E. Uehling, Jr., and Howard Wettstein (Minneapolis: University of Minnesota Press, 1981), 27. 42 Anscombe, An Introduction to Wittgenstein’s Tractatus, 28. Anscombe goes on to say that “the passage about the ‘elucidation’ of names, where he says that one must be ‘acquainted’ with their objects, gives him the lie." 43 Ibid., 12.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 In the sequel I will try to show through an historical reconstruction of

probable influences on Frege's intellectual development that the interpretation of Frege

as a philosopher of language is a distortion of his thought. I will show that Frege's

motivations were wholly epistemological in the rationalist tradition.

Rational and Historical Reconstructions of Frege

The fundamental problem with the standard interpretation of Frege, as

most vigorously advanced by Dummett, and with analytic philosophy in general, is their

lack of concern with history. As Sluga has pointed out, the interest of analytic

philosophers in the historical development of philosophy has been “eclectic and

problem-oriented, rather than systematic and genetic-causative.’’44 The reason for this is

the “obsession of analytic philosophers with questions of meaning, conceptual analysis,

and necessary truth."48 Since “historical events are not readily grasped in such terms,"

from the point of view of analytic philosophy “history appears as messy, full of mere

factuality, beyond the strict methods of philosophical inquiry."48 Sluga argues that

“analytic philosophers have had little sense of their own enterprise as an historical

phenomenon." Sluga lays the blame on an attitude among analytic philosophers of

being too certain about the finality of their own methods.

Such observations are not confined to only to Sluga. Richard Rorty has

argued in similar vein that some “analytic philosophers who have attempted ‘rational

reconstruction' of the arguments of great dead philosophers have done so in the hope of

treating these philosophers as contemporaries, as colleagues with whom they can

** Sluga, “Frege and the Rise of Analytic Philosophy” in Inquiry 18 (1975): 471. 45 Ibid. 48 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. exchange views."47 He goes on to say that “Analytic historians of philosophy are

frequently accused of beating texts into the shape of propositions currently being

debated in philosophical journals." We should not fcrce dead philosophers to take sides

in the current debates, or in debates, which occurred at other times. There is a

perceived dilemma, according to Rorty, that being whether to anachronistically impose

our own (or later) problems on dead philosophers, or to confine our interpretation of the

dead philosophers to the context of their times. But there is really no dilemma, he says,

"We should do both of these things, but do them separately.”

This is the error committed by Dummett in Frege: Philosophy of

Language and Interpretation of Frege's Philosophy, and elsewhere in his writings.

Dummett does not distinguish these things completely. His exposition of Frege is, in

part, historical reconstruction, and, in part, a rational reconstruction. If Dummett treated

his interpretation of Frege in full knowledge of its anachronisms, his interpretation would

not be objectionable. Instead his exposition of Frege owes more to later developments in

the philosophy of language than to the problem-situation actually dealt with by Frege

himself. The problem with Dummett’s interpretation, and with what I am here referring to

as the ‘standard interpretation’ of Frege, is that they give too little emphasis to the

genesis of Frege's thought and the historical problem-situation. The standard

interpretation is flawed by an excessive concern with the problems of contemporary

philosophy of language and analytic philosophy to be an accurate interpretation of

Frege’s actual thought. Thus Frege’s thought has been twisted to fit the modem

problem-oriented interests of some contemporary analytic philosophers and/or

philosophers of language. On this view, Dummett’s attempted rational reconstruction is

47 Richard Rorty, “the historiography of philosophy: four genres" in Philosophy in History, p. 49-75

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 a paradigm for the kind of historical distortions which philosophers who follow the tenets

of the standard interpretation adhere.

In reply to Sluga's criticisms of his approach, Dummett called Sluga’s

historical approach “nonsense".48 “In interpreting a philosopher," according to Dummett:

there can be no substitute for thinking through, rigorously and in detail, what his arguments are and how they are supposed to work, what hidden assumptions must hold good if they are to be cogent, what answers could be given to objections, what relation one thesis has to another, in short for subjecting his work to logical analysis.49

For Dummett, “historical comparisons do not provide an alternative, or preferable, path

to the same goal as logical analysis.”50 According to Dummett, “Sluga's adherence to a

historical mode of discussion frequently makes his writing resemble art history, with its

talk of influences and tendencies, more than philosophy."51 Part of my overall purpose in

this paper will be to seek a balance between these two methodologies of Frege

exegesis: a logical analysis and rational reconstruction and logical analysis of Frege's

thought which will be sensitive to the historical problem-situation.

What makes Dummett's view of Frege particularly disturbing is his

intolerance with revisionist interpretations of Frege. Though he acknowledges the

existence of alternative interpretations Dummett has taken a dogmatic approach to his

own exegesis of Frege’s work, and has little patience for ‘revisionists'. His intolerant

attitude is expressed in his “An Unsuccessful Dig",52a review of Baker's and Hacker’s

Logical Excavations (1984). Baker and Hacker’s interpretation of Frege is probably the

most critical work on Frege yet published. Baker and Hacker, who examined Frege from

a Wittgensteinian point of view and are highly skeptical of many developments in

48 Dummett, The Interpretation of Frege’s Philosophy, 528. 49 Ibid. 50 Ibid. 51 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 analytic philosophy, opposed Dummett’s interpretation of Frege. Dummett’s attitude

toward them is vitriolic: “It is regrettable that they preferred to attempt a hatchet job on a

philosopher they lack the goodwill to understand.”53 For Dummett, revisionist

interpretations of Frege are unacceptable. Weiner has rightly challenged this attitude.54

In “Principles of Frege Exegesis,” Dummett offers us “the general principles that should

govern the interpretation of [Frege’s] writings."55 One reason given by Dummett, I think

correctly, why we ought to be cautious in any interpretation of Frege is the fragmentary

nature of the data. Many of Frege’s writings were destroyed by fire in the bombing of

Munster during the Second World War. However, Dummett ignores his own advice

regarding over jealous exegesis of slender data. He jealously tries to set the standard for

any ’true’ interpretation. He says, for example, “what we should never do is to interpret

what [Frege] said in his mature period in the light of his earlier writings.”58 Dummett

claims that “what is said repeatedly is thereby shown to be something which Frege took

seriously and about which he had a settled opinion.” On the other hand, Dummett also

says, “We are not entitled to assert the converse, that what is said only once is not to be

taken seriously.” The reason he gives is the insufficient data.

Granting the insufficiency of the data, it is not clear why we ought to

follow Dummett’s advice giving more weight to certain or other extant writings. The

insufficient data suggests, on the contrary, that the frequency of Frege's statements on a

given topic is not always to be trusted, and the incompleteness of the data would dictate

caution in all respects. Dummett counsels us that caution is warranted especially in the

cases where Frege’s repetition is not so much due to his insistence on a given point

52 Dummett, Frege and Other Philosophers (Oxford: Oxford University Press, 1991J, 158-198. 53 Dummett, “An Unsuccessful Dig" in Frege and Other Philosophers, 198. 54 Weiner, Frege in Perspective (Ithaca: Cornell University Press), 13. 55 Dummett, “Principles of Frege Exegesis" in The Interpretation of Frege’s Philosophy, 6-35.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 tnan on his dissatisfaction with an explanation and his repeated efforts to get it right.

Dummett adds that we ought not lift remarks out of context; for example, taking

something from a later period to justify an interpretation of remarks in an earlier period.

The ‘proper1 interpretation of Frege will show, according to Dummett, that greater weight

ought to be given to Grundgesetze than to other of Frege's works; as it “was intended by

Frege to be a definitive work, what it contains should be given more weight than

anything Frege wrote elsewhere."

Dummett goes on to say, that Frege’s avowed aim in Grundgesetze, as

envisioned in Begriffsschrift and Grundlagen, was to prove the truths of arithmetic to be

analytic; that is, that they are derivable by means of definitions from purely logical

principles. He says that it is not enough for Frege to show that arithmetic can be

constructed from some arbitrary logical theory, he must show that that logical theory is

the logical theory. The logical theory is the one required for the analysis of deductive

reasoning in general. It is not merely concerned to state the laws governing correct

inference, but with everything required for the justification of correct inference. There

may be forms of inference peculiar to different disciplines or areas of discourse; but such

forms are not the subject of the most general logical theory which underlines all areas of

subject-matter. “All this means that logic must be the theory applying to any language

capable of expressing thought.”*7 Thus, according to Dummett, the correct logical theory

must be that which underlies natural language. If these conclusions are correct, then,

according to Dummett, "there is a substantial body of Frege’s theory - precisely that

comprising his philosophy of language - of which no definitive exposition, comparable to

Grundgesetze, or even carrying an authority equal to that of Grundlagen, exists.” This, in

56 Dummett, The Interpretation of Frege's Philosophy, 7. 57 Ibid., 15-16.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 summary, is the core of Dummett’s interpretation of Frege’s project, as essentially

concerned with providing a semantic theory for the logic, which underlies natural

language. If we interpret Frege ‘correctly’, according to Dummett, we ought to arrive at

the same conclusion.

The sheer volume of Dummett's commentary of Frege’s work, his

encyclopedic knowledge of Frege's original published and unpublished work, and the

length and complexity of his arguments are daunting and difficult to assess. It would be

impossible within the compass of this paper to assess everything that Dummett has

written about Frege. Moreover, Dummett’s tentative and exploratory style makes it

almost impossible to assess what his own views of Frege actually are. John Passmore

has rightly pointed out this difficulty in assessing Dummett’s writing on Frege. According

to Passmore, “No sooner is one on the point of ascribing to him a definite doctrine than

there is a sudden twist in the argument; unexpected difficulties arise, new alternatives

present themselves.”98 It is therefore difficult to pin Dummett down in his assessment of

Frege. So I will focus on what I consider to be two key distortions of Frege thought, and

which bear directly on my main thesis. The first has to do with Dummett’s interpretation

of Frege as primarily a philosopher of language, and the second has to do with his claim

with respect to Frege's place within the philosophical tradition.

Frege, as Philosopher of Language

The origin of the interpretation of Frege as philosopher of language stems

mainly from a series of three articles published between 1891 to 1892. The articles are

“Function and Concept” (1891), “Concept and Object" (1892), and “On Sense and

Reference” (1892). In these articles, Frege discusses philosophical aspects of the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 ontologically interacting hierarchy of (i) functions and objects, and (ii) senses and

references. It is from these articles that latter day philosophers of language derive the

fundamental notions of Fregean semantics.

The earliest of these articles was written by him in the form of an address to the

Jena Medical and Scientific Society. The aim of the article was to elucidate some of the

fundamental ideas in his Begriffsschrift, where his starting point was the function in

mathematics.39 He explains that the mathematical term ‘function’ has over time been

extended in generality to include expressions in arithmetic, multiplication,

exponentiation, analytic geometry, and higher analysis.80 He assimilates the notion of a

mathematical function and argument with that of a concept and object in logic. According

to Frege, “We thus see how closely that which is called a concept in logic is connected

with what we call a function [in mathematics]."61 He goes on to say:

The linguistic form of equations is a statement. A statement contains (or at least purports to contain) a thought as its sense; and this thought is in general true or false, i.e., it has a general truth-value, which must be regarded as what the sentence means, just as (say) the number 4 is what the expression ‘2+2’ means or London what the expression ‘the capital of England’ means.62

In “Function and Concept" Frege describes the evolution of the notion of

mathematical ‘function’. He assimilates mathematical functions with concepts in logic.

He introduces the distinction between ‘incomplete’ and ‘complete’ functions, and

‘saturated’ and ‘unsaturated’ concepts. An incomplete function is lacking an argument,

while in a complete function an argument is specified. Analogously, unsaturated means

58 Passmore, Recent Philosophers (La Salle: Open Court, 1985), 75. 59 Frege, “On Function and Concept”, Collected Papers on Mathematics, Logic and Philosophy, eds. Brian McGuinness, trans. Max Black, V. H. Oudman, Peter Geach, Hans Kaal, E.-H. W. Kluge, Brian McGuinness, R. H. Stoothoff, (Oxford: Blackwell, 1984), 137. Hereafter, I will refer to this reference as Collected Papers. 80 Ibid., 144. 61 Ibid., 146.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 that a concept is lacking an object, while in a saturated concept an object is specified.

“Statements in general, just like equations or inequalities or expressions in Analysis, can

be imagined to be split up into parts; one complete in itself, and the other in need of

supplementation, or ‘unsaturated’. Thus, e.g. we split up the sentence ‘Caesar

conquered Gaul* into ‘Caesar* and ‘conquered Gaul*. The second part is unsaturated' - it

contains an empty place. Frege also distinguished first and second level functions and

functions of more than one argument where greater multiplicity or complexity is allowed.

In “On Sense and Reference” Frege explores the fundamental question of

whether equality (or identity) is a relation between objects or between names or signs of

objects. Identity is a central concern for mathematics and semantics in general.

Unfortunately, to illustrate his point Frege used an example not from mathematics, but

from ordinary discourse - the identity of the morning star and the evening star. This is

followed in the same paper with a discussion of oblique contexts. His discussion

suggests a concern with semantics of ordinary language; yet it should be clear from the

paper that Frege's actual concern is identity statements in mathematics to which the

greater part of the ending of the paper reveals. In this paper, Frege distinguishes

between the ‘sense’ and 'reference' of words and sentences or ordinary language.

Words may be possessed of sense and reference. Words may or may not have a

referent. But all words have a sense. The sense of a word is the 'mode of presentation',

i.e. the aspect of the word that expresses or distinguishes it from other words, and

determines its reference. The reference of a word is the object that it names. The

sense of a sentence is the thought, or proposition, that it expresses. The reference of a

sentence is its truth-value. The truth-value of a sentence may be either true or false.

82 Ibid., 146.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 Philosophers, whose interests lie in the area of language, point to these

articles (in particular, “On Sense and Reference") to substantiate their claims that Frege

was primarily interested in the semantics of ordinary language. However, Frege was not

motivated by semantic questions. His interests were in the epistemology of

mathematical concepts. He was led to invent his Concept-Script as initially set forth in

Begriffsscrift, in order to investigate sources of mathematical knowledge. The found the

invention of the Concept-Script necessary due to the inadequacies of ordinary language.

After he wrote the Foundations, Frege found it necessary to investigate and then provide

an account of the objective 'sense' and 'reference' of words and sentences, as

expressions in ordinary language, in order to provide an adequate account of thee

workings of a fragment of ordinary language. Frege was only interested in a fragment of

ordinary language, and not the semantics of every kind of word or expression in ordinary

language. This shows that Frege’s interest in semantics was limited to only that part of

ordinary language that was important to his investigations in mathematics and the logical

structure of his Concept-Script.

In order to advance the standard interpretation of Frege as primarily a

philosopher of language, Dummett has actually redefined terms used by Frege to make

him appear to be more interested in semantics and language than in mathematics, logic

or epistemology. In The interpretation of Frege’s Philosophy, Dummett has argued, “the

part of philosophy which I have been calling 'theory of meaning’ was called by Frege

simply ‘logic’.”63 Frege does not actually use the term ‘theory of meaning’ in reference to

his own work. To resolve this tension Dummett simply revises Frege’s terms. For

Dummett, a theory of meaning provides “a general account of how language works,...a

63 Dummett, Frege: Philosophy of Language, 669.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 framework within which we can describe every feature of the use of sentences, and of

how we are able to grasp, from the structure of any sentence, what the various features

of its use are.”64

According to Dummett, Frege “effected a revolution of philosophy.”65 He

does this “by taking the theory of meaning as the only part of philosophy whose results

do not depend upon those of any other part, but which underlies all the rest."66 What

underlies all the rest is what Frege called 'logic' and what Dummett calls 'theory of

meaning’.

Dummett acknowledges that since Frege generally characterized ‘logic’

as the theory whose object of study is 'truth'; we may also name it ‘theory of truth'.87

According to Dummett, ‘theory of meaning’ is to be preferred to ‘theory of truth’ because

the notion of truth is an integral part of a general account of meaning.88 Dummett goes

on to say that what he calls ‘theory of meaning' is often called ‘philosophical logic', but

rejects this term as suggestive of logic as an independent theory like physics or

psychology.69 Dummett concludes that logic is embedded in the theory of meaning; and

thus the term ‘theory of meaning' is the more apt description of what Frege intended. He

acknowledges, yet ignores the fact that Frege never actually uses the term ‘theory of

meaning’.

Instead, for Dummett, a theory of meaning is what underlines all other

theories. And according to Dummett, “Much with which Frege was concerned would

today be called by many ‘philosophy of language’." By redefining Frege’s term ‘logic’,

84 Ibid., 675. 85 Ibid., 669. 86 Ibid., 669. 87 Ibid., 670. 88 Ibid., 670. 89 Ibid., 670.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 first as ‘theory of truth’, then as ‘philosophical logic’, then as ‘theory of meaning’, and

finally as ‘philosophy of language', Dummett can make the claim that Frege actually

inaugurated a new era founded on any of these theories. In this way, he transforms

Frege from a logician and mathematician, interested in the foundations of mathematical

and scientific knowledge with secondary interests in language, into philosopher of

language interested in expressions of meaning. Dummett claims that “philosophy has,

as its first, if not its only task, the analysis of meanings."70 This may accurately describe

Dummett’s view, but this is a misrepresentation of Frege's thought.

Dummett continues this line of Frege exegesis in The Interpretation of

Frege’s Philosophy. In the chapter entitled "Was Frege a Philosopher of Language”,

Dummett writes: “Frege says that, while all sciences have truth as their goal, the

predicate 'true' defines the subject matter of what he call logic.” It thus becomes natural

to use the ‘the theory of truth’ understood in analogy with ‘the theory of knowledge’, as a

name of this branch of philosophy. Now, the notion of truth, as the object of

philosophical inquiry, has always been recognized by philosophers as closely allied to

that of meaning.” In this passage, Dummett first correctly attributes to Frege the view

that ‘all sciences have truth as their goal'71, and then acknowledges that ‘the theory of

truth' is often understood by philosophers as analogous with ‘theory of knowledge’.

Dummett goes on to advance his own philosophical view that “the object

of philosophical enquiry, has always been recognized by philosophers as closely aligned

to that of meaning." The inference is that such a view ought to be attributable to Frege.

70 Ibid., 669. 71 Frege, “Logic” in Posthumous Writings, (Chicago: University of Chicago Press, 1979), 2. For Frege, “The goal of scientific endeavor in truth" In the essay "Logic" in Posthumous Writings, 126, he says: “The word 'true' specifies the goal. Logic is concerned with the predicate 'true' in a special way. The word ‘true’ characterizes logic. True cannot be defined. We cannot say: an idea is true if it agrees with reality.”

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 This last statement cannot be textually linked to Frege; nor does Dummett attempt to

demonstrate textually that other philosophers hold such views. Undoubtedly, there are

some philosophers who hold this view, but would they all agree that 'meaning' is to be

aligned with any theory of knowledge or theory of truth? Dummett wants to advance his

own view that Frege had a theory of meaning, and that Frege's theory of meaning was

the same as his theory of truth. It is my view that Frege was indeed concerned with

truth, and that Frege possessed a theory of knowledge, especially as it concerns

science, as Dummett suggests. However, Frege’s logic is concerned with the

fundamental standards of science, not with meaning. The central notion behind Frege’s

logic is that in a properly constructed symbolism meaning with take of itself.

What motivates Dummett’s assessment of Frege, as being centrally

concerned with the philosophy of language and theory of meaning, cum theory of truth,

is the following: Dummett, like many philosophers of language, is frustrated with the

failure of philosophy to make progress, like the natural sciences, and to establish itself

as a systematic science. Traditional epistemological approaches in philosophy, with

theories of perception or various forms of intuition as the underlying cognitive theory,

have failed to achieve the desired results; so philosophy of language has replaced it as

the systematic approach within philosophy. According to Dummett, Frege showed us

the way by establishing philosophy as a theory of meaning.72

Dummett sees the theory of meaning replacing epistemology, as first

philosophy. Theory of meaning becomes, for him, the foundation underlying

metaphysics. Modern philosophy, beginning with Descartes, rejected metaphysics, as

first philosophy of the Scholastics, and replaced it with epistemology, as first philosophy.

72 Passmore, Recent Philosophers, 76.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 For Dummet!, Frege's work represents the beginning of the ‘linguistic turn’, meaning a

return to metaphysics and logic, but in the guise of theory of meaning. In sum, Dummett

characterizes Frege’s work as rejecting epistemology, and embracing the theory of

meaning; this constitutes a return to metaphysics, as first philosophy.

Contrary to Dummett, I hold that Frege does not have a theory of

meaning, nor is Frege’s logic a theory of meaning. There are no textual references in

Frege indicating that he held any theory of meaning at all. Frege did hold a theory of

truth. It consisted in the notion that ‘truth’ is devoid of any meaning whatsoever, it is

indefinable, but it cannot be dispensed with. He says:

How is it then that the word ‘true’, though it seems devoid of content, cannot be dispensed with? Would it not be possible, at least in laying the foundations of logic, to avoid this word altogether, when it can only create confusion? That we cannot do so is due to the imperfections of our language. If language were logically more perfect we would perhaps have no further need of logic, or we might read it off from the language. But we are far from being in such a position. Work in logic is, to a large extent a struggle with the logical defects of language.73

Thus, if Frege had had his way, he might have avoided the use of the word 'true'

altogether. Frege’s conception of logic is that it is concerned with the analysis of truth.

The goal of logic is the true. However, Frege’s logic is not a theory of truth; rather it is

concerned with validity, the logical analysis of true inferences from judgments, which we

hold to be true.

Notably, in contrast to Frege, since Tarski the notion of truth in formal

languages has been considered definable. Tarski’s work systematically formulized the

relation between expressions and the object they denote. Thus, the Tarskian definition

of truth is the formal relation between a statement and what is in fact the case with

respect to objects in the world. A statement is true if is accurately describes a state of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 affairs actually existing in the world. Philosophers of language following Tarski have

applied his definition of truth to ordinary languages. Tarski’s definition of truth, as

correspondence with reality cannot be associated with Frege because he explicitly

rejected the correspondence of language with reality as a basis of truth. In the essay

“Thoughts” Frege says:

It might be supposed from this that truth consists in the correspondence of a picture to what it depicts. Now a correspondence is a relation. But this goes against the use of the word ‘true’, which is not a relative term and contains no indication of anything else to which something is to correspond. If I do not know that a picture is meant to represent Cologne Cathedral then I do not know what to compare the picture with in order to decide on its truth. A correspondence, moreover, can only be perfect if the corresponding things coincide and so just are not different things. It is supposed to be possible to test the genuineness of a bank-note by comparing it stereoscopically with a genuine one. But it would be ridiculous to try to compare a gold piece stereoscopically with a twenty- mark note. It would only be possible to compare and idea with a thing if the thing were an idea too. And then, if the first did not correspond perfectly with the second, they would coincide. But this is not at ail what people intend when they define truth as the correspondence of an idea with something real. For in this case it is essential precisely that the reality shall be distinct from the idea. But then there can be no complete correspondence, no complete truth. So nothing at all would be true; for what is only half true is untrue. Truth does not admit of more or less. - But could we not maintain that there is truth is certain respect? But which respect? For in that case what ought we to do so as to decide whether something is true? We should have to inquire whether it is true that an idea and a reality, say, correspond in the specified respect. And then we should be confronted by a question of the same kind, and the game could begin again. So the attempted explanation of truth as correspondence breaks down. And any other attempt to define truth also breaks down. For in a definition certain characteristics would have to be specified. And in application to any particular case the question would always arise whether it were true that the characteristics were present. So we should be going around in a circle. So it seems likely that the content of the word ‘true’ is sui generis and indefinable.74

73 Frege, ‘My basic logical insights" in Posthumous Writings, 252. 74 Frege, Thoughts" in Collected Paper on Mathematics, Logic and Philosophy, 352-3.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 Thus, for Frege, the correspondence theory of truth does not hold; such a theory

o f truth would be circular, and involve us in an infinite regress similar to Plato’s

Third Man’. Rather, truth is unique, a kind of its own, indefinable.

For Frege, what is true, is that which is valid. A thought is true if is has

validity. Logic is the theory of normative thought: The ‘laws of truth’ are normative laws

of logical inference: "the laws of logic are nothing other than the unfolding of the content

of the word ‘true’."75 “Logic has a close affinity with ethics. The property ‘good’ has a

significance for the latter analogous to that which the property ‘true’ has for the former."78

Logic is concerned with the establishment of normative laws of thought, i.e. laws of logic,

not with descriptive laws of how people think. How people think is the province of

psychology. Logic is to be demarcated from psychology: "it is the business of the logic to

conduct an unceasing struggle against psychology."77

Logic is concerned with the objectivity of truth, which means the

recognition of truth independent of our thinking it to be true: “What is true is true

independent of our recognizing it as such.”78 As such, logic is an epistemological method

in being concerned with the grounds and justifications for thinking something to be true.

For Frege, “.. .this is where epistemology comes in. Logic is concerned only with those

grounds of judgment which are truths."79 The demarcation of logic from psychology

associates logic with epistemology. Logic becomes the tool used in the scientific goal of

discovering truth: “the goal of scientific endeavor is truth.''00 Frege's consistent

references to logic as being demarcated from psychology, its normative rather than

75 Frege, Posthumous Writings, 3. 76 Ibid., 4. 77 Ibid., 6. 78 Ibid.. 2. 79 Ibid., 3. 80 Ibid., 2.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 descriptive character, its concern with the analysis of truth, and the laws of truth,

confirms its connection with epistemology, rather than semantics. Dummett’s

redefinition of logic as theory of meaning ought therefore to be soundly rejected.

By associating Frege’s logic with a theory of meaning, Dummett

advances the view that truths of reason are essentially ’linguistic’. The consequence of

Dummett's view would be that the sentences formulating the truths of logic are true in

virtue of the rules of language, and hence that they are true in virtue of the way in which

we use words. He is thereby claiming that truths of reason are ‘conventional meanings'.

Nothing could be more remote from Frege’s actual views. As is seen in the quotation

from Frege’s essay “My basic logical insights", which was written near the end of his

career, Frege held just the opposite view. Far from believing that truths of logic are

merely rules, or conventions of language, or that the truths of logic are true in virtue of

the way we use words; Frege believed that natural language is defective, and not to be

trusted, as the basis of scientific knowledge. Frege believed that logic “is to a large

extent, a struggle with the logical defects of language."8'

It might be objected that Frege often described logic as being concerned

with ’normative laws'. As such, logic must be concerned with rules of language use.

However, by normative laws, Frege did not mean logic is concerned with rules of

language use. By “normative laws”, Frege is rather concerned with “thought” in a

normative sense. He was making an analogy of logic with ethical duty. What

distinguishes an ethical duty is that it is a requirement that cannot be defeated by any

other requirement.82 Normative laws are ethical requirements of correct thought. While

Frege goes to great pains to separate logic from psychology, his analogy of logical with

81 Ibid. 82 Chisholm, Theory of Knowledge (Englewood Cliffs: Prentice Hall, 1989), 60.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 normative laws confirms the intemalistic nature of his philosophy of logic. Epistemic

justification is imposed by the conscious state in which one happens to find oneself.83 If

we are required by normative laws to hold certain beliefs, in order that we may be

deemed as acting in accordance with reason, then it must be part of our conscious state

that such beliefs are in accordance with the normative laws. We must first hold such

beliefs as possessing the required epistemic justification. Internalist conceptions of

epistemic justification are characteristic of idealism and rationalist epistemology.

In contrast to the internalist version of epistemic justification, the

externalist version of epistemic justification is closely allied with realism, and modem

empiricist principles of verification (or falsification). Externalists hold there must exist a

reason, or justification, outside the subject, to guaranty that something is true. The

extemalization of knowledge evolved out of the movement toward the objectivity of

knowledge, which developed in the nineteenth century. Extemalization of knowledge

achieves the highest degree of objectivity in verification theories of meaning.

Frege, as Philosophical Revolutionary

The second of Dummett’s distortions is connected with the first. It has to

do with Frege’s place in the history of modem philosophy. He has argued that prior to

Descartes the dominant idea in medieval philosophy was logic, and that the entire

history of modem philosophy since Descartes has been dominated by the idea of the

primacy of epistemology. He claims, that “Descartes’ revolution was to make

epistemology the most basic sector of the whole of philosophy.’’84 “Descartes made the

question, ‘What do we know, and what justifies our claim to this knowledge’? The

starting-point of all philosophy: and, despite the conflicting views of the various schools,

83 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 it was accepted as the starting-point for more than two centuries."85 Following Descartes,

the 'theory of knowledge' became the foundation of philosophy.85 It is this orientation

which makes post-Cartesian philosophy different from that of the scholastics..."87

According to Dummett, Descartes shifted the dominant focus in

philosophy from logic to epistemology. "Descartes' perspective continued to be that

which dominated philosophy until this century, when it was overthrown by Wittgenstein,

who in the Tractatus reinstated philosophical logic as the foundation of philosophy, and

relegated epistemology to a peripheral position. Frege, unlike Wittgenstein, made few

overt pronouncements about the relative positions of philosophical logic and of

epistemology in the architecture of the subject as a whole: but by his practice he

demonstrated his opinion that logic could be approached independently of any prior

philosophical substructure...." Thus, according to Dummett, Frege is of a single mind

with Wittgenstein in believing that logic is foundational for philosophy.

Dummett claims that "Frege's fundamental achievement was to alter our

perspective in philosophy, to replace epistemology, as the starting point of the subject,

by what he called 'logic'."88 Dummett says that “Frege’s basic achievement lay in the fact

that he totally ignored the Cartesian tradition..."89 The seminal work of Frege and

Wittgenstein in mathematical logic, therefore, resulted in a shift of the dominant place of

epistemology back to logic. According to Dummett, then, Frege's conception of logic,

though Frege himself was not explicit in this regard, marks the beginning of a new era in

which logic holds the foundational place in philosophy, replacing epistemology. This is

84 Dummett, Frege: Philosophy of Language, xxxiii. 85 Ibid., 666-7. 88 Ibid.,.676. 87 Ibid., xxxiii. 88 Dummett, Truth and other Enigmas, 441. 89 Dummett, Frege: Philosophy of Language, 667.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 a view similarly held by Kenny, who says, “The Cartesian tradition had placed

epistemology in the forefront of philosophy; the empiricist tradition had confused the

study of logic with an inquiry into human mental processes. Frege disentangled logic

from psychology, and gave it the place in the forefront of philosophy which had hitherto

been occupied by epistemology."901 concur with Dummett that logic has returned to a

more prominent position within the last hundred years, and that modern philosophy has

paid comparatively less attention to logic than to epistemology. Dummett’s and Kenny’s

view of the history of modem philosophy is in need of serious revision on two counts.91

First, the claim that logic (whether redefined as theory of meaning, or a linguistic theory)

is foundational for human knowledge, is itself, an epistemological claim. Second, after

Descartes established epistemology as the central concern of philosophy, logic

remained a part of the modem philosophical tradition, and did not disappear, as

Dummett and Kenny would have us believe. Logic was not resurrected again by Frege,

as the new foundation for philosophy. For Frege, logic was the tool, which had

remained a vital part of the modem philosophical tradition, which Frege used to

deductively demonstrate that reason is the epistemological source of the justification for

mathematical knowledge. I maintain that Frege’s philosophy was epistemological in its

outlook in the tradition stemming from Descartes, Leibniz, and Kant.

Frege’s Cartesian Perspective

Frege's philosophy lacks any systematic or comprehensive outlook; and this has not

gone unnoticed by commentators.92 The lack of a systematic philosophical outlook is the

90 Kenny, Frege, An Introduction to the Founder of Analytic Philosophy, 210. 91 Sluga,"Frege: the early years" in Philosophy in History, eds. Rorty, Schneedwind, and Skinner, (Cambridge: Cambridge University Press, 1984), 330. 92 Wettstein, Howard K., Has Semantics Rested on a Mistake? And Other Essays (Stanford: Stanford University Press, 1991), 136.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 primary reason why there are differences of opinion regarding significance of his work,

and its place in contemporary philosophy. Dummett traces the anti-Cartesian revolution

of twentieth century philosophy to Frege. He wants to claim for Frege the seminal idea

of making logic, or in Dummett’s reformulation of it, the theory of meaning, as the

starting point of philosophy, instead of theory of knowledge. He views Frege's work as a

contribution to philosophy of language and theory of meaning, with logic as a new

foundation for philosophy. Although Dummett admits that Frege never made any such

claims93, he attributes the following views to Frege:

Only with Frege was the proper object of philosophy finally established: namely, first, that the goal of philosophy is the analysis of the structure of thought, secondly, that the study of thought is to be sharply distinguished from the study of the psychological process of thinking; and finally that the only proper method for analysing thought consists in the analysis of language.9*

By thought, what Dummett means is the objective andeternally existing contents of

thought, a public view of language similar to what wefind later on in Wittgenstein.

I maintain however there is an underlying philosophical outlook in Frege’s

work which adheres to the private view of language meaning which is clearly Cartesian.

Such a view of Frege seems hardly possible given the influence of his work on twentieth

century analytic philosophy. But the evidence for Frege’s Cartesian philosophical

perspective is seen in his implicit representational theory of mind. Frege holds a 'mirror

of nature’ view of the world, and the objects in it, both real and abstract. For Frege, the

mind is the repository of images and conceptual representations.95 Despite Frege’s

efforts to separate subjective from objective ideas, language only becomes meaningful

by association with conceptual representations in the mind. Even if we concede

93 Dummett, Truth and Other Enigmas, 443. 94 Dummett, Truth and Other Enigmas, 458. 95 Wettstein, Has Semantics Rested on a Mistake? And Other Essays, 137.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 Frege’s notion of a Third Realm’ as the locus of objective thoughts, such thoughts are

only made meaningful by association with representations.

Frege is clearest in demonstration of his acceptance of the

representational view of mind in the essay “Thoughts”. He introduces the notion of

representations, or ’ideas’, as follows:

Even an unphilosophical man soon finds it necessary to recognize an inner world distinct from the outer world, a world of sense-impressions, of creations of his imagination, of sensations, of feelings and moods, a world of inclinations, wishes and decisions. For brevity’s sake I want to use the word ‘idea’ to cover all these occurrences, except decisions.96

In other words, For Frege, the inner world is the object of our awareness.

However, Frege distinguishes the object of inner awareness from the object of

thought. An idea, or object of awareness, must always be distinguished from the

object of thought. Thus, he says:

What is a content of my consciousness, my idea, should be sharply distinguished from what is an object of my thought.97

Since we are not the owners of thoughts, according to Frege, we therefore

‘grasp’ thoughts:

We are not owners of thoughts as we are owners of our ideas. We do not have a thought as we have say, a sense-impressions, but we also do not see a thought as see, say, a star. So it is advisable to choose a special expression; the word ‘grasp’ suggests itself for the purpose.96

In a footnote Frege holds that “the expression ‘grasp’ is as metaphorical as

‘content of consciousness’. The nature of language odes not permit anything

else.”

In thinking we do not produce thoughts, we grasp them. For what I have called thoughts stand in the closest connection with truth.99

96 Frege, Collected Papers, 360. 97 Ibid., 366. 98 Ibid., 368. 99 Ibid., 368.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45

It is significant, and revealing of Frege’s representational view of mind, that

grasping a thought presupposes a thinker, someone with the capability of

thinking, and thereby grasping the thought.

The grasp of a thought presupposes someone who grasps it, who thinks. He is the owner of the thinking not the thought.100

He goes on to say:

Although the thought does not belong with the contents of the thinker’s consciousness, there must be something in his consciousness that is aimed at the thought. But this should not be confused with the thought itself.101

Although a thought does not belong to the thinker per se, for Frege, it is clear that

there must be something in the thinker’s consciousness itself aimed at the

thought.

In addition to demonstrating that Frege held a representational

view of mind, the passages I have quoted above are revealing too of other

similarities between Frege’s philosophy of mind and that of Descartes. In the

Principles §32, Descartes distinguishes two modes of thinking: the perception of

the intellect and the operation of he will. According to Descartes:

All modes of thinking that we experience within ourselves can be brought under two general headings: perception, or the operation of the intellect, and volition, or the operation of the will. Sensory perception, imagination and pure understanding are simply various modes of perception; desire, aversion, assertion, denial and doubt are various modes of willing.102

This is suggestive of the divisions of the mind given by Frege. Descartes talks

about “modes” of the mind similarly to Frege distinctions of inner mental activity,

except Frege separates “decisions” for Descartes “desire”; the separation is

100 Ibid., 369. 101 Ibid., 369.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 essentially the same. Both Frege and Descartes hold that there are

ontologically separate kinds of entities, mind and objects of thought.

Frege's tireless efforts to make representations objectively abstract only

obscures the true psychologistic tendency of his thought. The reference of a name

depends upon the association of a sense with the name. For according to Frege:

The regular connexion between a sign, its sense, and its reference is of such a kind that to the sign there corresponds a definite sense and to that in turn a definite reference.103

Moreover, a sentence that contains thought depends upon sense for its meaning, not its

reference.104 Again, the sense of a sentence depends ultimately on the conceptual

representation for meaning, not the reference of the sentence. This is wholly contrary

to the public language view of meaning stemming from Wittgenstein, and contrary to the

view of Frege which Dummett has suggested.

This conceptual representational view of Frege has implications for his

epistemology, philosophical logic and mathematics. As is well known, Frege rejected

empiricist principles as the foundation of the arithmetic; he grounded the truths of

arithmetic in logic. The representational view of Frege that I am advancing is consistent

with his view of logic and objective ideas as based on reason.105 In the Foundations

Frege says:

It is in this way that I understand objective to mean what is independent of our sensation, intuition and imagination, and of all construction of mental pictures out of memories or earlier sensations, but not what is independent of reason, - for what are things independent of reason?

And, again:

102 John Cottingham, Robert Stoothoff, and Dugald Murdoch, eds. The Philosophical Writings of Descartes, vol i (Cambridge: Cambridge University Press, 1985; reprint 1992), 204. 103 Frege, “On Sense and Reference" in Translations from the Philosophical Writings of Gottlob Frege, 58. 104 Ibid., 62. 105 Frege, Foundations of Arithmetic, 36.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47

Now objectivity cannot, of course, be based on any sense-impression, which as an affection of our mind is entirely subjective, but only, so far as I can see, on reason.106

I maintain that Frege held a traditional representational view of thought,

and a traditional view of epistemology, that is .in essential respects the same outlook

stemming from Descartes. Thus, Frege holds a psychologists account of knowledge

similar to that which “runs though most epistemology before the twentieth century."107

This account of knowledge, and particularly the notion of proof, is common to Descartes,

Leibniz, Kant, Frege, and many other philosophers before the twentieth century. “On

the psychologists account, we suppose that the question of whether a person's true

belief counts as knowledge depends on whether or not the presence of that true belief

can be explained in an appropriate fashion."108 In the cases involving proofs of

arithmetical knowledge, Frege explicitly rejects the notion that a true belief is possible

given an empirical source, i.e. intuition. Rather, a true belief involving proofs of

arithmetical knowledge can only be based on the logical source, i.e. laws of logic. Laws

of logic are axioms that do not admit o f proof. To explain in an appropriate way a

person’s belief in such an axiom, it is sufficient to point out that that person was in the

right state of mind.109 Thus, to believe an axiom is true, it is sufficient that it is evident to

me, or self-evident, that it is true.

On the interpretation that I wish to advance, Frege held a view of

epistemology grounded in what might be called 'logical intuition’, or self-evident truths of

reason. These are truths that are to be distinguished from those which are grounded in

empirical sources. The standard objection to intuition as a warrant for truth is that it

1C6 Ibid., 38. 107 Kitcher, ‘ Frege’s Epistemology", 243. 108 Ibid., 243.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 does not seem to be able to settle rival claims to knowledge. It is often the case that two

different people in thinking about the same thing, may have quite different ideas.

Philosophers often disagree on whether every event has a cause, the exact nature of

the cause of a particular event, or whether existence is a perfection. But there is little

controversy regarding the necessity of the law of contradiction, law of excluded middle,

the law of identity, or the principle stating that equals subtracted from equals result in

equals. These are all instances of logical intuition, i.e. logical self-evidence, or truths of

reason. The doctrine of logical self-evidence is a special kind of intuition, i.e. logical

intuition, which is opposed to pure intuition or empirical intuition. The term 'intuition' is

anathema to Frege when it comes to arithmetic knowledge, and throughout his writing

he rejects any notion of intuition as the source of, or validation of, arithmetic truths; and

he does not use that term to describe self-evidence. This shows that Frege defines

intuition in the Kantian sense; while self-evidence is reserved for conceptual knowledge

that does not depend on Kantian forms of intuition. However, Frege does not reject pure

intuition as the source of geometric truths. In fact, he explicitly affirms Kant’s

characterization of them as synthetic a priori truths.

The view of which I want to advance of Frege is highly controversial. I

believe there are deep tensions in his writings revealing that, although he was avowedly

anti-psychologistic, he was in essential respects a psychologists philosopher. As is

well known, Frege rejected what he termed 'psychologists' claims to knowledge for

mathematical knowledge. His ejectionof psychologism obscures the fact that he

routinely embraced a psychologists epistemology regarding logical truths in the modem

sense. But this reading is consistent with the Kantian epistemology regarding the status

1“ Ibid., 244.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 of conceptual knowledge, as the source of objective ideas. Most modem interpreters of

Frege adhere to the orthodox reading of Frege, that of a vehement anti-psychologist

philosopher, logician and mathematician. Weiner, for example, believes that Frege is

“committed to a nonpsychologistic view about the ultimate ground for justification of

primitive logical laws."110 Dummett maintains that “the psychological error that [Frege]

wishes to guard against is . . . psychologism."

The case for psychologism in Frege’s thought has not gone unnoticed by

some contemporary philosophers. There is support for the view I am advancing. Susan

Haack finds Frege's arguments against psychologism “less conclusive, and at least

some form of psychologism more plausible, than it is nowadays fashionable to

suppose.”111 Baker and Hacker have found Frege’s arguments against psychologism full

of “blunders”, and “a galaxy of conceptual confusions.”112 Philip Kitcher has attributed to

Frege a “psychologistic account of knowledge".113

The polemic against psychologism that prevailed in Germany in the later

half of the nineteenth century and first quarter of the twentieth century about which I

have referred elsewhere in this chapter has done much to blur the relation of psychology

and epistemology during the twentieth century. Frege was a central figure in this

polemic from the standpoint of analytic philosophy, The polemic obscures the

110 Weiner, Frege in Perspective, 61. 111 Susan Haack, Philosophy of Logics (Cambridge: Cambridge University Press, 1978; reprint, 1988), 238. 112 Baker and Hacker, “Frege’s Anti-psychologism” in M. A. Nottumo, Perspectives on Psychologism ( Brill: Leiden, 1989), 74-127. 113 Philip Kitcher, “Frege’s Epistemology", Philosophical Review 88 (1979): 235-262.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 psychologists presuppositions that underlie Frege's philosophy, and which are

characteristic of the Cartesian philosophical perspective preceding the linguistic turn.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 3

THE HISTORICAL PHILOSOPHICAL AND SCIENTIFIC SETTING

Modem Philosophy and Scientific World-view

There were several broad movements in philosophy, science and

mathematics shaping the intellectual climate leading up to and into the nineteenth

century that influenced Frege's intellectual development and shaped his philosophical

outlook. These movements had a profound influence on him. They may seem foreign to

us now from the standpoint of the late-twentieth century. But there can be no clear

understanding of Frege’s work and thought without taking into account these

developments, and their relevance to his work.

The classical conception of science from Aristotle until Descartes was

based on an ontological interpretation. Science was viewed as knowledge of the

universal (i.e. the essence, causes and attributes of the particular), of necessity, or what

eternally is, and of truth in the sense of true being. The truth of judgments was

considered grounded in the metaphysical certainty of universal and necessary concepts.

After Descartes, the ontological conception of science was rejected in favor of a

gnoselogical conception. The self-certainty of scientific truths became accessible to the

individual subject. Universality, necessity and truth came to be fundamental features of

scientific judgments themselves, defining their structure and acceptability. Scientific

judgments were no longer grounded in metaphysical certainty; they were grounded in

the reasoning subject. The self-certainty of knowledge became the fundamental

principle, and mathematics became the guiding model. The replacement of the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 ontological by the gnoselogical conception was the crux of Kant’s characterization of

science. According to Kant, "any theory is termed a science if it is supposed to be a

system, that is, a totaiiiy of knowledge organized in accordance with principles."114 Tnus,

the characteristics of knowledge: universality, necessity and truth are guaranteed

respectively by theoretical, systematic and cognitive features.115 Kant followed

Descartes and the rationalists in fulfilling these requirements by means of the

mathematization of knowledge: “I affirm however, that, in every particular branch of

natural knowledge, there can be found only as much genuine science as there is

mathematics."116

In the late seventeenth and eighteenth century, Newtonian physics had all

but replaced metaphysics, and modem scientific knowledge founded on the principles of

Newton, Galileo, Copernicus and others, had become the accepted scientific world view.

The question of how we can know with certainty know that the new science was true

became a central concern of philosophers. Many, like Hobbes, Locke, and Leibniz, saw

the laws of Euclidean geometry as inherent in the design of the universe. Hume, notably

in contrast, in his Treatise of Human Reason (1739) denied the existence of natural laws

in the universe concluding they were merely habituations of the human mind. Hume’s

influence was overshadowed by Kant in his Critique of Pure Reason (1781). Kant

maintained that the human mind provides certain modes of organization, or pure

intuitions, of space and time. Our minds are constructed in such a way that our

knowledge of the phenomenal world is shaped by the pure intuitions of space and time.

The organizing modes, or pure intuitions, of space and time are prior to experience.

114 Kant, Metaphysical Principles of Natural Science (Indianapolis, Bobbs-Merrill, 1970), A VI. 115 Herbert SchnSdelbach, Philosophy in Germany 1831-1933 (Cambridge: Cambridge University Press), 81.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 Kant was concerned with the limits of human knowledge, and recognized the subjective

input into knowledge. However, he wholly rejected the notion that humans could have

access to knowledge of things-in-themselves beyond human consciousness. In

consequence, our judgments concern merely the phenomenal world.

Kant accepted Leibniz’s a priori and a posteriori distinction for the sources

of knowledge, and was the first to distinguish analytic and synthetic judgements. Kant’s

distinctions divided all human knowledge into three kinds: He classified sense

perceptions as synthetic a posteriori judgements. While judgments involving pure

reason and the application of the categories of the understanding without any intuitions

or sense perception were classified as analytic a priori judgments. In order to make

room for judgements involving metaphysical knowledge, Kant allowed for synthetic a

priori judgments. Analytic a posteriori judgements had no place in Kant’s system. The

synthetic a priori category included judgements of geometrical and arithmetical

knowledge and casual judgements involving knowledge of the laws of nature. It was the

accepted view by the first part of the nineteenth century among most philosophers,

including mathematicians, that the physical world as perceived by humans must be

Euclidean; and thus, all judgements involving spatial perception were synthetic a priori.

Post-Kantian Idealism

Nineteenth-century philosophy in Germany was largely a reaction to Kant,

who was concerned with the limits of human knowledge, recognized the non-empirical, a

priori sources of knowledge, and rejected the notion that metaphysics could give us

knowledge of thing-in-themselves beyond human consciousness and the empirical

world. There was first, following Kant, the rapid rise of post-Kantian, or German,

116 Kant, Metaphysical Principles of Natural Science, A VIII.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 idealism in reaction to Kant’s critical philosophy. After the death of Hegel in 1831

German idealism experienced a nearly total decline and feel into disrepute, though it

was taken up in England.

The German idealists took themselves to be true spiritual successors of

Kant, and did not regard themselves as reacting against his ideas. The leading

exponents were Fichte, Schelling and Hegel. Kant had attached the claim of

metaphysics to an adequate theory of human knowledge. The German idealists

transformed Kant’s theory of knowledge into a metaphysics of reality; where reality was

viewed as a self-manifestation of human reason. The idealist movement was a

succession of speculative metaphysical systems marked by a strong confidence in

human reason and the scope of philosophy. The movement began with Fichte’s

rejection of Kant’s ‘things-in-themselves’, as inconsistent and inexplicable on Kant’s own

premises that anything independent of mind could be knowable. For the German

Idealists, all things had to be regarded as products of human thought. To avoid

subjectivism and inevitable solipsism, and starting from the position of Kant’s

transcendental ego, the idealists transformed it into supra-intelligence. They held that

the ultimate principle in reality consisted in an absolute subject possessing infinite

reason. Reality, in which all things are in principle knowable, is the process of self-

expression, which manifests itself into infinite thought or Absolute reason.117 For the

idealists, subject and object are correlative.

Whereas Kant was concerned with the limits of human knowledge, and

recognized the subjective input into knowledge, but rejected the notion that metaphysics

could give us knowledge of 'things-in-themselves' beyond human consciousness, post-

117 Copleston, A History of Philosophy, vol. vii, (New York: Doubleday/lmage Books, 1963)1-31.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 Kantian idealism was thoroughly anthropomorphic. Under Hegel, philosophy takes on

an historical dimension; it is seen as an historical process constantly developing toward

Absolute truth.118 The key epistemic problem for Hegel is not how we can know anything

at all, but how we can move from a partial and limited historical perspective to absolute

knowledge. The historicity follows from the subjective component of individuals

incapable of transcending the historical moment. The notion of truth is understood from

the perspective of history and evolving culture. Anthropomorphism manifests itself in

Hegel’s emphasis on the evolution of Spirit as manifested in the development of human

society. The Absolute is definable as Spirit or self-thinking thought. Human

consciousness is transformed into reality as a whole.

Hegelian idealism rejected Kant’s a priori-a posteriori and analytic-

synthetic dichotomies. All propositions are analytic, not synthetic. Mathematics is

associated with analysis, thus not synthetic. Mathematical entities are abstractions

produced by us, and can be defined in terms of what we put into them. Hegel regards

definitions like ’the shortest distance between to points is a straight line’ as stipulate, and

thus analytic. The subjective and objective are fused into one state of mind.

Hegelian theory of knowledge differs from the traditional subjectivist

epistemology of rationalists and empiricists like Descartes, Locke, Berkeley, Hume,

Leibniz and Kant. Hegel was a kind of Heraclitean-Platonist, or Neo-Platonist, whose

world of Ideas was constantly evolving through time. Hegel’s Ideas or Forms where like

those of Plotinus; they were thoughts thinking themselves and inhabiting a supra,

Absolute Spirit. Despite its anthropomorphic origins, Hegelian Absolute spirit is not the

creation of man. It is the hypostasized Objective Spirit that moves man and all

118 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 civilization. Like Plato’s Forms or Ideas that inhabited a divine realm, Absolute Spirit is

indeed otherworldly. Although the origin of knowledge for Hegel has subjective roots in

man, Absoiute Spirit is totally objective in nature, thus not subjective, but separated from

man.

Hegelianism was brought down rapidly after the death of Hegel in 1831

by the advance of the physical sciences and internal dissension from within.119 The

growth and advance of the natural sciences, and also the rapid new industrialization and

related social ills, led to the decline of Idealism, and its replacement by naturalism and

materialism. By mid-century the dominant position, which had been held by the

speculative philosophy of Hegel, was replaced almost totally by the natural sciences.

Naturalism. Materialism, and Positivism

After Hegel, traditional natural philosophy was no longer the model of

scientific approach that it had been since Aristotle. Philosophy and science had been

conceptually equivalent. Empirical and mathematical methods of investigation of nature

gave rise to polemics between the contrasting views of natural philosophy and natural

science. The successes of empirical approaches to natural science during the first half

of the nineteenth century resulted in the rapid ’empiricization' of all the physical

sciences. Empiricism became the defining characteristic of natural science, and science

became synonymous with ‘empirical science’.

In response to the changes brought on by the natural sciences, many

philosophers adopted either a materialistic, naturalistic, or positivistic stance. The turn

toward materialism, naturalism and positivism, which are all philosophically closely

related, developed out of a rejection of absolute idealism. Absolute idealism held that all

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 matter constituting the empirical world is constituted by the mind. While naturalism and

positivism, which are closely related to materialism, share the philosophical standpoint

that everything in reality, including minds or anything apparently non-material, is

ultimately reducible to matter, and the complex motions of material particles.120

Empirical scientists rejected the supernatural principles, theological

interpretations, and speculative excesses of post-Kantian idealism, especially the

Hegelian variety. The naturalistic worldview held that everything is explicable in terms of

scientifically verifiable concepts. Naturalism holds that what is studied by the natural

and human sciences is all that there is. There is no need to look for explanations

outside of the world.121 The entire universe is composed of natural objects; natural

processes are changes in natural objects; and nature is a system of natural order and

processes. Human beings are no less subject to natural laws than are other parts of

nature. The rising naturalism was roughly equivalent to secularism, which, like

humanism, rejected the religious and spiritual interpretations of human behavior, and

social and cultural developments. The emphasis was on unity of behavior; human

conduct and institutions were held to be more complex instances of the behavior of

lower organisms. Some scientists of the period adopted the materialist outlook, as a

philosophical expression of the material discoveries of natural science. Naturalists have

believed since Darwin that higher forms of life evolve from lower forms of life and these

ultimately from non-living matter, without the intervention of the supernatural.122 The

classic expression of the naturalistic worldview in the nineteenth century was the

1,9 Passmore, A Hundred Years of Philosophy (New York: Basic Books, 1966), 46. 120 Jones, A History of Western Philosophy: Kant and the Nineteenth Century, vol. iv, (New York: Harcourt, Brace, Jovanovich, 1975), 381. 121 Flew, A Dictionary of Philosophy, Revised Second Edition, (New York: St. Martin’s Press, 1984), 240. 122 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 ‘positivism’ of French philosopher Auguste Compte (1798-1857). Positivism is

characterized by its acceptance of Kant’s limit of knowledge to phenomena, and its

rejection of the synthetic a priori. Positivism is characterized more by its interest in how

things happen than why things happen. All knowledge is systematic collection and

correlation of the succession of phenomena. It rejects unverifiable speculation about

first causes and final ends. The important exponent of positivism in the German

speaking region was Ernst Mach (1838-1916), the Austrian physicist and philosopher.

Mach’s philosophy exhibited an extreme empiricism that rejected any notion of a priori

sources of knowledge. He is widely regarded as the father of logical positivism, and was

radically empiricist. He rejected all powers of the mind to know or understand things;

everything was considered reducible to sensation, i.e. the view known as

phenomenalism. Mach’s foundational approach to knowledge based all knowledge on

sense experience, and advanced the fundamental unity of sciences based in sensation.

Empirical science in Germany adopted the ‘inductivist’ methodology of

John Stuart Mill (1806-1873), whose System of Logic first appeared in German

translation in 1849123, and was widely read and highly influential in Germany.124 Inductive

science was regarded as the science of reality.125 Inductivism reduced Kant’s a priori,

including all concepts and natural laws, to empirical generalizations. This reduction

eliminates synthetic a priori knowledge, and thus implies the elimination of metaphysics.

Frege, notably, rejected the empiricism of Mill’s logic and mathematics, and accepted

the Kantian categories of knowledge that included synthetic a priori knowledge.

123 In the Foundations of Arithmetic, Frege referred to the German translation of the 4th edition of Mill’s System of Logic published by J. Schiel in 1849. 124 Schnadelbach, 85. 125 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 Psychologism and Anti-Psvcholoqism

The increased specialization of the sciences gave rise to a science of

psychology modeled on the empirical sciences. Philosophy in Germany in the early

nineteenth century meant Hegelian idealism, the philosophy of Spirit, and reflection.

The new descriptive, or empirical psychology as it was also known, began as a

‘psychology without a soul’ and eventually developed into the science of human

behavior.128 Thus, empirical psychology differed from the old ‘psychology of reflection’,

which was not essentially distinct from philosophy. The new descriptive psychology,

considered as an empirical science, eventually led to the problem of circularity of

psychologism in logic, and by extension to mathematics.127 If logic derives from

psychological processes and mathematics is thus a creation of human thought, then

there can be no certainty in logic or mathematics, since human thought processes and

creations were known to be fallible.

The historical development of psychologism is difficult to trace. Its

genesis, however, is highly controversial in Frege exegesis because of the implications

for Frege’s philosophical outlook. The most plausible view regarding the development of

psychologism is that it grew out of empirical sciences with the development of

descriptive psychology as a separate empirical science. Thus, psychologism developed

out of naturalism and materialism.128 This is the accepted scholarly view regarding its

origins. An authoritative description of its development is found in SchnSdelbach.

However, see also Sluga129, and Baker and Hacker.130

128 SchnSdelbach, 74. 127 Ibid. 128 Kusch, Psychologism (London: Routledge, 1995), 109. 129 Sluga, Gottlob Frege (London: Routledge, 1980),18. 130 G. P. Baker and P. M. S. Hacker, Logical Investigations (Oxford: Oxford University Press, 1984).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 In contrast to the accepted view, Dummett maintains that psychologism

developed out of neo-Kantianism. He wants to argue that Frege was a realist having

little in common with German idealism and Neo-Kantianism. On the other hand, Sluga,

in taking the accepted view of the origins of psychologism, has argued that

psychologism arose out of naturalism in Germany in the middle of the nineteenth

century.131 Sluga has rightly argued that naturalism is rooted in a radical empiricism; and

the adherents of naturalism believed that all human knowledge is built upon a sensory

foundation. For naturalists, a priori reasonings and concepts were easily explained as

abstractions from sensory experien'ce. The naturalists were sympathetic with the British

empiricists; hence Mill’s inductivist logic became widely read in Germany. Dummett has

challenged Sluga’s claims for the origin of psychologism, arguing instead that, ironically,

psychologism originated from Neo-Kantianism at Frege’s own University of Jena with

Fries. The beginnings of psychologism indeed seem to be traceable to Neo-Kantian

origins in the philosophy of Fries and Beneke.132 However, the view that Dummett has

argued for, that Neo-Kantianism is inherently psychologistic, is a distortion of historical

facts. There were many varieties of Neo-Kantianism, including varieties that were anti-

psychologistic. Moreover, the roots of psychologism are traceable to the naturalism the

empirical sciences.

Dummett would like to label all forms of Neo-Kantianism as psychologistic

in order to advance the standard view of Frege as a realist and anti-psychologistic

philosopher with no connection with idealism or Neo-Kantianism. Since Frege’s

philosophy of mathematics, logic and language are considered paragons of analytic

philosophy, according to Dummett, Frege could not have been a Neo-Kantian because

131 Sluga, Gottlob Frege, 18. 132 Beck, “Neo-Kantianism,” in The Encyclopedia of Philosophy, 468-473.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 all Neo-Kantians were psychologistic. Moreover, since, as is well known, the standard

interpretation maintains that Frege was a devout anti-psychologistic philosopher and

thus anti-idealist, it is inconceivable for Frege to be a Neo-Kantian. But Dummett’s

version of historical events in German philosophy of the nineteenth century is

inaccurate. Dummett ignores the link between Frege, Neo-Kantianism and other like-

minded idealist philosophers. Beneke and Fries were not representative of all Neo-

Kantians. Towards the end of the nineteenth century, there were Neo-Kantians arguing

against psychologism. The historical evidence shows that internal tensions among

followers of Kant due to the complexities of Kant's philosophy resulted in several

manifestations of Neo-Kantianism. Dummett’s historical interpretation of Neo-

Kantianism and its relation to Frege exegesis ought therefore to be rejected.

According to Kohnke, psychologism results from “the transformation of

logic into theory of knowledge and theory of science, the intensive analysis of the history

of philosophy, and an increased admission into philosophy of knowledge derived from

the natural and human sciences."133 After the death of Hegel, absolute idealism fell into

disrepute, and philosophy lost its dominant position to the natural sciences. Philosophy

adjusted to the new naturalistic and positivistic attitude of the ideal of the empirical

sciences. The naturalistic approach meant the philosophers attempted to solve

traditionally philosophical problems of epistemology, logic and ethical questions by

means of empirical approaches. Simply put, psychologism is the naturalistic reduction

of all mental states to physiological and biological principles of empirical science.

With the development of the natural sciences there arose the

development of experimental psychology. Experimental psychologists, who attempted

133 KOhnke, Klaus Christian, The Rise of Neo-Kantianism (Cambridge: Cambridge University Press, 1991), 56.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 to explain reasoning in terms of sensations, images, associations and physiological

mechanisms, excluded logical factors. They thed to give logic and reasoning a causal

explanation in terms of psychological factors. Some mathematicians and logicians, like

Boole, accepting the explanation of logic as a psychological process, tried to explain

logic in terms of ‘laws of thought’. The increase in the rigor of mathematical analysis

brought with it an interest among some mathematicians in increasing in the deductive

rigor of logic and logical systems by the elimination of any appeals to intuition or

psychological factors. The term ‘psychologism’ was used by logicians to refer

pejoratively to insufficiently formalized mathematical or logical systems and by logicians

who rejected any incursion into mathematics and logic by psychology. In similar fashion,

the term ‘logicism’ was used pejoratively by psychologists to refer to psychological

theories insufficiently tested by experience.134

Tensions arose between the new breed of experimental and descriptive

psychologists who were evolving with the new naturalism out of the traditional fields of

natural science and philosophy. More and more, departments of psychology were

established at the major universities in Germany, Austria and throughout Western

Europe, Britain and America. The numbers of joint chairs of psychology and philosophy

in the late nineteenth century shows the increasing tendency to link psychology and

philosophy.

Kusch has convincingly shown that the entire anti-psychologism

movement from its inception to its end was ill-defined. Philosophers who applauded the

aims of anti-psychologism were enthusiastic yet inconsistent in their use of the term

‘psychologism’ to one another. There was little agreement among philosophers as to

134 Piaget, Logic and Psychology {New York: Basic Books), 2.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 whom was to be included in the list of psychologistic philosophers.135 According to

Kusch, whoever wrote about logic and epistemology between 1866 and the 1920s were

in danger of being accused of psychologism.136 The lack of defining characteristics and

inconsistencies in the accusations of psychologism leveled by some philosophers

against others indicates the charges of psychologism were really baseless hyperbole, or

ad hominem attacks, aimed at discrediting philosophical opponents.

The term psychologism was first applied by the Hegelian Johann Eduard

Erdmann in 1866 his Die Deutsche Philosophie seit Hegels Todo, but without criticism of

Beneke’s philosophy. Beneke was a privatdozent at the University of Berlin from 1820

until 1854. In collaboration with Jakob Friedrich Fries who was a professor at Jena from

1816 until 1843, Beneke held that all philosophical inquiry is grounded in introspection,

and truth reducible to subjective self-observation.137 They held psychology to be the

foundational philosophical discipline on which logic, epistemology, metaphysics, ethics,

and religion were reducible. Fries and Beneke rejected the post-Kantian idealism of

Fichte, Schelling and Hegel. Beneke and Fries wanted to replace the philosophical

speculations of Fichte, Schelling and Hegel with a new rigorous philosophy grounded in

psychology. They viewed Kant as their predecessor; but they rejected Kant’s

transcendental ground for truth and knowledge of a priori forms of intuition independent

of experience. They saw psychology as the source of knowledge, and their views are

closely connected to empiricist views of psychology as the source of knowledge.138

Another Neo-Kantian, Wilhelm Windelband, in 1880 was the first to

criticize psychologism, as the view that empirical psychology is the basis of ail

135 Kusch, 122. 136 Kusch, 95-121. 137 Nicolas Abbagnano, “psychologism," in The Encyclopedia of Philosophy, ed. Edwards (New York: Macmillan, 1972), 520-521.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 philosophy, and to link it to Beneke.139 Windelband was a member of the Baden school

of Neo-Kantianism. He regarded Beneke as:

. . . the most consistent and most radical proponent of psychologism . . . Not only does he think, like Fries, that epistemology and ail other disciplines are to be based upon psychology, he even denies that the task of psychology could be the identification of a priori knowledge: for him there is no a priori knowledge, and the topic of psychology is the history of the development of empirical consciousness.140

In 1884 Windelband published a paper entitled “Kritische Oder genetishe method"

endorsing the Kant’s transcendental-critical method as the overcoming of psychologism,

and characterized all post-Kantian instances of psychologism, as unfortunate lapses, in

which genetic method was used to justify empirical theory, and concluded that

psychologism must end in relativism.141

Neo-Kantian Carl Stumpf (1848-1936) published a paper in 1892, entitled

“Psychologie und Erkenntnistheorie", in which was distinguished Kant’s theory of

knowledge from psychological tendencies in German philosophy. He claimed that

German philosophy suffered from a split between ‘Kantian criticism of knowledge’, or

'Kritizismus', and ‘psychologismus’. According to Stumpf,

‘criticism’ is the conception of epistemology which tries to free the latter from all psychological foundations, and we call ‘psychologism’ (a term first used by J.E. Erdmann) the reduction of all philosophical research in general, and all epistemological enquiry in particular, to psychology.142

Frege’s separation of the objective and subjective within Kant’s epistemological

framework fits Stumpf s distinction between criticism and psychologism. Stumpf

obtained his doctorate from Gottingen in 1868 under Lotze. Frege also studied

philosophy there under Lotze. Stumpf is known to have corresponded with Frege in

138 Ibid. 139 Kusch, 102. 140 Quote from Kusch, 102. 141 Kusch, 102.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 1882. His letter expressed interest in Frege's work in logic. They likely influenced each

other. Stumpf was a student of Brentano, and a teacher of Husserl.

Lotze in his Logik also systematically developed the Kantian point of view.

According to Lotze, the psychological act of thinking is completely distinct from the

content of thought. The psychological act is a temporal phenomenon, whereas the

content of thought has an objectively valid mode of being.143 Sluga has also linked Lotze

to Neo-Kantian views by his sharp separation of the psychological from the logical, in

this separation, Lotze was looking back to Kant. According to Kant, logic is formal and

the forms of thought are formal and not empirical; hence logic, in so far as it is

concerned with the investigation of the forms of thought, must be a pure a prion

science.144 Lotze is known to have influenced Husserl and Brentano; and Sluga has

argued that Lotze also influenced Frege.

In contrast, British empiricist philosopher J. S. Mill defended

psychologism in the mid-nineteenth century in his System of Logic (1843), where he

explicitly states that introspection is the basis of axioms of mathematics and principles of

logic.145 Mill also classified logic under psychology in his Examination of Sir William

Hamilton's Philosophy (1865). Mill’s logic was translated into German and became

widely read in Germany by naturalist and materialist philosophers and scientists who

were receptive to Mill’s empiricist views on the inductive basis of logic and mathematics.

It is ironic that while Neo-Hegelianism was on the rise in England, the rise of naturalism

and materialism in Germany in the mid-century resulted in increased interest among

German philosophers and scientists in traditional English empiricism. Mill became very

142 Quote from Kusch, 103. 143 Abbagnano, 521. 144 Sluga, Gottlob Frege, 53. 145 Mill, System of Logic. See also, Abbagnano, 520.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 influential among scientists and mathematicians who accepted the view of psychology

as the foundation for all human knowledge. Since, as is well known, Frege rejected

psychologism in mathematics and logic, Mill became one of Frege's central targets; and

thus he rejected Mill’s empiricism in his Foundations of Arithmetic (1884).148

Important Neo-Kantians, among them philosophers of the Baden school,

also known as the Southwestern School of Neo-Kantianism, of which Windelband and

Rickert were representative, defended the independence of values from psychological

experience because they held psychology could never establish their absoluteness and

necessity.147 Similarly, the Marburg school, of which Cohen and Natorp were

representative, held that the validity of the sciences, like that of ethics and aesthetics,

does not depend on psychology; rather, it was their view that the validity of those

sciences depend of the laws proper to them.148

Significantly, Natorp and Cohen held that ‘thought’ or ‘consciousness’

does not designate a psychic reality subject to introspection, but rather the objectively

valid content of knowledge.149 It was their view that the objectively valid is the totality of

possible objects of knowledge, and therefore the preferred methodology for the

development of the sciences.150 By the time Frege was starting his academic career in

the 1870s and 1880s, the average Neo-Kantian was “strongly empiricist and agnostic."151

Many philosophers had largely surrendered to psychologism and philosophy, as a

science founded on empirical experience was at bottom nothing but the synthesis of

148 Frege, Foundations of Arithmetic, 9-13. 147 Abbagnano, 520-1. 148 Ibid. 149 Ibid. 150 Ibid. 151 Klaus Christian KOhnke, The Rise of Neo-Kantianism, 262.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 Kantianism and positivism.192 However, there is evidence that Frege either corresponded

with or had close associations with several well-known Neo-Kantians who had rejected

the psychologism of Beneke and Fries. These associations demonstrate the plausibility

of their anti-psychologistic influence on Frege, and his shared philosophical views with

Neo-Kantians like Windelband, Rickert, Stumpf, Natorp, and Cohen who all

distinguished epistemology from psychology.

Cohen was the founder to the Marburg school, and his work Frege caught

the attention of Frege.153 Cohen is credited with first developing the philosophical view

characteristic of the Marburg Neo-Kantians. They were adverse to the subordination of

consciousness to undifferentiated experience, as was the tendency of scientific

naturalism; and they wanted to protect the integrity of the free individual from the

excesses of monism and determinism, as had been the tendency of absolute idealism.

According the Cohen,154 truth is always that which is in agreement with reason, and the

laws of reason are independent of experience.

Cohen went beyond Kant’s limiting principle of ‘things-in-themselves’. For

Cohen, there is no objective world outside of cognition; and cognition is no longer finite,

as it was for Kant. Cohen’s reformulation of Kant came close to absolute idealism,

which Neo-Kantianism had originally attempted to refute. Cohen saw Kant as the

epistemologist of Newtonian physics. He saw his reformulation of Kant as an adaptation

of Kant’s transcendental analysis to the requirements of later nineteenth-century

science. Cohen rejected the physiological and psychological interpretation of Kantian

apriorism, thus removing it from the empiricism of Helmholtz, Lange, Zeller, and others.

152 KOhnke, 263. 153 Frege, “Review of H. Cohen, The Principle of the Method of Infinitesimals and its History", in Gottlob Frege: Collected Papers, 108-11. 154 Thomas E. Willey, Back to Kant (Detroit: Wayne State University, 1978), 108-110.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 Cohen's reformulation of Kantian epistemology rejected the earlier

empirical bias of Neo-Kantianism, replacing it with conceptualism. Cohen's

conceptualism may be seen as either a return to a kind of metaphysics of mind similar to

the idealism that Neo-Kantianism was intended to replace, or a more scientific version of

Kantian critical philosophy which sought to provide a rational basis for modem science.

Cohen replaced the metaphysics of Being with logic as a realm of values. He

considered logic the queen of the sciences. The similarity of Cohen's views to those of

Frege is striking.

Dummett has claimed that anti-psychologism in Frege’s thought is

evidence for Frege's anti-idealism. His claim is based on two misconceptions regarding

Neo-Kantianism. First, that Beneke and Fries, who were indeed advocates for a

psychological reading of Kant, were representative of all Neo-Kantian thinking. Second,

that all idealism is essentially psychologistic. These presuppositions are not correct. As

the historical record shows, Frege’s anti-psychologism is consistent with certain varieties

of Neo-Kantianism, namely, the Marburg School and the Southwestern School.

Moreover, the record shows that Frege had close contact with important members of the

very Neo-Kantian schools whose members exhibit anti-psychologism.

Neo-Kantianism

The rise of the natural sciences, displacing the historical pre-eminence of

natural philosophy as traditional science, brought with it an identity crisis of sorts for

philosophy. Philosophy no longer enjoyed the stature that it once held as the ideal of

rational thought; the rapid expansion and increasing specialization of the empirical

sciences had replaced it. In fact, the materialist and naturalist thesis was that the

systematization of empirical knowledge gained in the natural sciences had finally put an

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 end to the need for philosophy155 The materialism and naturalism were part of the

realist movement that interpreted all knowledge as empirical. Significantly, that realist

thesis was first rejected by Helmholtz, and then by others. Helmholtz presented his

rejection in the form of a physiological reinterpretation of Kant’s Critique of Pure Reason

at the 1855 dedication of a Kant memorial. This reinterpretation became the basis of the

older forms of Neo-Kantianism. Later, Herman Cohen, the founder of the Marburg

School, was to give a strictly logical reinterpretation of Kant’s Critique of Pure Reason.

Thus, philosophy was rehabilitated with the emergence of Neo-Kantianism in the form of

a theory of knowledge. To philosophy was attributed the function of the presupposition

and conceptual framework for all the sciences.

By the mid-nineteenth century there arose in Germany a movement

epitomized by Otto Liebmann in his Kant und die Epigomen (1865) in the exclamation

‘Back to Kant!’156 Liebmann taught at the University of Jena, and was a colleague of

Frege. This slogan was the rallying cry of the movement. The movement developed out

of the peculiar social and cultural situation in German science and philosophy.157 The

movement was loosely united by a rejection of speculative philosophical system

building, a rejection of irrationalism, and a conviction that philosophy could be a science

only if it returned to the methods of Kant.158 Thus there was a widespread interest among

scientists and mathematicians in Kantian epistemology. Neo-Kantians sought to find a

middle course between the extremes of absolute idealism and naturalism.159 Science

and the philosophy of Kant were united in Germany's greatest scientist of the period,

155 SchnSdelbach, 103. 158 Passmore, A Hundred Years of Philosophy, 46; also Copleston, vol. vii, p.361 157 Beck, "Neo-Kantianism," in The Encyclopedia of Philosophy, ed. Edwards, 468-469 158 Beck, “Neo-Kantianism." 159 Willey, Back to Kant, 81.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 Hermann von Helmholtz.160 Kant’s Critique of Pure Reason inspired particularly those

interested in the theory of knowledge.

Neo-Kantianism is characterized by its re-acceptance of the analytic-

synthetic and a priori-a posteriori dichotomies, after their rejection by absolute idealism.

It is evident from references throughout his works that Frege was greatly inspired by

Neo-Kantians, and accepted the Kantian epistemological framework. He saw his own

work in logic and mathematics within that framework. The 'Back to Kant' movement

inspired not only those, like Frege, who were interested in epistemology. Interest in

Neo-Kantianism was not confined to epistemology. Those interested in religion and

ethics were inspired by his Critique of Practical Reason, and still others interested in art

and value were inspired by the Critique of Judgment. Neo-Kantianism emphasized

theory of knowledge as the foundation of philosophy. Many Philosophers, in imitation of

science, focused their attention on Kant’s theory of knowledge.181 They turned away form

the excesses of the speculative philosophy of Hegel, in which all judgments were seen

as analytic, and returned to a reappraisal of Kant's critical philosophy, which held that

human knowledge consists of both analytic and synthetic judgments.

The renewed emphasis on epistemology stimulated interest among

German philosophers in traditional rationalist and empiricist explanations for the sources

of knowledge. The rationalist elements of Kant's critical philosophy were re-examined

and emphasized by German philosophers interested in rationalist sources of knowledge.

There was also a resurgence of interest in the rationalism of Leibniz among German

philosophers during the mid-century. The renewed emphasis on epistemology also

stimulated an interest in British empiricism, which had always emphasized an

180 Willey, ibid. 181 Passmore, A Hundred Years of Philosophy, 46.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 epistemological outlook.162 Thus, it is not surprising to find Frege wanting to contrast his

work with Locke, Hume and Mill. This is the philosophical setting in which Frege found

himself when he began his university studies.

Neo-Kantianism was not a homogeneous system of thought.183 The term

denotes several philosophical movements united in its reverence for Kantian ideas, but

disparate in the way they traced their inspiration back to Kant. At least six different,

often opposing, Neo-Kantian schools are distinguishable:164 (1) the Marburg school; (2)

the Heidelburg or Baden school; (3) a physiological school represented by Herman von

Helmholtz (1821-1894) and Friedrich Lange (1825-1875); (4) a realist school

represented by Alois Riehl (1844-1924); (5) the Gbttingen school of Leonard Nelson

(1882-1927), following the ideas of Jacob Fries (1773-1843); and (6) a sociological or

relativist school represented by Georg Simmell (1853-1918), and of this last school the

most important was Wilhelm Dilthy (1833-1912)165.

The ‘Back to Kant' slogan was considered a point of departure, not an

oath of allegiance to the old-fashioned. However, there are at least four common

Kantian assumptions, which seem to unify Neo-Kantianism as a philosophical

movement. (1) The use of transcendental method as opposed to the psychological or

empirical, meaning that they were concerned with the prior conditions of knowing and

willing. (2) They were conceptualists, and thus they denied intuition as a source of

genuine knowledge. They believed instead in reason as the basis of synthesis. The

derivation of genuine knowledge from empirical content is ruled out. (3) Their

epistemologies are idealist; knowledge of objects is shaped or constructed by the mind,

162 Passmore, A Hundred Years of Philosophy, 47. 183 Copleston, 367. 164 Flew, “Neo-Kantianism" in A Dictionary of Philosophy, Willey, ibid. mentions seven types of Neo-Kantianism.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 not given to it. (4) To understand Kant is to go beyond him; they all rejected that notion

that reality, or ‘things-in-themselves’ as the ultimate ground of experience, is not

knowable.168

Notably, some Neo-Kantian schools focused attention on consideration of

the justification of knowledge. In so doing, they turned away from Kant’s distinction

between analytic and synthetic judgments as resting on their content.

Many of Frege’s views are similar to the views held by representatives of

two Neo-Kantian schools: the Marburg school and the Baden school. He is also known

to have had contacts with Marty,'87 a member of the Austrian School of Franz Brentano.

The Marburg school is associated with Hermann Cohen (1841-1918) and Paul Natorp

(1854-1924). Both were contemporaries of Frege, and concentrated principally on

logical, epistemological and methodological themes.168 As mentioned above, the

Marburg school held there is an objectively, as opposed to subjectively, valid content of

knowledge, and thus rejected psychologism. Cohen abandoned Kant’s doctrine of

transcendental aesthetic, and devoted himself entirely to the logic of pure thought or

pure a priori knowledge, as the basis of a mathematical physics. Cohen claimed that

logic possesses a wider field of application beyond the field of mathematical natural

science to the field of the mental sciences which in no way affects the fundamental

relation of logic to knowledge in mathematical natural science. Cohen’s views were

expressed is his System der Philosophie (1902-12).189 Natorp occupied a chair at

165 Beck, “Neo-Kantianism." 166 Willey, 37. 167 See letter from Frege to Marty in Gottfreid Gabriel, Hans Hermes, Fredrich Kambartel, Christian Thiel, and Albert Veraart, eds., Philosophical and Mathematical Correspondence, Abridged from German Edition by Brian McGuinness, trans. by Hans Kaal. Chicago: University of Chicago Press, 1979), 99.; see also letter from Stumpf to Frege, ibid., 171. 188 Copleston, 362. 189 Ibid., 362.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 Marburg, and shared Cohen’s general outlook. The Marburg school survived into the

twentieth century, and ended with Ernst Cassier (1874-1945), who made contributions to

theory of knowledge.170 He tried to show that the logical development of mathematics

does not require any recourse to intuitions of space and time. Thus, he held a

philosophy of mathematics more ‘modem’ than Kant.171. The textual evidence to show

that Frege accepted some views associated with that school is abundant, including the

rejection of temporal and spatial intuition and notion of the objective validity as the

justification of human knowledge. That Frege was familiar with some of Cohen’s work in

the philosophy of mathematics is evident in his “Review of H. Cohen, Das Prinzip der

Infinitesimal-Method under seine Geschischte" (The Principle of the Method of

Infinitesimals and its History). Despite the Kantian framework of Cohen’s book, Frege

rejected many of Cohen’s claims regarding the foundations of infinitesmals.

Significantly, Frege’s review shows his reverence for Kant and the preeminence to which

he held Kant’s work in the philosophy of mathematics; and it also confirms Frege’s sharp

separation of psychology from epistemology. In his opening remarks of his review of

Cohen’s work, he says:

Since the subject matter of mathematics recedes into the background and is dominated by thought more than the other sciences, and since mathematical ideas have been developed into a richer and more subtle structure than elsewhere, this science is especially suited to sen/e as a basis for epistemological and logical investigations. Here is a quarry which could sill be worked to great profit. The reason why so little has been done along this line except by Kant may well be that facility in both philosophical and mathematical thought and an adequate knowledge of both fields are only rarely combined in one and the same person.172

In his closing remarks, Frege concludes:

170 Ibid., 267. 171 Ibid., 363. 172 Frege, Collected Papers, 108-111.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 I agree with Cohen that knowledge as a psychic process does not form the object of the theory of knowledge, and hence, that psychology is to be sharply distinguished from the theory of knowledge.173

Frege’s sharp distinction between psychology and epistemology contrasts starkly

with Wittgenstein's later view of equating the two disciplines.

While the Marburg school emphasized investigation into the logical

foundations of the natural sciences, the Baden school associated with the work of

Wilhelm Windelband (1848-1915) and Heinrich Rickert (1863-1936)174emphasized the

philosophy of values and the social sciences.175 For Windelband, philosophy

investigates the principles and presuppositions of value judgments, and the relation

between the judging subject and values as norms or ideals in virtue of which judgments

are made.176 Just as ethics is concerned with moral value and aesthetics is concerned

with beauty, so logic concerns truth; thus logic aims at value or norm.177 Logic, ethics

and aesthetics presuppose the values of truth, goodness and beauty.178 Thus, there is a

transcendental norm-setting or value-positing consciousness that lies behind empirical

consciousness.179 All individuals appeal implicitly to universal absolute values, and there

is a transcendental consciousness that bonds all individuals.180 Value judgments,

whether moral, aesthetic or logical, in Windelband’s philosophy, are axiological by

nature, rather than descriptive. Value judgments express what ought to be the case,

rather than what is the case. The true is that which ought to be thought. Moreover, the

173 Ibid., 111. 174 Copleston, 364-5. 175 Ibid. 178 Ibid. 177 Ibid. 178 Ibid. 179 Ibid. 180 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 ultimate axioms of logic cannot be proved; but we must accept them if we value truth,

unless we are prepared to reject all logical thinking.

Windelband’s philosophy of value was further developed by Rickert, his

successor to the chair of philosophy at Heidelberg. Rickert claimed there is a realm of

values possessing a transcendent reality but not actually existing; that the subject

recognizes them but does not create them.181 The Baden school too rejected

psychologism as the basis of philosophy.182

There is a close affinity in Frege’s views regarding the normative

character of logical laws to both Windelband’s philosophy of value and Rickert's

philosophy of the transcendent character of values. This is most evident in Frege’s

notion regarding the indefinability of truth, the normative nature of logical laws, and

transcendent nature of the thoughts in the “third realm’’ described by Frege is his essay

“Thoughts.’’ This reveals the affinity of Frege's views with views held by notable Neo-

Kantian contemporaries.

The Marburg and Baden schools were likely sources of influence on

Frege. Though there is no evidence in Frege's own writings as to his formal association

with any o f these schools, Frege was personally familiar with several important figures of

the Marburg school and the Baden school. His review of Cohen’s book is just one point

that shows his familiarity with the Marburg school. Liebmann, with whom Frege was

closely associated, was affiliated with both the Marburg and Baden schools. Liebmann,

who was eulogized by Windelband in 1912, as “the truest of the Kantians”,183 was linked

closely to Frege. Kuno Fischer who spent 16 years as a professor at Jena was closely

associated with Frege, and later went to Baden where Windelband was one of his

181 Ibid. 182 Abbagnano, idem.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 students.184 Neo-Kantian ideais were pervasive in Germany during the period from about

1870 until 1920; and there is ample evidence in his writings of Kantian presuppositions

shaping his outlook on epistemology and mathematics. That Frege is not personally

associated with one of these schools shows only that he was not a Kantian scholar; his

main interests were in mathematics, and Neo-Kantianism only provided the philosophical

framework from within which he positioned himself as a philosopher and mathematician.

In contrast to the historical situation and developments that I have

outlined, Dummett has argued that in the state-controlled universities in Germany

Hegelianism was still prevalent in the mid- to late-nineteenth century.185 He later

amended this to “idealism, in one form or another, post-Kantian or Neo-Kantian, did

dominate German philosophy, at least as practiced by professional academic

philosophers, throughout the century."186 What remained of the Hegelian form of idealism

in Germany in the last half of the nineteenth century was "a watered-down version of

Hegelianism."187 In fact, contrary to what Dummett maintains, by the turn of the century

Neo-Kantianism was a powerful philosophical movement in Germany. Neo-Kantianism

was first and foremost an academic movement; its genesis is traceable to the evolution

of German academic philosophy from about 1848.168 Neo-Kantianism began with Otto

Liebmann and ended with Ernst Cassier, who was the last Marburgian, and with Bruno

Bauch, an associate of Frege and the last Heidelbergian.189 It became the ‘School

Philosophy’, or Schulphilosophie. Most the chairs of philosophy were held by professors

183 Willey, 82. 184 Willey, 63. 185 Dummett, Frege: Philosophy of Language, first edition, p. 683 188 Dummett, The Interpretation of Frege's Philosophy, 500. 187 Passmore, A Hundred Years of Philosophy. 188 Kdhnke, 7. 189 Lewis White Beck, “Forward” in KOhnke, Klaus Christian, The Rise of Neo-Kantianism (Cambridge: Cambridge University Press, 1991).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 who were in some degree representatives of the movement.190 The University of Jena,

which Frege attended, was a stronghold of Neo-Kantianism, as was the University of

GQttingen.

Neo-Hegelianism

Neo-Hegelianism was an idealistic movement originating in Britain in the

late-nineteenth century in reaction to the excesses of empiricism. Russell and Moore

are noted for their revolt against the Neo-Hegelianism of Bradley, McTaggart and

Bosanquet. There is a tendency among analytic philosophers to see Frege, as an ally of

Russell and Moore in the overthrow of Neo-Hegelianism. Frege is often therefore

viewed as a realist combating the excesses of idealism. Dummett, for example, called

Frege "a realist in revolt against the prevailing idealism of his day."191 It is clear from the

context that Dummett had the Hegelian form of idealism in mind when he made this

statement. This gaff by Dummett is illustrative of how Dummett has read the historical

evidence in a zealous effort to support the aims of modem problems in analytic

philosophy. The historical facts show, however, that Hegelian idealism was dead in

Germany by the end of the nineteenth century. Neo-Hegelianism was emerging in

England at the same time, about 1865192, when Hegelian idealism had mostly died out in

Germany, and was being replaced by Neo-Kantianism. Sluga rightly challenged

Dummett’s error.193 Dummett later recanted his claim of Frege's opposition to

190 Copleston, 361. 191 Dummett, Frege: Philosophy of Language, 197. 192 Passmore, A Hundred Years of Philosophy, 49. According to Passmore, the philosophy of Hegel was first presented to Great Britain in a relatively intelligible form in J.H. Stirling's The Secret of Hegel (1865). This was followed by Wallace’s The Logic of Hegel (1874) and Caird's Hegel {1883). 193 Sluga, “Frege as Rationalist" in Studies in Frege, ed., Schim (Stuttgart-Bad Cannstatt: Frommann, 1976), 27.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hegelianism.194 Dummett nevertheless maintains that Frege was a realist, and was

opposed to all manifestations of idealism. In order to avoid mistakes such as this one by

Dummett, Frege’s thought must be viewed within the context of historical developments,

not later twentieth century philosophical disputes. This illustrates an attempt of a

modem analytical philosopher to reconstruct Frege to meet modem philosophical

objectives.

The evidence suggests Frege's influence by both idealism through Lotze,

and by Neo-Kantianism through his other contemporaries. This view is consistent with

the intellectual climate that existed in late nineteenth century Germany, rather than that

which existed in Britain at the turn of the century.

Movement Toward Objectivity

Just as the rise of naturalism and natural sciences brought with it a

rejection of the irrationalism of speculative idealist philosophy in Germany, it brought

with it a renewed search for truth and objectivity. The dissatisfaction with naturalism and

the excesses of speculative absolute idealism resulted in the development of a new

philosophical discipline of Erkenntnistheorie, i.e. epistemology, in the mid-nineteenth

century.195 The term epistemology, theory of knowledge, came into English usage

about 1856.196 The movement sought to distinguish explicitly and consistently that facts

are merely recognized by the mind, and not made by the mind.197 While the main

tendency throughout the nineteenth century was towards the conclusion that things, and

facts about things are dependent on the operations of the mind. Epistemology grew out

m Dummett, Frege: Philosophy of Language, xxiii. See also Dummett, The Interpretation of Frege, 497. 195 Hacking, Ian, Why Does Language Matter to Philosophy? Cambridge: Cambridge University Press, 1975),165. 196 Webster’s Ninth New Collegiate Dictionary, Merriam-Webster 78

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the need to distinguish between the subjectivity and objectivity of claims to

knowledge. Epistemology is neither concerned with the fact that people hold different

views, nor with the reasons why they came to hold such views. These are the concerns

of psychology. Epistemology grew out of the interest in establishing why people are

justified in claiming knowledge of some whole class of truths, and thus whether objective

knowledge was in fact possible at ail. The new discipline developed out of Neo-Kantian

attempts to secure the scientific objectivity of claims to knowledge of objects of

experience and to declare theoretical knowledge of what transcended experience to be

impossible.198 The objectivity of knowledge is of central interest among philosophers

within several of the Neo-Kantian schools, particularly the Marburg and Baden Schools.

It is evident also in the philosophy of Lotze.

The objectivity movement was a theme of major philosophical importance

by the end of the nineteenth century. Due to the connection of this movement with the

development of epistemology as a philosophical discipline, it is not surprising, given

Frege's interest in objectivity and his rejection of psychologism, that he would be

interested in epistemology. Frege’s concern with the objectivity and justification of

claims to knowledge links him with Neo-Kantians of similar interests. Mathematics

became of increasing importance in science in order to meet the demands for scientific

objectivity. Frege’s work in the foundations of mathematics is directly concerned with

justifications of claims to mathematical knowledge and the objectivity of mathematical

knowledge. Frege’s interest in the foundations of mathematics was an epistemoiogical

enterprise. His motivations are consistent with the general aims of other scientists and

philosophers in the nineteenth century who understood the importance of objectivity.

197 Passmore, A Hundred Years of Philosophy, 175. 79

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Lotze’s philosophy provided an alternative systematic account of the

objectivity in opposition to the psychologism that many considered rampant during the

nineteenth century in Germany. He reformulated the original Kantian outlook in his

Logik, and separated psychologism out of the act of thinking from the content of thought;

thinking is considered to be temporal and the content of thought, which is atemporal, has

validity.199 In his book Gottlob Frege, Sluga points to the probable influence on Frege of

Lotze’s notion of objective validity, and the general importance of the movement toward

objectivity in mathematics and the natural sciences.

The movement toward objectivity culminates by the end of the nineteenth

century in the redefinition of ‘psychical’ or ‘mental’ states. The Cartesian doctrine that

our knowledge of the mental is direct and certain underlies the redefinition. The

subjective idea became the ’act’, and the objective idea became the ’content.' The ‘act’

is the manner in which a mind is related to an object, and an object is that which the

mind has before it as the 'content' of a mental act. These distinctions are looked upon,

from the perspective of twentieth-century analytic philosophy, as a break with the

Descartes-Locke tradition; that is to say, the traditional view that mental or psychical

states refer to subjective ideas. This act-content distinction provides the framework for

an epistemological separation of psychological and logical notions. Avowed anti-

psychologistic philosophers, such as Frege, and the Husserl following his conversion

subsequent to Frege's criticism, and numerous other philosophers from the mid

nineteenth to the early twentieth century, made this distinction in order to separate the

subjective from the objective contents of thought.

198 Beck, “Forward” in Kflhnke, ibid., xi. 199 Beck, “Forward." 80

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The objectivity of knowledge is of central importance in the Austrian

School of Franz Brentano, who first made the ‘act’ and ‘content’ distinctions explicit in

Psychology from an empirical standpoint published in 1874. Brentano further

distinguished two fundamental classes of mental phenomena: 'presentations’ and

‘judgments’.200 These distinctions correspond exactly to Frege’s distinctions between ‘a

content that can become a judgment’ and a ‘judgment’.201 For Brentano, like Frege,

every object which can be judged enters into consciousness in two ways: first as an

object of presentation, and second as an object of affirmation or denial. Presentations

and judgments differ in only one of two ways: in difference of ‘content’, i.e. a difference

between the objects to which presentation and judgment refer, or to a difference in the

fullness with which they have the same content.202 There is similarity in Frege’s use the

term ‘mode of presentation’, and his explication that “in judgment something is affirmed

or denied”.203

The central thesis in Brentano’s Psychology from an Empirical

Standpoint204 is that “every mental phenomenon is characterized by what the Scholastics

of the Middle Ages called the intentional (or mental) inexistence of an object.” According

to Brentano, “This intentional in-existence is characteristic of mental phenomena. No

physical phenomena exhibit anything like it. We can, therefore, define mental

phenomena by saying that they are those phenomena which contain an object

intentionally within themselves."205 And, “Further we have found that the intentional in

existence, the reference to something as an object, is a distinguishing characteristic of

200 Brentano, Psychology from an Empirical Standpoint (London: Routledge, 1995), 201ff. 201 Frege, Begriffsschrift, 12. 202 Brentano, 202. 203 Brentano, 88. 204 Brentano, 88. 205 Brentano, 89. 81

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. all mental phenomena.”206 Brentano did not use the term ‘intentionality’, but later

philosophers applied it to Brentano's ‘intentional in-existence’.

Brentano held a view remarkably similar to Frege’s ‘context principle’ in

respect to the linguistic practice of the ascription of truth to the existence of abstract

things:

I answer that this is explained by the fact that not every word in our language taken by itself means something. Many of them signify something only in combination with others.207

Brentano, like Frege, distinguishes abstract mathematical entities from phenomenally

existing objects: "language makes use of many fictions for the sake of brevity; in

mathematics, for example we speak of negative quantities less than zero, of fractions of

one, of irrational and imaginary numbers, and the like, which are treated exactly like

numbers in the strict and proper sense."206 Brentano’s technical term ‘fictions’ is not

meant to imply that mathematical entities are not meaningful; it rather points up the

characteristic that such entities are not phenomenal. There is no indication that Frege

studied Brentano. However, Frege held a theory of intentionality similar to Brentano’s

that is most evident in the essay “Thoughts". Frege's technical terms ‘thought’ and

‘sense’, as that which the mind aims, closely resembles Brentano’s ‘intentional in

existence'. Frege does not describe objects or contents as instantiations of the mind.

Frege insists that logical objects are objective and, as such, are not mental. But Frege’s

technical terms ‘sense’ and ‘thought’ play a wholly ‘intentional’ role in his theory of

reference. Brentano makes frequent references to Lotze’s metaphysical views in

206 Brentano, 97. 207 Brentano, “On Objects of Thought”, dictated on February 22,1915, in the Appendix to the 1924 edition of Psychology from an Empirical Standpoint, 322. 208 Brentano, 322-3. 82

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. support of his own views. Husserl maintained throughout the three-fold distinction of

act, content and object, and credited Brentano as one of his major influences. Frege’s

views that Russell later rejected the content and object distinction shows that Frege’s

thought, in this respect, was closer to Brentano and Husserl than it was to Russell’s

mature position. The links between Lotze, Brentano, Husserl and Frege underscore the

idealist and rationalist current among philosophical schools on the continent, in contrast

to the realism of Russell and Moore existing by the end the nineteenth century and the

beginning of the twentieth century.

There are no attributions to Brentano in Frege’s writings, as there are in

Husserl's writings, but there is clear textual evidence that Frege held similar views

corresponding in many respects to Brentano’s notion of intentionality. The similarity

suggests possible influences on Frege's thought. Brentano’s philosophical views

regarding psychology were widely known during the last quarter of the nineteenth

century in German and Austrian universities. Frege is known to have corresponded with

at least three of Brentano’s students, Anton Marty, Carl Stumpf and Edmund Husserl.

Marty and Stumpf were close colleagues at Prague in 1882.209 Marty, Stump and

Husserl studied under Lotze. Stumpf obtained his doctorate at GiJttingen under Lotze210,

under whom Frege also studied. Husserl’s Philosophy of Arithmetic, which was

criticized by Frege for its psychologism, examined Frege’s ideas from Brentano’s

empirical standpoint.211 Thus, though he does not mention Brentano in his own writing,

Frege must have been aware of Brentano’s philosophically psychological standpoint

since Frege read and critiqued Husserl’s Philosophy of Arithmetic (1891).

209 Frege, Philosophical and Mathematical Correspondence, 99. 210 Ibid., 171. 211 Hill, Word and Object in Husserl, Frege, and Russell: The Roots of Twentieth Century Philosophy{Athens: Ohio University Press, 1991), 3. 83

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Husserl was a student of Brentano, as was Alexius Meinong, and Stumpf.

Husserl, Brentano, Meinong, Marty and Stumpf are often referred to as the Austrian

school.212 Frege is known to have corresponded with Marty and Stumpf.213 Stumpfs

letter to Frege of September 9,1892 refers to Brentano. Russell studied Brentano, and

initially accepted Brentano’s distinction between act, content and object, but later

rejected the distinction between content and object.214 Russell also studied Alexius

Meinong, a student of Brentano, for whom he had had a great deal of respect.215 It is my

contention that there are significant, albeit little noted and misunderstood, connections

between Brentano, Meinong, Husserl, and Frege, and Russell in respect to their mutual

concerns with the objectivity of thought and the validity of knowledge. The connections

between Brentano, Meinong, and Husserl are close despite Frege’s avowed anti

psychologism. The charge of psychologism was vigorously denied by all of them. That

Frege was openly opposed to psychologism does not him necessarily make him an anti-

psychologistic philosopher.

Brentano held an intuitionist theory of mathematical truth validated by

self-evident experiences which is a modem variation of Descartes general theory of

truth.218 For intuitionists, every true mathematical statement is justifiable by a

construction. This is a self-evident experience, not external perception.217 in order for

self-evident experience to validate scientific, i.e. public knowledge, it must be

212 Copleston, 431. 213 Frege, Philosophical and Mathematical Correspondence, 99 and 171. 214 Russell, My Philosophical Development, (London: Unwin Hyman), 100. 215 Ibid., 64. 218 KOmer, The Philosophy of Mathematics, (London: Hutchinson & Co., 1960),136. 217 Ibid. 84

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. intersubjective.218 Intersubjectivity is the means by which each individual possesses

common understanding of universal notions.

Brentano was criticized for his extreme psychologistic tendencies.

However, that is a charge he vehemently denied.219 I maintain the psychologistic

tendencies in Brentano’s thought are no more severe than Frege’s own notion of the

grasping of sense. Despite Frege's avowed anti-psychologism, his thought must be

seen in close relation to Brentano within the movement toward objectivity, and

interpreted in light of its similarities with Brentano’s distinctions of act, content, object,

and his theory of judgment.

Moreover, I maintain that Frege’s philosophical standpoint was

psychologistic in important respects. This was a characteristic of his thought, which has

largely gone unnoticed by most contemporary interpreters. The fact that Frege was

avowedly anti-psychologistic and viewed by most analytic philosophers as the archetype

of anti-psychologism has obscured his close connections with Brentano, Husserl, and

other Continental philosophers, especially neo-Kantians, with similar interests in

accounting for the objective validity of human knowledge.

There is clear textual evidence for the notion of ‘intentionality’ used by

Frege in the same sense as used by Brentano, though he does not use Brentano’s

technical term for it, in Frege’s essay “Thoughts", where he says, for example:

Obviously we could not call a picture true unless there were an intention involved. A picture is meant to represent something. (Even an idea is not called true in itself, but only with respect to an intention that the idea should correspond to something.)220

218 Ibid. 219 Brentano, 306. 220 Frege, “Thoughts” in Collected Papers, 252. 85

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The italics are mine, but Frege’s meaning is clear. Later, in the same essay,

where he explains how ideas are distinct from things of the outer world, Frege

says:

Fourthly: every idea has only one owner; no two men have the same idea. For otherwise it would exist independently of this man and independently of that man. Is that lime-tree my idea? By using the expression ’that lime- tree’ in this question I am really already anticipating the answer, for I mean to use this expression to designate what I see and other people too can look at and touch. There are now two possibilities. If my intention is realized, if I do designate something with the expression 'that lime-tree’, then the thought expressed in the sentence That lime-tree is my idea’ must obviously be denied. But if my intention is not realized, if I only think I see without really seeing, if on that account the designation ‘that lime- tree’ is empty, then I have wondered into the realm of fiction without knowing or meaning to. In that case neither the content of the sentence That lime-tree is my idea’ nor the content of the sentence That lime-tree is not my idea’ is true, for in both cases I have a predication which lacks an object.221

Again, my italics, but clearly the notion of intentionality is deeply imbedded in

Frege’s theory of reference. Without intention there can be no designation of

anything as the content of a sentence. Frege is even more explicit, in the same

essay, where he says: “Although the thought does not belong with the contents

of the thinker’s consciousness, there must be something in his consciousness

that is aimed “ at the thought."223

Thoughts, though they are supposed to be objective, for Frege, depend upon the

consciousness of the intending subject. Frege tries to avoid psychologism by

placing thoughts in an objective realm, but they ultimately depend upon the

rationality of the subject.

221 Frege, “Thoughts", 361-2. 222 My italics. 223 Thoughts" in Collected Papers, 369. 86

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The Mathematical Setting

The movement toward objectivity in closely tied to mathematics. Truth in

scientific knowledge was seen more and more as dependent upon the objective

certainty of mathematics and geometry. The search for greater objectivity in science,

particularly the physical sciences, resulted in the development of a new philosophical

discipline of the theory of knowledge, or epistemology.

The movement toward objectivity within mathematics, was stimulated, in

part, by the discovery of non-Euclidean geometries which called into question the

philosophical grounding of mathematical knowledge, in part, by the theoretical demands

of mathematical analysis.

The paradigm of mathematical and scientific knowledge for 2000 years

was Euclidean geometry. The distinctive features of Euclidean geometry is that

geometrical laws are formulated in universal form, the wording of the laws is rigorous

and absolute, and the entire system of Euclidean geometry consists of deductive, or

logical, proofs. Deductive proofs are to be distinguished from inductive inferences.

These terms are closely related to the distinction between a priori and a posteriori

knowledge. A deductive proof is a chain of reasoning that succeeds in establishing a

conclusion by demonstrating deductively, or logically, from premises that are known to

be true a priori. An inductive inference conjectures a general conclusion that goes

beyond the known empirical, or a posteriori, data.

The premises of Euclidean geometry are comprised of axioms, postulates

and definitions. The axioms are regarded as “common notions” applicable to any

science. Euclid’s five basic axioms are:

1. Things which are equal to the same thing are also equal to one another. 87

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another. 5. The whole is greater than the part.224

In addition to axioms, Euclidean geometry uses postulates. The basic difference

between the axioms and the postulates is that the postulates are particular to the given

subject matter of geometry, and the axioms are more general propositions whose

application is broader than geometry. Euclidean postulates consist of the following:

1. A straight line can be drawn from any point to any other point. 2. Any finite straight line can be extended continuously in a straight line. 3. Given any point and any distance, a circle can be drawn with that point as its center and that distance as its radius. 4. All angles are equal to one anther. 5. If a straight line falling on two straight lines make the interior on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than two right angles.225

In order to clearly and adequately fix the meaning of each term used, the Euclidean

method requires that each term is defined before being used in any proof. Euclid gives

the definitions at the beginning of Book I of the Elements, of which the following are

representative:

1. A point is that which has no part. 2. A line is breadthless length. 3. The extremities of a line are points. 4. A straight line is a line, which lies evenly with the points on itself. 5. A surface is that which has length and breadth only. 6. A plane surface is a surface, which lies evenly with the straight lines on itself. 7. A plane angle is the inclination to one anther of two lines in a plane that meet one another and do not lie in a straight line. 8. When a straight line set up on anther straight line makes the adjacent angles equal to one anther, each of the equal angles is called right, and the straight line standing on the other is called perpendicular toit. 9. A figure is that which is contained by any boundary or boundaries.

224 Euclid, The Elements, trans. Health, 2n ed. (Cambridge: Cambridge University Press, 1925; reprint. New York: Dover, 1956), 155. 225 Ibid, 154-5. 88

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10. A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another. 11. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.228

The Euclidean axioms, postulates and definitions are the starting points of proofs in first

plane, and then solid geometry. Ultimately, all geometric knowledge is demonstrated

deductively from basic assumptions, consisting only of the specified axioms, postulates

and definitions. The aim of Euclid’s axiomatization of geometry was to strengthen proofs

and facilitate the proof of new laws. The resulting organization is elegant and logically

perspicuous.

Euclidean geometry was the paradigm of mathematical knowledge for

more than two thousand years. The discovery of non-Euclidean geometries called into

question the reliability of claims to knowledge involving geometrical proofs based on

pure intuition. This was seen as a crisis for geometrical knowledge. It was also a crisis

for the objectivity of arithmetical knowledge and the sciences in general which in turn

owed their objectivity to the certainty of pure intuition. If the certainty of Euclidean

geometry, which was based on pure intuition, was called into question, then how could

arithmetical and scientific knowledge be secured?

The axioms adopted by Euclid were supposed to be self-evident truths

about the physical world. However, one of Euclid’s axioms, the parallel axiom, was

neither provable nor self-evident. Simply put, the parallel axiom states that: two lines will

meet on that side of a transversal where the sum of the interior angles is less than two

right angles.227 Though no one really doubted its truth, it was not clearly self-evident as

228 Ibid, 153-4. 227 Kline, Mathematical Thought from Ancient to Modem Times, vol. i, ii, and iii (Oxford: Oxford University Press, 1972), 861-81. 89

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. were the other axioms. There is some question whether Euclid himself considered the

parallel axiom self-evident, as he proved as many theorems as he could without it.

Suspicions regarding the parallel axiom have concerned philosophers for centuries.

The history of non-Euclidean geometry starts with efforts to prove the

parallel axiom by Rolemy and Proclus in the fifth century by deducing it from some or all

of the other nine Euclidean axioms that were regarded as unquestionably self-evident.

Another route taken was to replace the parallel axiom by a more self-evident axiom.

Ptolemy and Proclus were followed by many, including the efforts of Nasir-Eddin (1201 -

74), Wallis (1693), Fenn (1769), Legendre (1752-1830), and Saccheri (1667-1733).228

Klugel (1739-1812) and Lambert were the first to recognize the possibility of alternative

geometries.229 Gauss (1777-1855), a German mathematician at Gottingen, became the

first to be convinced that the parallel axiom could not be deduced from the remaining

Euclidean axioms in 1799, and by 1813 had developed what he first called anti-

Euclidean geometry, then astral geometry, and later non-Euclidean geometry.230 Gauss

never published his results that became known only through his unpublished work and

correspondence with Bolai and others. Bolai (1802-1860), a Hungarian, and

Lobatchevsky (1793-1856), a Russian, are generally credited with publishing the first

organized accounts of non-Euclidean geometry between 1829 and 1833.231 Gauss’s

notes and correspondence on non-Euclidean geometry were first published in 1855 after

his death. Bolai’s and Lobatchevsky's work did not become widely known until 1866-

6 7 232 This was about the time Frege began his university education. The creation of

228 Kline, ibid. 229 Kline, ibid. 230 Kline, ibid. 231 Kline, ibid. 232 Kline, ibid. 90

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. non-Euclidean geometry was the most consequential event in mathematics since the

development of Euclidean geometry in ancient Greece.

The realization that the parallel axiom could not be proved from the other

axioms showed that it was independent of the other axioms. This meant that other

axioms, contradictory to the parallel axiom, could be adopted, i.e. assumed or

postulated, in its place. Non-Euclidean geometries are all the result of postulating

different axioms in place of the Euclidean parallel axiom to create entirely new

geometries; the assumed axioms are known as parallel postulates.

Kant had sought to place geometrical, mathematical and scientific

knowledge on a firm foundation in the Critique of Pure Reason. For Kant, scientific

knowledge meant Newtonian physics. All human knowledge could be categorized into

just three kinds of judgments: analytic a priori, synthetic a priori, and synthetic a

posteriori judgments. Judgments involving knowledge claims of geometry, arithmetic

and the laws of nature (Newtonian physics) were held by Kant to be synthetic a priori

judgments. According to Kant, knowledge of spatial relations is guaranteed by pure

intuition of the Euclidean structure of space. All geometric proofs in mathematics are

therefore Euclidean. The a priori status of Euclidean geometry meant that all

geometrical knowledge secured by pure intuition could be relied upon as certain

knowledge.

The discovery of non-Euclidean geometry and the fact that non-Euclidean

geometries were consistent relative to Euclidean geometry were great blows to Kant’s

theory of geometrical knowledge. The existence of non-Euclidean geometries seemed

to show that we do not after all possess a priori knowledge of space. This implies that

geometrical knowledge must be a posteriori. This realization placed geometry on the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. same level as mechanics. Since geometrical knowledge could no longer be relied upon

as intuitively certain, such knowledge must then consist of only inductively valid truths,

instead of deductively valid truths. Hence, with the advent of non-Euclidean geometries,

geometrical knowledge no longer enjoyed the status of certainty that it had formerly

possessed for more than two thousand years.

Now, it is significant for an understanding of Frege’s thought that he never

disputed Kant’s views concerning geometrical knowledge. Instead, Frege says:

. . . I consider Kant did a great service in drawing the distinction between synthetic and analytic judgements. In calling the truths of geometry synthetic and a priori, he revealed their true nature. And this is still worth repeating for even to-day it is often not recognized.233

It is Frege’s view that Kant was correct in stating the synthetic a priori nature of

geometrical knowledge. Frege was well aware of the existence of non-Euclidean

geometry. Reimann was the teacher of one of Frege’s own teachers, Ernst Abbe.234

However, in an article he wrote between 1899 and 1906, Frege held that only one

geometry could possible be true. He says:

No man can serve two masters. One cannot serve both truth and untruth. If Euclidean geometry is true, then non-Euclidean geometry is false, and if non-Euclidean geometry is true, then Euclidean geometry is false... Whoever, acknowledges Euclidean geometry to be true must reject non- Euclidean geometry as false, and whoever, acknowledges non-Euclidean geometry to be true must reject Euclidean geometry.235

Frege clearly did not accept the modem hypothetical approach to non-Euclidean

geometry. This distinguishes Frege’s philosophical views from those of Hilbert. It is

probable that Hilbert was motivated by advent of non-Euclidean geometry to develop

formally consistent and logical deductive axiomatization of geometry from axioms that

233 Frege, Foundations of Arithmetic, 101-2. 234 Sluga, Gottlob Frege, 46. 235 Frege, “On Euclidean Geometry" in Posthumous Writings, 169. 92

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. were derived from explicit definitions. That such a project did not interest Frege shows

that he (Frege) was satisfied that geometry was based on intuitive axioms. Frege

believed the choice between the Euclidean and non-Euclidean geometry was a matter of

the truth or falsity of the axioms. According to Frege, if we are to accept Euclidean

geometry as true, then “non-Euclidean geometry will have to be counted amongst the

pseudo-sciences."236 Despite the evidence showing the relative consistency of non-

Euclidean geometries, Frege held fast to the Kantian view that humans are possessed of

pure intuitions of Euclidean space that must be characterized as true. This confirms

Frege’s epistemological standpoint stemming from Kant.

Mathematicians knew several non-Euclidean geometries by the 1870s.

The hyperbolic geometry of Lobatchevsky and the elliptic geometry of Reimann were by

then well known.237 Though geometry had lost the status of certainty that it had once

enjoyed, the consistency of Euclidean geometry remained unquestioned by

mathematicians. It was the view of most mathematicians, including Gauss, Bolyai,

Lobatchevsky, and Riemann, that Euclidean geometry was the necessary geometry of

the physical world. It was not conceivable that the geometry of our perception of the

physical world could be contradictory.238

The discovery of non-Euclidean geometries meant that truth and certainty

in mathematical knowledge must rest, not with the geometrical intuition, but rather upon

the logical source of knowledge underlying arithmetical proofs. The logical source of

knowledge was considered by Frege to be reason, or self-evidence. The rejection

intuition as the warrant of truth for arithmetic meant also the rejection of notions closely

related to intuition, such as empirical generalizations, formalized symbolism or

236 Frege, ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. psychological factors. Hence, Frege rejected all of these intuitive notions in the

Foundations of Arithmetic.

By the early eighteenth century and continuing into the late nineteenth

century mathematicians had been concerned about the looseness in the concepts and

proofs of the various branches of analysis.239 The concept of a mathematical knowledge

was not yet clear. Many theorems of analysis had not been demonstrated in a purely

logical manner. Many proofs of mathematics had relied upon intuitive or geometric

methods of demonstration. Since the geometric methods of Euclidean geometry had

been around for two thousand years, it had been assumed during the eighteenth century

and earlier that analysis could be grounded in geometry. But some mathematicians

began to become concerned about the rigor of mathematical concepts and the rigor of

mathematical proofs in the first half of the eighteenth century. The beginnings of this

movement coincide with the discovery of non-Euclidean geometries. Gauss seems to

be the first to express doubts as to the truth of Euclidean geometry, and his early work

disclosed other flaws in Euclid's axiomatic development. These two factors caused

many mathematicians to distrust geometry and look to arithmetic to ground analysis.

Rigorous analysis, and the effort to ground analysis on arithmetic began

with the work of Bolzano, Cauchy, Abel and Dirichlet, and culminating in the work of

Weierstrass, and his followers.240 The project became known as the arithmetization of

analysis established the real number system as the foundation for the whole of classical

analysis. Their work freed the calculus and its extensions from all dependence upon

237 Kline, 913. 238 Kline, 914. 239 Kline, 947. 240 Kline, 948. 94

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. geometrical, kinetic and intuitive notions.241 If analysis is to be grounded in the real

number system, it is desirable that the real number system be developed in a logical

fashion, without reliance on the intrusion of any form of intuition, whether from sense

perception, or pure intuition as Kant had supposed. The consistency of the real number

system itself could be secured by the consistency of a more basic postulate set for the

simpler system of natural numbers. The natural number system possesses an intuitive

simplicity due to its being handled over a long period of time without producing any

known inner contradictions. Thus, if the natural number system could be established on

purely logical grounds, then by definitions in terms of natural numbers242, the set of all

integers could also be established.243 In the same way, the set of all rational numbers244,

and finally the set of real numbers245 could be established. The project of establishing

the logical foundation for the natural number system was eventually carried out through

the work of Cantor, Dedekind, Frege and Peano.

Frege was educated as a mathematician. He believed that the concepts

of mathematics could be reduced to logical concepts. In studying the concept of

number, he encountered a difficulty in providing a logical analysis of the notion of

mathematical sequence. His investigation of this question led him to develop a new

mode of logical expression in order to avoid the impression and ambiguity of ordinary

language. He called the new mode of logical expression “Begriffsschrift”, which may be

literally translated into English as “Conceptual Notation." The results of his investigation

241 Kline 972 242 Natural numbers, df: N=1,2,3..., n. 243 Integers, df: Z=-n.... -3,-2,-1,0,+1 ,+2,+3,...+n. 244 Rational numbers, R=the set of fractions of the form: p/q where p and q are integers, and p is not divisible by 0. 245 Real numbers, df: R= set of rational and irrational numbers. 95

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. were published in 1879 in the work whose complete title was Begriffsschrift, a formula

language, modeled upon that of arithmetic, for pure thought.

Frege developed the Concept Notation to provide a perspicuous method

of proof that was intended initially to demonstrate a logical analysis of mathematical

sequence. However, he foresaw its application in demonstrating the validity of proofs of

differential and integral calculus.248 He claimed the formula language could also be

extended to geometry, kinetics, mechanics and physics.247 According to Frege, “The

latter two fields, in which besides rational necessity empirical necessity assets itself, are

the first for which we can predict a further development of the notation as knowledge

progresses."248 In a lecture Frege delivered before the Jenaische Gesellschaft fQr

Medicin und Naturwissenschaft (Jena Society of Medicine and Natural Science) in 1979,

he demonstrated application of the Conceptual Notation to geometrical relations.249

Frege claimed his formula language of Begriffsschrift could be used to

produce superior proofs in mathematics. He believed the method of proof then used by

mathematicians was deficit. In the Preface to Begriffsschrift250, Frege maintains there

are two ways of providing a proof. The first way, lacking the high degree of certitude

and rigor that must necessarily be demanded of a science of mathematics, involves

“apprehending a scientific truth” perhaps “conjectured on the basis of an insufficient

number of particular cases", or may be “seen to be a consequence of propositions

already established”, and may be “answered differently for different persons.” This is the

246 Frege, Begriffsschrift, in Frege to Gddel: A Source Book in Mathematical Logic, 1879-1931. Ed J. van Heijenoort (Cambridge: Harvard University Press, 1967), 7. 247 Ibid. 248 Ibid. 249 Frege, “Applications of the ‘Conceptual Notation’" in Conceptual Notation and Related Articles, trans. and ed. By Bynum (Oxford: Clarendon, 1972). 250 Begriffsschrift, in van Heijenoort, 5. 96

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. traditional method of proof practiced by mathematicians that is deficient by Frege's

standards.

The second way, is “more definite" and “it is connected with the inner

nature of the proposition considered”. Thus, for Frege, “the most reliable way of carrying

out a proof, obviously, is to follow pure logic, a way that, disregarding the particular

characteristics of objects, depends solely on those laws upon which all knowledge

rests."

The most obvious example of a traditional method of proof is the public

arrangement of symbols produced by mathematicians in the past or present.

Arrangements of symbols, and the rules for manipulation of the symbols, are relied upon

by other mathematicians. Such symbols stand in a relationship to what may be termed

‘ideal’ proofs. However, it is not easy to characterize that relationship. That is the target

of Frege’s criticism of the accuracy of proofs then current among mathematicians.

Frege proposes a method of proof that is characteristically deductive in its

concentration on the centrality of proof. It emphases the form and meaning of logical

statements. Although his method is deductive, it is nevertheless traditional. He

proposes to distinguish proofs by the kind of knowledge that secures them.

Accordingly, we divide all truths that require justification into two kinds, those for which the proof can be earned out purely by means of logic and those for which it must be supported by facts of experience. But that a proposition is of the first kind is surely compatible with the fact that it could nevertheless not have come to consciousness in a human mind without any activity of the senses. (Sense without sensory experiences no mental development is possible in the beings known to us, that holds for all judgments.) Hence it is not the psychological genesis but the best method of proof that is at the basis of the classification. Now, when I cam to consider the question to which of these two kinds the judgements of arithmetic belong, I first had to ascertain how far one could proceed in arithmetic by means of inferences alone, with the sole support of those laws of thought that transcend all particulars. My initial step was to attempt to reduce the concept of ordering in a sequence to that of logical 97

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. consequence, so as to proceed from there to the concept of number. To prevent anything intuitive from penetrating here unnoticed, I had to bend every effort to keep the chain of inferences free of gaps. In attempting to comply with this requirement in the strictest possible way I found the inadequacy of language to be an obstacle; no matter how unwieldy the expressions I was ready to accept, I was less and less able, as the relations became more and more complex, to attain the precision that my purpose required. This deficiency led me to the idea of the present ideography. Its first purpose, therefore, is to provided us with the most reliable test of the validity of a chain of inferences and to point out every presupposition that tries to sneak in unnoticed, so that its origin can be investigated.251

Several years after Begriffsschrift, in the Foundations of Arithmetic, published in 1884,

Frege puts the entire rigorization of analysis movement into historical perspective.

Starting with the concepts of function, continuity, and limit, the movement led eventually

to closer examination of negative and irrational numbers, and concluding ultimately with

the analysis of the concept of number itself. Frege claims;

The concepts of function, of continuity, of limit and of infinity have been shown to stand in need of sharper definition. Negative and irrational numbers, which had long since been admitted into science, have had to submit to a closer scrutiny of their credentials.

In all directions these same ideals can be seen at work - rigour of proof, precise delimitation of extent of validity, and as a means to this, sharp definition of concepts.

Proceeding along these lines, we are bound eventually to the concept of number and to the simplest propositions holding positive whole numbers, which form the foundation of the whole of arithmetic.252

Frege published the Foundations of Arithmetic in 1884. Dedekind

published his The Nature and Meaning of Numbers (Was sind und was sollen die

Zahlen) in 1887. In the second edition of his book in 1893, he makes reference

to the similarity of Frege’s work to his own, and confirms that Frege’s ideas in the

Foundations of Arithmetic, in fact, preceded his own. By the time that Frege and

251 Ibid, 5-6. 98

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedekind began their investigations into the foundations of arithmetic, it must

have seemed to Frege and Dedekind that analysis had been successfully

reduced to the theory of natural numbers.253

Kitcher, in the Nature of Mathematical Knowledge, challenged this

view of the history of analysis. Kitcher claims that Frege’s work on the concept of

number ought not to be viewed as being of central interest to mathematicians in

the late Nineteenth century. According to Kitcher, Frege's work was not in the

mainstream at all; mathematicians were not generally interested in theoretical

issues concerning the concept of number. Instead, they were concerned more

with the practical applications of mathematics. Thus, Frege ought to viewed as

isolated from the mainstream, which explains his relative obscurity among other

mathematicians.

Whatever we may think of their place among other

mathematicians, of central urgency for Frege and Dedekind was a method of

determining of the logical nature of numbers and a logical account of

mathematical induction. The details of their respective approaches may differ,

but they both viewed their investigation as an attempt to erect a new foundation

for arithmetic based on a logical definition of natural numbers. Their search for

the nature of natural numbers is an epistemological quest.

Despite the seeming similarity of their views in wanting to found

mathematics on logical principles, and their independently held belief in

themselves as logicists thinkers, there is a vast dissimilarity between their

respective positions. Dedekind, in Frege's view, was a psychologists logician.

252 Frege, Foundations of Arithmetic, 1-2.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedekind, for example, wrote that the laws of thought and numbers were free

creations of the human mind. In Grundgesetze der Arithmetik (1893) I Frege

criticized Dedekind for his psychologistic views of logic and mathematics.

253 Gillies, Frege, Dedekind and Peano, and the Foundations of Arithmetic (Assen, Netherlands: Van Gorcum, 1982), 8.

100

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4

FREGE’S INTELLECTUAL DEVELOPMENT

Frege’s Enigmatic Background

Friedrich Ludwig Gottlob Frege (1848-1925) is arguably one of the most

important and influential, yet enigmatic, philosopher of the twentieth century. The lack of

biographical information about Frege's personal life and intellectual development is due to

his own reticence, as well as, to the fact that his importance was not appreciated until long

after his death. Many of his original writings and correspondence, including a biography of

him by his adopted son Alfred, were destroyed in the bombing of MOnster during World War

II resulting in only fragmented sources from which to assess his views.254

There are only scant details of his personal life that we have learned from

Frege himself.255 He was bom in Wismar, Germany, in 1848, and raised a Lutheran. His

father, Alexander was the founder of school for girls. He died in 1866 before Frege began

his university education. His mother succeeded his father as principal of the school. She

supported Frege during his university education. Little is known about Frege's intellectual

development, or about those who might have influenced him, outside of a few references in

his works. There is good reason to believe the lack of information

has led to substantial misunderstandings regarding his intellectual development and actual

philosophical views.

254 “History of the Frege Nachlass" by the editors of Posthumous Writings. 255 Sluga, "Frege: the early years", 329. According to Sluga, these details are from a short biographical note appended by Frege to his Habilitationsschrift of 1874 from Kleine Schriften, ed. I. Angelelli. Hildesheim: Olms, 1967.

101

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 Much of what is known about him is second hand information handed

down through analytic philosophers beginning with Russell, Wittgenstein and Carnap.

Few philosophers took time to study Frege's thought directly, and most of his works

remained in the original German and untranslated into English until the later part of this

century when they have become more widely available to Anglo-American philosophers

in translation. This has led to misinterpretation of Frege's thought, and to a distortion of

Frege's historical place in the development of analytic philosophy.

Though his intellectual isolation is often cited, it is not a totally accurate

picture of Frege. He was an active member of several academic and mathematical

societies throughout his academic career.256 He is known to have maintained

correspondence with Couturat, Hilbert, Jourdain, Husserl, Russell, Schrader, Peano,

Wittgenstein and many others. He met Lukasiewicz, Wittgenstein, Vaiiati, and probably

many others, though much of his correspondence is no longer available to u s.257

His thoughts on logic and language directly influenced Peano, Husserl,

Russell, Wittgenstein and Carnap, and the subsequent development of analytic

philosophy. Russell came to realize that he shared with Frege a commonality of interest

in proving the logical foundations of mathematics. Wittgenstein acknowledges his debt

to Frege in the Preface to the Tractatus. Peano knew of Frege’s Begriffsschrift as early

as 1891, and wrote a review of Frege’s Grundgesetze der Arithmetik in 1893. Russell

learned of Frege through contact with Peano; and they became correspondents.

Carnap, who was perhaps Frege's most famous student from 1910-13, attributed to

258 Terrell Ward Bynum, trans. and ed., Conceptual Notation and Related Articles (Oxford: Clarendon, 1972), 6. 257 Bynum, 7. According to Bynum, there are some 25 known correspondents of Frege, including: Avenarius, Ballue, Darmstaedter, Dingier, Falchenburg, Honigswald, Huntington, Klein, Knoch, Koebner, Korselt, Lowenhein, Mayer, Pasch, Scheibe, Schlomiich, Ulrici, and Vaiiati.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 Frege his conception of the importance of “the task of logic and of mathematics within

the total system of knowledge."258

Frege’s critique of psychologism is said to have influenced the early

Husserl, and so indirectly it may be said that he had some influence in the development

of phenomenology and Continental philosophy, though it is analytic philosophy that has

been most influenced by him. There is recent evidence that Frege’s influence on

Husserl may not have been as great as once thought. Contrary to popular belief, it has

been argued by Mohanty259 that Husserl may actually have come to reject psychologism

independently of Frege's well known criticism of him,280 thus calling into question another

aspect of Frege's importance to philosophy. Nevertheless, given the significance of

Frege’s thought for the development of twentieth century philosophy in mathematical

logic and semantics, it is unfortunate that so little is known about him.

Frege earned his Ph.D. from the University of Gdttingen in 1873. Frege

was admitted to the University of Jena faculty as a Privatdozent (unpaid lecturer) in

1874. He was later elevated to the rank of Ordinary Professor. Frege's his entire

academic career was spent at the University of Jena in the mathematics department,

where he remained for 44 years, retiring in 1918. He died in 1925.

Frege devoted his entire professional career to teaching of mathematics

and logic, research into the foundations of mathematics and logic, and the writing of

essays and books on mathematical and logical topics. He published forty works during

258 Carnap, “Intellectual Autobiography" in The Philosophy of Rudolph Camap, ed. Paul Arthur Schilpp (La Salle: Open Court, 1963), 12-13. 259 Mohanty, in “Husserl and Frege: A New Look" in Readings on Edmund Husserl’s Logical Investigations, ed. J. N. Mohanty (The Hague: Martinus Nijhoff, 1977). 280 Frege, ‘ Review of Dr. Husserl’s Philosophy of Arithmetic” complete translation by E.W. Kluge in Readings on Edmund Husserl’s Logical Investigations, J. N. Mohanty (The Hague: Martinus Nijhoff, 1977), 6-21. See also the illustrative extracts of the same article by Frege, translated by P. T. Geach, in Translations from the Philosophical Writings of Gottlob Frege, 37-85.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 his lifetime, including four books, twenty-four articles, eight reviews and four comments

and remarks.261 His principal published works include: Begriffsschrift, or Concept

Notation (1879); Die Grundlagen der Arithmetik, or The Foundations of Arithmetic

(1884); "Function and Begriff", or “Function and Concept" (1891); "Ober Begriff und

Gegenstand", or "On Concept and Object" (1892); "Ober Sinn und Bedeutung", or "On

Sense and Reference" (1892; and Gmndgesetze der Arithmetik I, or The Basic Laws of

Arithmetic I (1893) and volume II (1903). Between 1918 and 1923 Frege published

three articles in the journal Beitrdge zur Philosophie des deutschen Idealismus that were

intended to be part of a larger work to be entitled Logical Investigations. Unfortunately,

the larger work was never completed. The titles of these articles and English

translations are: “Der Gedanke", or “The Thought” (1918): “Die Vemeinung", or

“Negation” (1918); and “Gedankenguge", or “Compound Thoughts" (1923). All of these

principle works, with the exception of the second volume of the Basic Laws of Arithmetic,

of which only portions have been translated, are available in English translation.

Philsophcial and Mathematical Education

There is reliable evidence of the university courses in which Frege enrolled, and some of

his personal contacts with professors and intellectual colleagues are also known. The

background developments in philosophy and mathematics during the later half of the

nineteenth century, together with university courses taken, the professors and

colleagues with whom he came in contact, are reliable indicators of probable influences

on him during his university years. Thus, an historical reconstruction of Frege's probable

intellectual development is possible despite fragmentary evidence and lack of

attributions to others by Frege himself.

281 Bynum, 7.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 After graduating from grammar school in 1869 at age 15, he spent two

semesters at the University of Jena (1869-1970) and five semesters at the University of

GOttingen (1871-1873).262 His formal studies included courses in mathematics, physics,

chemistry and philosophy. At Jena he studied philosophy with Kuno Fischer, and

mathematics with Ernst Abbe, Schaeffer and Carl Snell, and chemistry with Geuther. At

Gdttingen he studied mathematics with Clebsch, Schering and Voss, experimental

physics with Weber, and philosophy of religion with Hermann Lotze.283 Lotze, Abbe, and

Fischer where likely important influences during Frege’s formative years. Other

important figures associated with Frege were Otto Liebmann, Wilhelm Weber, and Ernst

Schering. In the article "Frege: the early years", Sluga has argued persuasively for

historical reconstruction of Frege's education, and the high probability of his influence by

Kant's philosophy, Gauss's mathematics and Lotze’s logic and applied mathematics.

Unfortunately, Frege left us very little in the way of attributions to those

who influenced his thought. We are left to conjecture about the probable influences on

his work arising from his university experiences and contacts with colleagues and

correspondents. This task is made particularly difficult because Frege did not tell us

who his actual influences were. Terrell Bynum has provided some tantalizing details

that enable us to reconstruct Frege’s probable influences in his Conceptual Notation.26*

Sluga has done more by pulling together the scant facts regarding the background and

interests of Frege's teachers.265 The particulars provided by Bynum and Sluga suggest

strong evidence for probable Neo-Kantian influence through Fischer and Abbe, and

262 Bynum, 3. 283 Bynum, 3; Sluga, "Frege; the early years", 334. 264 Bynum, ibid. 285 Sluga, Gottlob Frege.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 possible idealist influence through Hermann Lotze. There is evidence also for a prion

mathematical influences of Gauss though Weber and Schering.

Kantian Influences

The general intellectual climate prevailing in German universities at the time Frege

entered and completed his university suggests that he must have been educated in the

Kantian epistemological outlook. It would have been almost impossible for Frege to

have attended a German university in the late nineteenth century and taken courses in

philosophy and mathematics without coming under the influence of Neo-Kantian. Neo-

Kantianism was fast becoming the Schulphilosophie of German universities.268 Thus, we

need know little about Frege's actual university experiences to conjecture his probable

influence by Kantian doctrines.

Frege’s early and later writings confirm acceptance of the Kantian

epistemological outlook. Frege became a Ph.D. after presentation of his doctoral

dissertation “On a Geometrical Representation of Imaginary Figures in a Plane" at

Gfittingen in 1873. His dissertation exemplifies the Kantian outlook that informs much of

his later work. In the dissertation, which dealt with a straightforward question in

analytical geometry, Frege reveals his Kantian outlook. The first sentence of the

introduction reads:

When one considers that the whole of geometry rests ultimately on axioms which derive their validity from the nature of our faculty of intuition (Anschauungsvermdgen), the question of the meaning of imaginary figures seem to be justified, since we ascribe to them properties that commonly contradict any intuition (Anschauung).267

286 Copleston, 361. 267 Sluga, "Frege: the early years", 336. Sluga quotes this passage from Frege's dissertation: "Ober eine geometrische Darstellung der imagindren Gebilde der Ebene” ("On a Geometrical Representation of Imaginary Figures in a Plane") in K/e/ne Schiften, ed. I. Angelelli. Hildesheim: Olms, 1967.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 According to Sluga, it is Frege's use of a characteristically Kantian term,

AnschauungsvermQgen, confirms this reading as Kantian. This suggests Frege

believed, as did Kant, that geometry rests on the nature of our faculty of intuition, rather

than our having particular intuitions. The significance of this is that Frege believed

geometry to have an a priori source, and thus consists of synthetic a priori propositions.

This only hints at what Frege had in mind because there are no further arguments given

in the dissertation in which this passage alluding to Kantian notions.

In 1874, Frege completed his Habilitationsschrift.268 Here, although

adhering to the Kantian epistemological framework, Frege departs from the Kant in a

way that foreshadows his views concerning the a priori sources for numbers in the

Foundations of Arithmetic. He wrote "The elements of all geometrical constructions are

intuitions and geometry points to intuitions as the source of its axioms. Since the object

of arithmetic has no intuition, its principles can also not derive from intuition."289 Frege

later wrote in the Foundations of Arithmetic, "in calling the truths of geometry synthetic a

priori he [Kant] revealed their true nature."270 Frege did not abandon the Kantian view of

geometry in the Foundations of Arithmetic, though he did disagree with Kant the status

of numbers.

At the end of Frege’s career, after he had given up the logicist project that

had been the center of his early work, Frege nevertheless continued to adhere to the

Kantian epistemological framework. In two separate articles he wrote in 1924 and 1925

entitled “Sources of Knowledge of Mathematics and the mathematical natural Sciences”

and “A new Attempt at a Foundation for Arithmetic", Frege describes three distinct

288 “Rechnungsmethoden, die auf eine Ertweiterung des Grdssenbegriffes grOnden" 289 Sluga in "Frege: the early years", 339. Sluga quotes this passage from "Rechnungsmethoden, die sich auf eine Erweiterung des GrOssenbegriffs grunden" in Kieine Schriften, 1967, 50-84. 270 Frege, Foundations of Arithmetic, 101.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 sources of knowledge: sense perception, the logical source of knowledge, and the

geometrical and temporal sources of knowledge,271 which conform exactly with the three

Kantian faculties of knowledge. Frege's references to pure intuition, as sources of

geometrical axioms in his dissertation, the Habilitationsschrift and the Foundations of

Arithmetic, and his continued adherence to the Kantian principles, shows continuity in

his thought. Thus, it is clear that Kant's philosophy had a formative influence on Frege

during his university experience, and that influence served him throughout academic

career and post-academic life.

Frege was exposed to Kant’s philosophy through Kuno Fischer at Jena.

Fischer, a prominent Kant scholar, had just completed in 1869 the second edition (first

published in 1860) of the part of his monumental history of philosophy which deals with

Kant. Fischer is the greatest historian of philosophy at that time.272 Frege took Fischer's

course on Kant.273 It is significant that Fischer is known to have stressed the

transcendental, in contrast to the psychological, element in Kant's philosophy.274 Thus,

Frege's influence by Fischer was not likely the subjective elements of Kant’s philosophy,

but rather the objective elements. This would be consistent with our understanding of

Frege’s objectivism and his rejection of the subjective elements of Kant’s philosophy.275

Frege attended Ernst Abbe's courses in the theory of functions,

mechanics, gravitation, electrodynamics and experimental physics. Abbe also studied

under Kantian scholar Kuno Fischer. Abbe's professional interests were in the field of

applied mathematics. He became Frege's patron in later years, and was influential in

271 Frege, Posthumous Writings,267-74 and 278-81. 272 Beck, "Neo-Kantianism." 273 Sluga in "Frege: the early years", 333. Sluga cites Asser, G. et al, 1979. 'Gottlob Frege - PersOnlichkeit and Werk', in Begriffsschrift- Jenaer Frege Konference. Jena: Fr. Schiller Universitat, 6-32, as the source of this information. 274 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 Frege’s decision to study at Gbttingen and then return to teach at Jena.278 It is also

significant that Abbe worked with Hermann Lotze, and so through his contact with Abbe,

Frege was further exposed to Lotze's logic and applied mathematics.277

Among important Kantian influences on Frege during his tenure as a

professor at Jena was Friedrich Ernst Otto Liebmann. Liebmann was a professor of

philosophy at Jena from 1882 until 1908 and a colleague of Frege.278 Liebmann coined

the rallying cry of the ‘Back to Kant’ movement in Germany which developed during the

late-nineteenth century, and was closely connected to the Marburg and Baden Neo-

Kantians.279

Other Neo-Kantian contacts that Frege had at University of Jena included

Rudolph Eucken who was a professor of philosophy from 1874 to 1920.280 By some

accounts Eucken was a Neo-Idealist.281 Frege was familiar with Eucken’s work.282 One

of Eucken’s students was Max Scheler, who also became a professor of philosophy at

Jena from 1900 to 1906.283 Scheler’s proximity to Frege is significant because of his

anti-psychologistic and rigorously a prion philosophy of value.284

Lotzian Influences

Hermann Lotze was also very likely a significant influence of Frege’s

thought. Lotze was a notable exception to the general abandonment of speculative

metaphysics that occurred in Germany with the decline of Hegelian idealism referred to

275 Frege, Foundations of Arithmetic, 37n. 278 Bynum, 4n. 277 Sluga, "Frege: the early years", 332. 278 Bynum, 7. 279 Willey, 81. 280 Bynum, 6. 281 SchnSdelbach, 186. 282 Frege, Foundations of Arithmetic, 43n. 283 Bynum, 6.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 in Chapter 3. This is noteworthy for Lotze's possible influence upon Frege. In contrast

to the predilections of many of his Neo-Kantian contemporaries, Lotze was not prepared

to abandon metaphysics for epistemology.285 However, Lotze was influential in the

struggle against Hegelianism and materialism. Though not strictly speaking a Neo-

Kantian, Lotze’s writings became associated with Neo-Kantian viewpoints, and his

critique of Hegel helped sustain the Neo-Kantian movement.288 Lotzian metaphysics

owed much to Leibniz, and his philosophy has been referred to as Leibnizian

pluralism.287 Thus, his is an important possible source of Leibnizian influence on Frege.

Lotze completed his Logik in 1874, and his Metaphysic in 1879.

Metaphysics, for Lotze, was not speculative, it is an inquiry into the

universal conditions, which everything that is to be counted as existing or happening at

all, must be expected to fulfill.288 Lotze's philosophy came to be called 'Ideal-Realism'.

By 'realism' he meant that mechanical conditions determine the way things happen, and

by 'Idealism' he meant the view that everything happens in accordance with a plan, or in

order to fulfill an Ideal purpose.289 In other words, by Ideal-Realism Lotze meant

objective validity. Lotze never developed a unified metaphysical picture of the world.

But his views were immensely influential during the late nineteenth century in Germany

as well as among English Neo-Hegelians. Frege was probably influenced by Lotze's

Ideal-Realism or objective validity, a conception in contrast to extreme realism.

284 Schnadelbach, 186. 285 Passmore, A Hundred Years of Philosophy, 47. 288 Willey. 40. 287 Willey, ibid. 288 Passmore, A Hundred Years of Philosophy, 47-48. 289 Passmore, A Hundred Years of Philosophy, 48-49.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 111 Hans Sluga argued for the positive influence of Lotze on Frege.290

According to Sluga, it was through Lotze that Frege was influenced by idealism. Michael

Dummett has been vigorously challenged this suggestion.291 It is important for

Dummett’s rational reconstruction of Frege’s thought that Frege must not have been an

idealist. The significance for Lotze's influence on Frege, according to Sluga, is three

fold. First, In his Logik, Lotze distinguished between subjective mental acts and their

objective mental contents.292 Second, Lotze was the first major philosopher of the

nineteenth century to reassert the Leibnizian claim that mathematics belongs together

with logic. Third, Lotze agreed with Kant that there are no instances in mere sense-

impressions of the principle of identity. In other words, additional principles beyond that

of pure intuition are required to derive mathematical truths. Thus, Lotze rejected the

Kantian doctrine of truths of arithmetic based on pure intuition of space and time. For

Lotze, truths of arithmetic are based on an ‘intuitive’ grasp of the realm of objective

ideas, which realm is the concern of logic. Thus, Lotze argued for a compromise

between Leibniz and Kant. His position was very close to Frege in that respect.

Dummett has argued293, and Sluga concurs with him on this one point294,

that Frege never once mentioned Lotze. But Sluga has made a convincing argument

based on the historical evidence in favor of accepting Lotze's influence on Frege. First,

he studied the philosophy of religion under Lotze at the University of Gdttingen in

1871.29S Lotze had succeeded Johann Herbart as professor of philosophy at Gdttingen in

1844, and remained there until 1881. Lotze was a veritable polymath who studied

290 Sluga, Gottlob Frege. 291 Dummett, The Interpretation of Frege’s Philosophy 292 Sluga, "Frege: the early years", 343. 293 Dummett, The Interpretation of Frege’s Philosophy, 501. 294 Sluga, "Frege: the early years", 342. 295 Bynum, 3.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 philosophy, mathematics and medicine and held doctorates in medicine and philosophy

from Leipzig. His first shorter work in logic was published in 1843. The larger expanded

version, which Lotze referred to as the first part of a planned “System of Philosophy”296,

was published with editions, first in 1874, and the second in 1880. It is likely that both

versions were known to Frege, considering his own interest in logic. Lotze was well

known and highly respected in academic circles throughout Germany, and his influence

was considerable during his lifetime.297 It is inconceivable that Frege would not have

been awara of Lotze’s wide range of interests, especially in those areas where their

interests coincided in logic and mathematics. Second, there is textual evidence that

Frege knew Lotze’s, Logik. Frege used the term Hilfisgedanke, which is a term coined

by Lotze and not used in other writings. Third, there is the testimony of Bruno Bauch, a

colleague of Frege's at Jena for many years. Bauch characterized Frege's work as "not

independent of Lotze's" in an essay, which was intended to be an introduction to Frege's

"The Thought”. Bauch’s essay was published in Beitr&ge zur Philosophie des deutschen

Idealismus ("Articles on the Philosophy of German Idealism"). This is the same volume

of the journal in which Frege's paper "The Thought" first appeared. According to Sluga,

Bauch's essay referred to four elements of Lotze's thought relevant to understanding

Frege. First, there is Lotze's anti-psychologism. Second, his mentioned the distinction

between an object of knowledge and its recognition. Third, there was Lotze’s

reformulation of Platonism as an ontology-free theory. Fourth, there was his account of

296 Lotze, in the Preface to the first edition of Logic, trans. Bernard Bosanquet (Oxford: Clarendon, 1888), ix. 297 Gotesky, “Lotze, Rudolf Hermann”, The Encyclopedia of Philosophy, vol. 5, ed. Paul Edwards, 87-89.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 concepts as functions.298 Moreover, it is significant that Frege's article appeared in a

journal devoted primarily to German idealism.

Michael Resnik has also argued for the plausibility of Lotze's influence on

Frege.299 Sluga points to the similarity of Frege’s distinction of the ‘objective’ versus the

‘real’ compared to Lotze’s distinction between the ‘objective’ or ‘valid’ versus the ‘real’ or

‘existent’ (Se/'n). Resnik sees this as providing persuasive evidence for Frege’s

transcendental idealism.300 Beth has pointed to Frege's view that only identity judgments

can be accepted, as another indication of Lotze's likely influence of Frege.301

Dummett dismisses, I think incorrectly, Siuga's assessment of Lotze's

formative influence on Frege's philosophy. Sluga has presented persuasive, if not

conclusive, evidence of Lotze's probable influence on Frege. Dummett, himself,

confirms that there is additional evidence to show that Frege was aware of Lotze’s

thought in some important respects. In an article called "Frege's 'KernsStz zur Logik'"

Dummett compares Frege’s piece, translated as "17 Key Sentences on Logic" in

Posthumous Writings, to Lotze's work. Although there is no mention by Frege of Lotze

by name in the piece, Dummett admits that it is evident that Frege's piece forms "a

series of comments by Frege upon Lotze’s Introduction" to Logik, the first edition of

which was published in 1874 and the second in 1880.

It is notable that Lotze's Logik was well known and widely respected, and

no one with any interest in logic in the late nineteenth century, whether in Germany,

England, or America, could have ignored it. The first two volumes were translated into

298 Sluga, "Frege: the early years", 342. See also, Sluga, Gottlob Frege, 53. 299 Resnik, Frege and the Philosophy of Mathematics, 163-9. 300 Resnick, 164. 301 E.W. Beth, Mathematical Thought (Dordrecht: D. Reidel, 1965), 51.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 English in 1884 by Bernard Bosanquet302, a leading British Neo-Idealist philosopher.

Bernard Bosanquet was a prominent defender of Bradley's Absolute Idealism against

the heresies of the Personal Idealism of Seth and McTaggart. Notably, Bosanquet is

one of the Neo-Idealists against whose philosophy Russell and Moore revolted. Russell

was very familiar with Lotze's work in mathematics.303 That Frege neither refers to Lotze

by name in any of his extant writings nor attributed his direct influence by Lotze, does

not demonstrate lack of influence on Frege. The records show that Frege studied

philosophy of religion under Lotze, and so would likely have been exposed to Lotze's

logic and mathematics directly. Thus, I conclude that Frege was probably influenced by

Lotze, an historical influence that is not fully appreciated by analytic philosophers who

are disposed to accept the standard interpretation of Frege, as anti-idealist, in the mold

of Russell and Moore.

Mathematical and Logical Influences

Among the positive mathematical influences on Frege while he was a

student at Jena and GQttingen were the professors of mathematics Wilhelm Weber and

Ernst Schering. Through Weber and Schering Frege was very likely exposed to the

mathematical ideas of Carl Friedrich Gauss, with whom they were close collaborators.304

Gauss is the probable source of several significant mathematical views with connections

to Frege’s views on the foundations and workings of mathematics. These include

emphasis on the need for greater precision in mathematics, and the application of

mathematics to in science, as well as the logical rigor of Greek mathematicians. In

302 Passmore, A Hundred Years of Philosophy, 85. 303 Russell, An Essay on the Foundations of Geometryambridge: {C Cambridge University Press, 1897; reprint, New York: Dover, 1956), 93ff, p.99ff and p.108ff; and The Principles of Mathematics, p.221 andp.446ff. 304 Sluga, "Frege: the early years", 334.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 addition, Gauss was an admirer of Kant's Critique of Pure Reason, but rejected the

Kantian claim that geometry and arithmetic are based on the a priori intuition of space

and time. Of particular importance for our understanding cf Frege, according to Sluga,

"is the idea that empirical science rests on foundations of pure mathematics, that

empirical research involves the use of mathematical methods, which gives Frege's work

on the foundations of mathematics its significance for him.”305 Further evidence that

Frege was not only familiar with Gauss's work, but positively influenced by it, is found in

Frege’s appeal to Gauss’s views in correspondence to Hilbert306 and Huntington307.

In the field of logic, Frege was familiar with the English logicians Boole

and Jevons, whose works he read in German translation. He was also studied the

works of the German logician Schroder and Leibniz, and Italian Peano. Frege criticized

the formalism of Peano, whose logical notation could not account for the conceptual

content of logical expressions.308 He rejected the empiricism of Mill,309 and rejected the

categorical-deductive logic of classes of Boole310 and Schroder311. Frege held in high

esteem only Leibniz's notion of a lingua characterica, closely linked in Leibniz’s mind to

a calculus ratiocinatur that would make possible a computation of conceptual content.312

Frege’s publication of Begriffsschrift ('Concept-Notation') was the first

work he produced on logic and in which he attempts the completion of Leibniz's project

for a lingua characterica. It was a major milestone in mathematical logic, though it went

308 Sluga, "Frege: the early years", 335. 306 Frege, Philosophical and Mathematical Correspondence, 45. 307 Ibid., 58. 308 Frege’s “On Mr. Peano’s Conceptual Notation and My Own" in Collected Papers, 234-48. 309 Frege, Foundations of Arithmetic, 9. 310 Frege, “Boole’s logical Calculus and the Concept-Scripf in Posthumous Writings, 9-52. 311 Frege, “A Critical Elucidation of some Points in E. Schroder, Vorlesungen uber die Algebra der LogifC, in Collected Papers, 210-228.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 almost unnoticed by his contemporaries. He was motivated to invent the Begriffsschrift

in order to solve a problem he was studying in the concept of number involving the

analysis of numerical sequence. He wanted to give a logical analysis of the notion of

numerical sequence using logical consequence, instead of inductive intuition. But he

found the imprecision of ordinary language prevented him from doing so with clarity. He

invented the Begriffsschrift as a means of expressing the 'conceptual content', i.e. the

logical relevant features, of an assertion. The logical notation forces the explicit

statement of any logically relevant features of any assertion used in a proof. The formal

notation prevented anything intuitive from entering unnoticed in the logical proofs.

Proofs in the system were limited to only those proofs that could be obtained from a

small number of evidently true logical axioms. His main innovations were the quantifier-

variable notation for the expression of generality, and the complete axiomatization of

first-order predicate logic with identity, including a version of second-order predicate

logic used to develop a logical definition of the ancestral of a relation. Frege's

development of the Begriffsschrift is the first modem version of mathematical logic. The

use of mathematical logic in the twentieth century made the methodology of analytical

philosophy possible. It is largely due to the seminal role he played in developing the

methodology of logical analysis that Frege deserves to be called the father of analytic

philosophy.

Lelbnlzian Influences

There was a renewed interest in Leibniz that awakened in Germany

during the mid-nineteenth century, and Frege fell under its influence. The Erdmann

312 Frege, “Boole’s logical Calculus and the Concept-Scripf in Frege, Posthumous Writings, 9,10 and 13; Begriffsscrift in van Heijenoort, 6-7; and “On the Aim of the ‘Conceptual Notation’” in Bynum, 91.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 edition of Leibnitii Opera Philosophies was published in 1840, and this was soon

followed by Gerhardt's extensive editions of Mathematische Schriften in 1849-1863 and

Die Philosophischen Schriften von IN.G. Leibniz in 1875-90. Leibniz’s philosophical and

logical works. Frege was familiar with at least the Erdmann collection, and quotes from

it appear in the Foundations of Arithmetic.313 That the development of Frege’s thought

was influenced by Leibniz is nothing new. It is well known that there is an obvious

parallel in Frege and Leibniz on the nature and role of an ideal language.314 Frege

operated with the Leibnizian notion of identity.315 What I want to point out is that the

nature of his influence on Frege is mainly rationalist. This has been ignored by most

commentators on Frege, especially those who accept the standard interpretation,

because they see Frege as closely related in his logical philosophy to twentieth-century

logicians who were interested in the semantic features of logical languages, rather than

to a rationalist ideal of a universal language.

Frege clearly conceived of his work as an extension of Leibnizian

conceptions of logic and mathematics.316 The notion of a mathesis universalis is

traceable to the rationalist vision of Descartes for a universal mathematics as the

rational basis of a description of reality. The notion of a universal mathematics did not

go unnoticed by Leibniz who was the first to anticipate the possibilities for a

mathematical logic.

Frege developed the Begriffsschrift for use initially in mathematics to

secure the certainty of mathematical propositions. But he had further ambitions for its

313 Frege, Foundations of Arithmetic, 7,9,23,31. 314 Bynum, 15. 3,5 Ignacio Angelelli, Studies on Gottlob Frege and Traditional Philosophy (Dordrect: D.Reidel, 1965), 51-55; also, Reinhardt Grossman, Reflections on Frege’s Philosophy (Evanston: Northwestern University Press, 1969), 126.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 eventual use in other sciences. Eventually, Frege hoped to add basic vocabulary of the

special sciences, such as geometry, kinetics, mechanics and physics.317 His aim was

the completely rigorous deductive development of any science whatsoever.318 This

ambition, though never realized, marks him as a rationalist thinker.

The basis of Frege’s logical system are “the laws upon which all

knowledge rests.” In this Frege follows Leibniz in maintaining that all knowledge is

divisible into truths of reason or truths of fact. According to Leibniz, truths of reason, or

necessary truths, are based on the principle of contradiction, which are to be

distinguished from truths of fact, or contingent truths, based on the principle of sufficient

reason. Frege exactly follows Leibniz’s dichotomy in the Begriffsscrift where he too

divides “all truths that require justification into two kinds, those for which the proof can be

carried out purely by means of logic and those for which it must be supported by facts of

experience.”319

The distinction between truths of reason and truths of fact was given by

Leibniz in § 31 and 32 of the Monadology.

Our reasonings are based upon two great principles: first, the Principle of contradiction, by virtue of which we judge that false which involves a contradiction, and that true which is opposed or contrary to the false; and second, the Principle of sufficient Reason, by virtue of which we observe that there can be found no fact that is true or existent, or any true proposition, without there being sufficient reason for its being so and not otherwise, although we cannot know these in most cases.

316 Frege, Foundations of Arithmetic, 48,50,52,67 and 76; Begriffsschrift in van Heijenoort trans. 6-7; and Frege, The Basic Laws (Los Angeles: University of California Press, 1964), § 9. 317 Begriffsschrift in van Heijenoort, 7. 318 Thomas Ricketts, “Gottlob Frege" in The Cambridge Dictionary of Philosophy, ed. R. Audi, (Cambridge: Cambridge University Press, 1995), 282. 319 Begriffsschrift in van Heijenoort, 5.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 The principle of contradiction is often given by Leibniz the status of a

necessary assumption on which all reasoning is dependent.320 According to Leibniz:

One cannot go infinity in his proofs, however, and therefore some things must be assumed without proof - not silently and by stealth, indeed, dissimulating our own laziness as philosophers customarily do, but keeping clearly in mind what we have used as our first assertions, after the example of geometricians who, to show their good faith, acknowledge at the very start the assumed axioms they are to use, sop that they may be sure that all the conclusions are proved at least hypothetically form these assumptions.321

The principle of contradiction, already found also in the rationalist philosophy of

Descartes322, is at the basis of both Frege’s and Leibniz’s logical systems. According to

Frege, “We cannot (at the same time) affirm a and deny a."323 For Leibniz, necessary

truths, or truths of reason, are either identical propositions or they are reducible to

identities by definitions or the analysis of their terms or concepts. Identical axioms are

the indemonstratable foundations of necessary truths, and thus the embodiment or

exemplification of the principle of contradiction; for, the proposition ‘A is either A, or no

not-A’ to be true, ‘A must necessarily be identical to A’.

Frege maintains with Leibniz that the necessary truths are innate.

Frege’s implicit acceptance of Leibniz’s notion of innate is confirmed in the Foundations

of Arithmetic where Frege describes Leibniz as holding the opposite view from Mill on

the nature of necessary truths. Frege says:

Leibniz holds the opposite view, that the necessary truths, such as are found in arithmetic, must have principles whose proof does not depend on examples and therefore not on the evidence of the senses, though

320 Macrae, Robert, “The Theory of knowledge" in The Cambridge Companion to Leibniz, ed. N. Jolly (Cambridge: Cambridge University Press, 1995), 192. 321 Leibniz, G.W., Philosophical Papers and Letters, edited by L. Loemker, second edition (Dordrecht: D. Reidel, 1969), 225. 322 Descartes, “Letter to Clerselier, June 1646", in Anthony Kenny, ed., Descartes Philosophical Letters, 197. 323 Begriffsschrift in van Heijenoort, 44.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 doubtless without senses it would have occurred to no one to think of them.

in the same passage, Frege explains Leibniz's meaning of the term 'innate'. Quoting

Leibniz, he says:

"The whole of arithmetic is innate and is in virtual fashion in us.” What he means by the term innate is explained by another passage, where he denies “that Everything we leam is not innate. The truths of number are in us and yet we still leam them, whether it be by drawing them forth from that source when learning them by demonstration (which shows them to be innate), or whether it be...".324

Leibniz considers the principle of contradiction an innate principle native to the mind of man:

For general principles enter into our thoughts, serving as their inner core and as their mortar. Even if we give no thought to them, they are necessary for thought, as muscles and tendons are for walking. The mind relies on these principles constantly.. ..32S

Since all necessary truths are reducible to identities, and all identities are simply

the principle of contradiction, and since all necessary truths must be innate

because they are not derived from the senses or induction, the principle of

contradiction must be innate.

There are at least three doctrines of identity in Leibniz’s

philosophical works. It is not clear which of these doctrines that Frege appealed

to in giving his definition number. The first of Leibniz’s doctrines is often called

Leibniz’s Law, which says that if A and B are identical, then everything that is

true of A is also true of B. This may be expressed in logical symbolization as:

[A = B -> (f) (f A s f B)]

324 Leibniz, New Essays on Human Understanding (Cambridge: Cambridge University Press, 1996), 1.1.20. 325 Ibid.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 The second doctrine is what is known as Leibniz’s ‘principle of identity of

indiscemibles'. This says, if everything that is true of A is true of B, and vice

versa, and hence there is no discernible difference between A and B, then A is

identical with B. This second doctrine is the inverse of the first doctrine stated

above. It may be expressed in logical symbolism as:

[(f) (f AsfB)->A = B]

The third doctrine is Leibniz’s claim that “those terms of which one can be

substituted for the other without affecting truth are identical", and often rendered

in Latin as Leibniz expressed it, as “Eadem sunt, quorum unum alteri substitui

potest saiva veritate.” This principle is basic to Leibniz’s logic and modem

philosophy of language. It provides the linkage between concept identity and

truth-conditions.328

Leibniz’s third doctrine of the principle of identity plays a central

role in Frege's logical and mathematical philosophy. In Begriffsscrift §8, Frege

carefully explains the importance of identity statements and the role of the

identity of proper names in the Concept-Script. Two proper names have the

same content when they are names of the same object. The statement "Gottlob

Frege is the author of the Begriffsschrift says that “Gottlob Frege” and “the

author of the Begriffsschrift name the same object. According to Frege,

Hence the need for a sign of identity of content rests upon the following consideration: the same content can be completely determined in different ways; but that in a particular case two ways of determining it really yield the same result is the content of a judgment. Before this judgment can be made, two distinct names, corresponding to the two ways of determining the content, must be assigned to what these ways determine. The judgement, however, requires of its expression a sign for identity of content, a sign that connects these two names. From this

328 Mcrae, 193.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122 follows that the existence of different names of the same content is not always merely an irrelevant question of form; rather, that there are such names is the very heart of the matter if each is associated with a different way of determining the content. In that case the judgment that has the identity of content as its object is synthetic, in the Kantian sense. A more extrinsic reason for the introduction of a sign of identity of content is that it is at times expedient to introduce an abbreviation for a lengthy expression. Then we must express the identity of content that obtains between the abbreviation and the original form.327

In his later essay "On Sense and Reference,” Frege explains that he was forced to the

view he held in Begriffsschrift because of the need to distinguish between uninformative

and informative statements. Informative statements concerning the same objects apply

different names to the object named.

In the Foundations of Arithmetic §62 Frege appeals to Leibniz’s second

doctrine, the principle of identity of indescemibles to establish a definition of natural

number. He asks the crucial question: "How, then, are numbers to be given to us, if we

cannot have ideas or intuitions of them?” He goes on to explain:

Since it is only in the context of a proposition that words have any meaning, our problem becomes this: To define the sense of a proposition in which a number occurs. That, obviously, leaves us still a very side choice. But we have already settled that number words are to be understood as standing for self-subsistent objects. And that is enough to give us a class of propositions which must have a sense, namely those which express our recognition of a number as the same again. If we are to use the symbol a to signify an object, we must have criterion for deciding in all cases whether b is the same as a, even if it is not always in our power to apply this criterion. In our present case, we have to define the sense of the proposition

The number which belongs to the concept F is the same as that which belongs to concept G"

That is to say, we must reproduce the content of this proposition in other terms, avoiding the use of the expression

The Number which belongs to the concept P

327 Begriffsschrift in van Heijenoort, 21.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 In doing this, we shall be giving a general criterion for the identity of numbers. When we have thus acquired a means of arriving at a determinate number and of recognizing it again as the same, we can assign it a number word as its proper name.

Thus, Leibniz’s second and third doctrines of identities are essential for Frege’s

logical system. They are the principles of providing the indemonstratable

foundations of necessary truths.

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FREGE’S RATIONALIST EPISTEMOLOGY

Frege’s Epistemological Motivations

It is my overall thesis that Frege was primarily concerned with and

motivated by epistemological questions concerning the foundations of mathematics and

scientific knowledge in general, and that he held a rationalist epistemology. This

interpretation of Frege is opposed to the standard interpretation, espoused by Dummett,

and others like him, who maintain that Frege was not interested in epistemology at all;

rather that he was interested in developing a theory of meaning in the semantic tradition.

Now, traditional epistemology, or ‘theory of knowledge’, concerns three

broadly circumscribed areas: (a) the nature and scope of human knowledge, (b) the

basis and presuppositions of knowledge, and (c) the reliability of claims to knowledge.328

Frege was not a systematic philosopher; and he was not concerned with the entire

scope and nature of human knowledge; nor do his interests extend equally to all facets

of epistemology. However, as will be seen, he was concerned with each of these

broader facets of epistemology to some degree.

Frege was primarily concerned with nature and scope of claims to

scientific knowledge, and not the nature and scope of human knowledge in general. As

mathematician, Frege was primarily concerned primarily with mathematical knowledge,

which he considered the paradigm for all scientific knowledge. However, for Frege, all

329 D. W. Hamlyn, “Epistemology, History o f in The Encyclopedia of Philosophy, vol. 3, ed. P. Edwards, 9-38. 124

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human knowledge is governed by the same laws of logic. For him, logic was the

foundation of human reason and rationality. The nature of Thought is in essentials the

same everywhere: it is not true that there are different kinds of laws thought to suit the

different kinds of objects thought about."329 Frege believed that we ought not claim

scientific knowledge about anything unless we are absolutely sure about it. He is

concerned with securing claims of scientific knowledge from skeptical challenge. For

Frege, securing claims of knowledge from skeptical challenge entails the removal of all

psychological influences or external aids such as words or numerals. He says that:

Such differences [in thought] as there are consist only in this, that the thought is more pure or less pure, less dependent or more dependent upon psychological influences and on external aids such as words or numerals, and further to some extent too in the finer or coarser structure of the concepts involved; but it is precisely in this respect that mathematics aspires to surpass all other sciences, even philosophy.330

The purpose of his Begriffsscrift was to eliminate the “gaps" and secure claims of

mathematical knowledge from such influences.

Dummett, as I have described, maintains that Frege inaugurated a new

era in philosophy, in which epistemology was replaced by Frege by theory of meaning

as first philosophy; thus metaphysics which had been considered first philosophy by

medieval philosophers, is once again returned to a position of preeminence. Far from

returning metaphysics to a position of first philosophy, and far from making theory of

meaning the new version of first philosophy, Frege was, in fact, a rationalist philosopher

who was motivated by epistemological considerations.

The view of Frege as rationalist was first enunciated by Sluga in “Frege

as Rationalist” and in his book Gottlob Frege, but not fully articulated. Sluga places

329 Frege, Foundations of Arithmetic, iii. 330 Ibid. 125

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The view of Frege as rationalist was first enunciated by Sluga in “Frege

as Rationalist” and in his book Gottlob Frege, but not fully articulated. Sluga places

greater emphasis on Frege's connection through Leibniz to Kant and German idealism

than to the Cartesian rationalist themes. In his book Gottlob Frege Sluga assimilates

rationalism with an interest in logic and aphorism; and in “Frege as Rationalist" he points

to the use by the traditional rationalist philosophers, like Descartes and Leibniz, of logic

as “a tool for the defense of their rationalistic conclusions."331 Sluga is correct as for as

this goes. However, in my view, Frege’s rationalism owes more to Descartes than Sluga

admits. The reason for this seems to be that interpreters place greater weight on

Frege’s logical theory and insufficient weight to Frege’s rationalist epistemology. The

rationalist elements in Frege’s thought have gone largely unnoticed by most of his other

interpreters with few notable exceptions. Tyler Burge points to the “rationalist

predilections" of Frege’s conception of ‘Sinn’ as opposed to modem empiricist

conception of meaning.332 Burge has also maintained that Frege “accepted the

traditional rationalist account of knowledge of the relevant primitive truths, truths of

logic."333 Sluga, Burge and Haack are few of the exceptions. The reasons for this are

complex. However, there is a tendency among analytic philosophers in the twentieth

century to embrace empiricism and to oppose all forms of rationalism.

Rationalism, narrowly defined, refers to the doctrines of a group of

philosophers of the 17th and 18th centuries whose most important representatives are

Descartes, Spinoza and Leibniz who held the following views: (a) it is possible to obtain

331 Sluga, “Frege as Rationalist”, 30. 332 Burge, “Frege on Sense and Linguistic Meaning” in The Analytic Tradition: Meaning, Thought and Knowledge, eds. D. Bell and N. Cooper (Oxford: Blackwell, 1990), 30.

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a knowledge of what exists by reason alone; (b) that knowledge forms a single system;

that knowledge possesses a deductive characteristic; and (d) the belief that everything is

explicable, and can therefore be brought under a single system.334 More widely defined,

rationalism is the view expressed by (b) and (d); that is, the view that everything is

explicable in terms of one system.

Frege falls squarely within the rationalist epistemological tradition on

several counts. First, he was committed to the traditional rationalist account of self-

evident primitive truths as the presupposition of all scientific knowledge. Second, he

accepted a foundationaiist epistemology. Third, he believed there are innate sources of

knowledge. Fourth, he was committed to the view of mathematics as a privileged model

of all scientific knowledge. Fifth, he believed deductive methods could secure the

reliability of claims of scientific knowledge. Sixth, he believed in the axiomatization of all

scientific knowledge. Seventh, he was committed to epistemological dualism.

Early analytic philosophers, such as Russell, Moore and Wittgenstein,

opposed not only radical empiricism, and its attendant psychologism, but also the

historicism, evolutionism, and the radical subjectivism of idealism. Radical empiricism,

as espoused by Mill and Mach, rejected any notion of a priori knowledge; all knowledge

for them was seen as empirical, and inferences were secured not by deductive

inferences, but rather by inductive generalizations. Russell and Moore accepted a

milder form of empiricism; matters of fact were seen as grounded in perceptual sources

of knowledge, and such truths were hence seen as essentially psychological in nature.

333 Burge, “Frege on Knowing the Third Realm” in Early Analytic Philosophy: Frege, Russell, Wittgenstein, ed. W. Tait (La Salle: Open Court, 1997), 1. 334 Flew, Dictionary of Philosophy.

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Russell believed that knowledge of logical relations and universals were a

priori conceptions of the mind analogous, but dissimilar, to the perception of particular

objects of sense perception.335 For Wittgenstein, what makes logic a priori is the

impossibility of illogical thought;338 the propositions of logic are tautologies;337 and the

propositions are logic say nothing, they are the analytic propositions.338 On the other

hand, Wittgenstein believed in “logical insight" as securing the logical forms in which the

propositions of science can be cast.339 They too accepted that there were a priori

sources of knowledge, which grounded formal or logical relations, universals and

mathematical concepts.

Rationalist and empiricist elements are found in the thought of Russell

and Wittgenstein who were direct intellectual heirs of Frege. Their interest in logic is

accompanied by a strong aphorism, but neither could be considered purely rationalist

thinkers. Their philosophy yields many concessions to empiricism. As analytic

philosophy developed, the logical positivists and the later Wittgenstein made gradually

more and more concessions to empiricism. Logical positivism rejected any notion of that

there could be a priori propositions that referred to matters of fact; and rejected the

traditional distinction between a priori propositions and empirical propositions.340 All a

priori truths were interpreted by them, not a truths or reason, but as empty tautologies.341

The logical positivists rejected all the fundamental tenets of rationalism: that thought is

335 Russell, Mysticism and Logic, 154. 338 Wittgenstein, Tractatus, §5.4731 337 Ibid, 6.1. 338 Ibid, 6.11. 339 Ibid, 6.33; 6.34. 340 Ayer, Language, Truth and Logic, 2n ed. (London: Victor Gollantz, 1946; reprint, New York, Dover, 1952),135. 341 Ibid; also Sluga, Gottlob Frege, 7.

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an independent source of knowledge, that it is a more trustworthy source of knowledge

than experience, or that it is the only source of knowledge.342

Now the tendency among most analytic philosophers is to reject all forms

of rationalist epistemology in favor of a naturalized epistemology. As a result, rationalist

elements in Frege’s thought are often ignored, or hardly mentioned, by Dummett,

Geach, Kenny, Resnik, and others, who are adherents of the new empiricism.

Frege's thought is squarely in the rationalist tradition of Descartes,

Spinoza and Leibniz. The evidence for Frege's rationalism is both explicit and implicit in

his thought; to categorize him otherwise would misrepresent his thought.

The rationalist picture of Frege that I wish to advance gives central place

to Frege's reliance upon self-evidence as the epistemological basis of scientific truths, in

particular the truths of mathematics, but also the truths of human knowledge in general.

This picture of Frege is wholly consistent with his concern with the epistemological

status of logic and mathematics. Mathematical knowledge and logic are given central

place in his thought. Mathematical truths are seen as having a priori origins grounded in

logical laws, which are self-evident. Human knowledge in general is grounded in self-

evident truths given to us by intuition, and inferences derived from sources of intuition

are secured by logical laws, and not inductive generalizations.

In addition, Frege’s vision for a lingua characteristics, first envisioned by

Descartes as the mathesis universalis, and subsequently articulated by Leibniz as

characteristics universalis, was later fully realized by Frege in his Begriffsschrift. This

fulfillment of this vision connects Frege directly to the rationalist tradition. Frege

342 Ayer, Language, Truth and Logic, 73.

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explicitly credits Leibniz with the idea of a “universal characteristic, of a calculus

philosophicus or ratiocinatof3*3

Later, under the influence of Kant, Frege held there are apriori forms of

judgment, both analytic and synthetic. Although Frege rejected Kant’s characterization

of mathematical knowledge as synthetic a priori knowledge, his adherence to the view

that mathematics is comprised of analytic apriori judgments, and his acceptance of

acceptance of synthetic a priori knowledge as the basis for geometry and natural laws

places him within the compass of rationalism.

The central concern of modem philosophy after Descartes has been

epistemology. The epistemological views of philosophers after Descartes have been

traditionally characterized as rationalists or empiricists depending on their divergent

views concerning the sources of human knowledge. Empiricists, such as Locke,

Berkeley and Hume, maintained that all knowledge including mathematical knowledge is

ultimately derived from sense experience. However, rationalists, like Descartes,

Spinoza, Leibniz, and Kant held that the most general and universal knowledge

(including mathematical truths) is either innately given to us or derived a priori without

dependence upon sense experience. It would be a caricature of the rationalist outlook,

to think of such thinkers as ‘pure apriorists’ who dispensed with sensory experience

entirely.

Descartes, Leibniz and Kant each accepted the role and importance of

empirical investigation in matters of science. What they have in common with Frege is

the belief that it was possible, by the use of reason alone, to gain a superior kind of

knowledge to that gained from sense experience. They all shared the belief in bom

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‘natural light’ or 'light of reason' that permits us to access to the most general, universal

and necessary truths, such as the truths of mathematics and science. Since the faculty

of reason is innate in all humans, logical knowledge, and by extension mathematical

knowledge, is possible for all of us without reliance upon sensory experience.

The rationalists believe the use of reason, and its reliability as the source

of basic principles, from which to gain other truths. Knowledge of reality is an organized

structure based on the foundation of certain truth. The certainty of basic truth is known

to reason by attentive minds. Truth is self-justifying, and of two general kinds: general

principles of reason and matters of fact. All experience is inherently deceptive; it should

be therefore analyzed using general principles, which are directly known to reason. All

knowledge is inferred from general principles by deduction. The validity of deduction is

grounded in the truth of general principles used as premises in the deduction. All of

these basic tenets of rationalism are consistent with Frege's thought.

The objection may be raised that there are few references in Frege’s work

explicitly avowing rationalist program or adherence to rationalist principles. Frege’s

abiding interest in mathematics together with his avowed aims to establish mathematics

as logical science, in effect, an extension of logic, is evidence for his rationalism. All of

modem mathematics after the time of Descartes’ arithmetization of geometry can be

seen a rationalist program securing scientific knowledge. However, Frege went farther

than traditional mathematical rationalism. He explicitly advocated a deductive system of

truths for all the sciences. His Concept-Script was the first step in the development of a

rigorous deductive epistemology.

343 Begriffsscrift in van Heijenoort, 6.

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There are explicit references to rationalist thinkers found in Frege’s

writings to whom he was favorably disposed. He acknowledges familiarity with the

works of several rationalist philosophers. In “Logic in mathematics” (1914) Frege says,

“If one counts logic as part of philosophy, there will be a specially close bond between

mathematics and philosophy, and this is confirmed by the history of these sciences

(Plato, Descartes, Leibniz, Newton, Kant)."344 In Foundations of Arithmetic §35, Frege

shows that he was familiar with Descartes writings on logic and positively influenced by

them. He refers to Descartes' Principles of Philosophy, Part 1 §60 concerning the

concept of number “the number (or better, the plurality) in things arises from their

diversity." In Foundations of Arithmetic and “Function and Concept” Frege shows his

familiarity with a version of the ontological argument for the existence of God discussed

by Descartes, and later by Kant.

There is good reason, therefore, to suppose that Frege was familiar with

other aspects of Descartes’ works, particularly as they might relate to Frege's interests

in logic and the philosophy of mathematics. It would be difficult to imagine, despite lack

of explicit references in Frege’s writings, that Frege was not aware of Descartes’

mathesis universalis in the Discourse on the Method, especially since he was a student

of mathematics and philosophy. Frege’s familiarity with Descartes' mathematical

philosophy is evident in his choice of a doctoral dissertation at GOttingen in 1873 on a

topic in analytical geometry. The title of his dissertation was “On a Geometrical

Representation of Imaginary Forms in the Plane."345 As a student, taking courses in

philosophy at Jena and Gottingen, Frege would surely have been introduced to

344 Frege, Posthumous Writings, 203. 345 Frege, Collected Papers, 1-55.

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Descartes' basic philosophical works, like Meditations and Discourse of the Method.

Descartes' method consists in breaking down a problem and taking it back to its simplest

essentials, until we arrive at basic truths which are simple and self-evident enough to

serve as reliable starting points, and from which the answers to more complex questions

may be deduced. It is hard to imagine that Frege would not have been aware of

Descartes interests in analysis and deductive inference given Frege’s own interests in

deductivism.

Self-evidence and Epistemological Foundationalism

Since Descartes there has been a presupposition that there are certain

things on can know about oneself, or basic truths that we can be certain about, without

the need of outside assistance. We can identify instances of knowing without any

criteria of knowing or of justification. For this reason traditional epistemology has been

called ‘intemalistic’.346 The concept of epistemic justification has also been

characterized as internal, immediate and objective. It is internal and immediate, with

respect to a particular instance of knowing, if one can find out directly upon reflection

what one is justified in believing at any time. Although it is internal, it may also be

regarded as objective if a particular instance of knowing itself constitutes an object of

knowing.347 It is part of my overall thesis that such presuppositions underlie Frege’s

philosophy. Frege’s philosophy is ‘intemalistic’ in respect to its reliance upon self

evidence, as an internal, immediate and objective basis for both the truth of logical laws

and the intuition of spatial truths of geometry.

346 Chisholm, Theory of Knowledge, 5. 347 Ibid, 7.

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There has been too little attention given to the role of self-evidence in

Frege’s thought. It is my thesis that a traditional rationalist notion of self-evidence

underlies Frege's logicism. If this is true then Frege's logiclsm owes more to rationalism,

and the Cartesian-Locke tradition of ideas, than it does to the linguistic turn.

Frege accepted the tradition rationalist account associated with the

paradigm of certainty afforded by Euclidean geometry. According to Frege, the truths of

geometry and logic, the rules of inference and identities are all self-evident truths. Frege

never thought that is was necessary to demonstrate the indisputable nature of this

account of logical or geometrical knowledge. He took it for granted that the

foundationalist account was the only acceptable theory of knowledge.

This Euclidean paradigm of knowledge built upon self-evident truths was

the accepted account of knowledge for Descartes, Spinoza, Leibniz and Kant.

Moreover, it has been the paradigm for virtually every mathematician in the Western

tradition leading up to the time of Frege. As is shown in Frege’s own writings, he was

clearly under he positive influence of Leibniz and Kant, both of whom accepted the

Euclidean account of knowledge.

Perhaps the most complete statement by Frege concerning self-evidence

and its relation to his logicist thesis is the following quotation from the Foundations of

Arithmetic:

§90. I do not claim to have made the analytic character of arithmetic propositions more than probable, because it can still always be doubted whether they are deductible solely form purely logical laws, or whether some other type of premise is not involved at some point in their proof without our noticing it. This misgiving will not be completely allayed even by the indications I have given of the proof of some of the propositions; it can only be removed by producing a chain of deductions with no link missing, such that no step in it is taken which does not conform to some

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one of a small number of principles of inference recognized as purely logical. To this day, scarcely one single proof has ever been conducted on these lines; the mathematician rests content if every transition to a fresh judgement is self-evidently correct, without enquiring into the nature of this self-evidence, whether it is logical or intuitive. A single such step is often really a whole compendium, equivalent to several simple inferences, and into it there can still creep along with these some element from intuition. In proofs as we know then, progress is by jumps, which is why the variety of types of inference in mathematics appears to be so excessively rich; for the bigger the jump, the more diverse are the combinations it can represent of simple inferences with axioms derived form intuition. Often, nevertheless, the correctness, of such a transition is immediately self-evident to us, without our ever becoming conscious of the subordinate steps condensed within it; whereupon, since it does not obviously conform to any of the recognized types of logical inference, we are prepared to accept its self-evidence forthwith as intuitive, and the conclusion itself as a synthetic truth-and this even when obviously it holds good of much more than merely what can be intuited. On these lines what is synthetic and based on intuition cannot be sharply separated from what is analytic. Nor shall we succeed in compiling with certainty a complete set of axioms of intuitions, such that from them alone we can derive, by means of the laws of logic, every proof in mathematics.

The bold italicized emphasis in the preceding quote is my own. Frege is claiming

here that arithmetic propositions are reducible to self-evident truths. The only

question is the nature of self-evidence to which they can be reduced. He

distinguishes two basic kinds of self-evidence: logical and intuitive, as the only

possible sources of justification for arithmetical inferences. If a judgment

concerning arithmetic is shown to be demonstrated by a chain of self-evident

deductions conforming to principles of inference recognized as logical, then the

truth is analytic. However, if the judgment is shown to be demonstrated by a

chain of self-evident deductions in which some of the steps admit of intuitive

justification, then the truth is synthetic. The epistemological significance of

Frege's distinction is that if the axioms of arithmetic are shown to be derived from

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logic, then the certainty of arithmetic will be shown to be secure in virtue of their

grounding in the logical source, and thus free from any intrusion of intuition.

Frege believes that the laws of logical inference are certain due to the fact

that they are self-evidently grounded in purely logical principles. But there of two

problems with Frege’s acceptance of self-evidence as certainty. First, it is possible for

the judgment made to be false; second, two or more people may not agree on which

judgments are self-evidently true. If judgment can be self-evident and yet turn out to be

false, or if two or more persons cannot agree on what is true, the required degree of

certainty is lacking. It would appear, then that the self-evidence of logical laws cannot

provide the adequate certainty. This objection seems conclusive, and it would that self

evidence could not possibly provide the degree of certainty required as the basis of

logical inference that Frege is looking for. However, there are certain matters about

which philosophers are seldom in disagreement. It is true that philosophers have often

disagreed about whether every event has necessary cause, or whether existence is a

perfection. But there is very little controversy over the necessity of the law of

contradiction, or about the principle that if equals are added (or subtracted) from equals

the result is equal. Similarly, there was little controversy in Frege's time concerning

whether a person could be mistaken about being in pain. Such cases are very plausible

as the basis of logical or intuitive truths. The reason for this is that such notions appear

entirely self-evident. There does not seem to be any thing more basic that could be

used to justify the truth of such basic notions.

Frege is explicit with respect to the self-evidentiary basis and

presuppositions of claims for scientific knowledge. He regards the basis of arithmetic

knowledge to be the self-evident principles of logic. The basis of geometric knowledge,

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as a special case of scientific knowledge, is the self-evident intuitions of spatial

principles, which are formally known as the axioms of Euclidean geometry. It is

noteworthy that a philosopher so noted for his opposition to psychologism should place

such high value on self-evidence. Frege is explicit in his reliance on self-evidence to

ground logical laws. Yet few philosophers and interpreters have given notice to Frege’s

reliance on self-evidence. Wittgenstein was perhaps the first to challenge Frege’s

reliance upon self-evidence. He noted “it is remarkable that a thinker as rigorous as

Frege appealed to the degree of self-evidence as the criterion of a logical proposition.”

Susan Haack, Tyler Burge and Peter Hacker are three modem exceptions.

Haack has observed that self-evidence underlies Frege’s logicism;348 Burge who

maintains that Frege accepted the traditional rationalist account of knowledge of

primitive truths of logic and geometry.349 Hacker points to the significance of self

evidence in the logicism of Frege and Russell and their reliance upon it as the basis for

laws of logic.350 The standard interpretation of Frege rejects or ignores Frege’s reliance

upon self-evidence. The reason self-evidence as a foundational principle in Frege’s

thought is either rejected or ignored is that it conflicts with Frege’s avowed anti

psychologism and anti-subjectivism. In addition, the notion of self-evidence, as the

basis of knowledge, conflicts with the public view of knowledge stemming from

Wittgenstein, that has become the accepted view of twentieth-century analytic

philosophers.

348 Haack, Deviant Logic Fuzzy Logic, 29. 349 Burge, ‘Frege on Knowing the Third Realm" in Early Analytic Philosophy, 1. 350 Hacker, Insight and Illusion (Oxford: Oxford University Press, 1989), 42ff.

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Frege thought the laws of logic are certified directly by a “logical source of

knowledge."351 Frege gives the law of the excluded middle, as an example of a logical

law: “we can say that every thought is either true or false, tertium non .”352datur He

believes the law of identity is “completely self-evident."353 According to Frege, we may

also form self-evident propositions by stipulating the definition of a word or sign. “A

definition differs from all other mathematical propositions in that it contains a word or

sign which hitherto has had no meaning, but which now acquires one through it." And,

“once a word has been given a meaning by means of definition, we may form self-

evident propositions form this definitions, which may then be used in constructing proofs

in the same way in which we use principles."354 In a footnote to the preceding statement,

Frege goes on to explain that “What I here call a principle is a proposition whose sense

is an axiom."

One basic disagreement between Frege and Russell, as opposed to

Wittgenstein, was that Frege and Russell conceived of logic as an axiomatic science. In

this axiomatic respect, they both believed logic is similar to geometry. The theorems of

logic may all be deduced by rules of logical inference from basic axioms, or truths of

logic. The basic axioms are self-evident truths. In contrast, Wittgenstein held that self

evidence is irrelevant to logic “because language itself prevents every logical

mistake".355 According to Wittgenstein, “What makes logic a priori is the impossibility of

illogical thought.”

351 Frege, Posthumous Writings, 267ff. 352 Frege, Posthumous Writings, 186. 353 Frege, Posthumous Writings, 62. 354 Frege, Collected Papers, 274. 355 Wittgenstein, Tractatus, 5.4731.

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At the top of this Chapter, I distinguished three broad areas

circumscribing concerns dealt with in traditional epistemology. Frege was particularly

concerned with the last of the broad areas: the reliability of claims to knowledge. There

are three problems that Frege dealt with extensively throughout his writings involving

reliability of claims to knowledge. The first was the separation of the logical from the

psychological. The second was the separation of the subjective from the objective

content of knowledge. The third was the nature of logical inference. The first two of

these problems constitute the first methodological principle cited by Frege in the

Foundations of Arithmetic: “Always to separate sharply the psychological from the

logical, the subjective from the objective."356

This principle is directly concerns the reliability of claims to knowledge.

The nature of logical inference involves proofs of the justification of claims of scientific

knowledge. In the Preface of Begriffsschrift he argues that the apprehension of scientific

truth is associated with degrees of certainty.357 All scientific truths come to be

established by their being connected with other truths through chains of inferences.356

He separates the proofs involving truths of scientific knowledge which require

justification into two kinds: “those for which the proof can be earned out purely by means

of logic and those for which it must be supported by facts of experience."359 The first

kind is deductive, and the second kind refers to inductive proofs.

Frege is primarily concerned with deductive proofs, not inductive proofs.

Significantly, Frege considered induction to be based on the theory of probability, which

356 Foundations, x. 357 “Begriffsschrift”, Preface, in van Heijenoort (ed.) From Frege to Gddel, 5. 358 Ibid. 359 Ibid.

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presupposes aiithmetical laws and thus is ultimately grounded in logical laws. Hence,

for Frege, even induction is deductively based on logical truths.380 The separation of the

logical from the psychological does not mean there are truths, which can be

apprehended without the use of consciousness. Frege explicitly states that propositions

of the logical kind are compatible with the fact that they could not come to

consciousness in a human mind “without any activity of the senses. Since without

sensory experience no mental development is possible in the beings known to us, that

holds of all judgements."361

Hence, for Frege, all human knowledge, or truths, have a genesis in

human consciousness. How we arrive at a given proposition could differ in different

persons, depending on the particular cases, but all rationality is essentially dependent

upon consciousness. What he means by separating the logical from the psychological is

how the proof to be earned out in order to establish its certitude free of psychological

influences; thus securing the objectivity of claims of scientific knowledge. In a logical

proof, there can be no gaps or incursions of empirical intuition in the inferences. Logical

proofs thus are to be distinguished from other proofs, which rely upon psychologically

based empirical intuitions involving matters of fact.

The standard interpretation of Frege rejects the notion that objectivity

rests upon consciousness of the subject. For example, Dummett claims that:

objectivity is in Frege’s philosophy a type of ontological claim, that of independence of any conscious subject. We may therefore look to Frege's assignment of objectivity to ascertain his ontological views: since thoughts, logical objects, and concepts are all of them objective, they can

380 Foundations, §10. 361 Begriffsschrift, ibid.

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none of them be identified with ideas, and so must form distinct ontological categories.382

However, Dummett’s claim cannot be reconciled with Frege’s own words. Frege

says that what is objective is “something that is exactly the same for all rational

beings, for all who are capable of grasping it."363 What is objective is something

“capable of being the common property of several thinkers."384 Frege means that

what is objective is reason, and what is not objective is empirical. He

distinguishes between “what is objective and what is handleable or spatial or

real" in the Foundations of Arithmetic, §26.

Frege was concerned primarily with the nature of justification of scientific

knowledge, and in particular, mathematical knowledge. In Begriffsschrift, Foundations of

Arithmetic and The Basic Laws his concern was with the nature and ground of arithmetic

knowledge, as a category of mathematical knowledge. Logic is a tool of research, or

proof-theoretic methodology, for Frege, and the laws of logic are the self-evident

principles by which logical reasoning proceeds in order to arrive at truths of scientific

knowledge. It was never his intention to make logic the foundation for philosophy, and

Frege never questioned the traditional foundational status of epistemology within

philosophy. He envisioned the use of his logical ideography as a tool to establish the

validity of proofs in the foundations of differential and integral calculus, and to geometry.

Once the validity of proofs in geometry were established, he believed that his logical

ideography could be extended even to proofs in the theory of motion, mechanics and

362 “Objectivity and Reality in Lotze and Frege” in Frege and Other Philosophers, 97-125. 363 Posthumous Writings, 7. 364 ‘On Sense and Reference" in Translations of the Philosophical Writings of Gottlob Frege.

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physics.385 Thus, Frege equates the justification of ail scientific knowledge with the

deductive rigor of logical proof grounded in self-evidence.

Frege’s effort to derive mathematical truths from logical laws is essentially

a research program into the source, or epistemologica! presuppositions, of mathematical

knowledge “in order to provide it with the most secure foundation."366 Logic is the tool of

his research. The epistemological presuppositions of mathematical knowledge

concerned Frege throughout his career. Though his logicist program was derailed by

Russell’s paradox, he retained an interest in the epistemological foundations of

mathematical knowledge. As shown in his articles the “Sources of Knowledge of

Mathematics and the mathematical natural Sciences" (1924/25)387 and “A new attempt at

a Foundation for Arithmetic" (1924/25),388 Frege was concerned at the end of his career

with an essentially epistemological investigation into the sources of mathematical

knowledge. However, at the end of his career he looked to geometrical sources as the

foundation for arithmetic.

Frege’s interest in the logical justification of inferences is motivated

entirely by his concern to establish first the reliability of claims to mathematical certainty,

and eventually the reliability of claims to the other special sciences. By grounding

mathematical truths in logical laws Frege hoped to secure the claims for the truth of

propositions of mathematical knowledge from skeptical challenge. Frege’s interest in

establishing a firm foundation for mathematical knowledge is part of a larger effort to

overcome skeptical challenges against claims for the truth of scientific knowledge in

388 Frege, Begriffsschrift in van Heijenoort, 7. 386 Frege, Begriffsschrift in van Heijenoort, 5. 387 Frege, Posthumous Writings, 267-74. 388 Frege, Posthumous Writings, 278-81.

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general. Frege confirmed his larger aim in Begriffsschrift where he envisions the

application of his logical theory and ideography to not only higher mathematics and

geometry, but also to the theory of motion, mechanics and physics.369 In short, Frege’s

epistemological views are essentially rationalistic.

Metaphysical and Epistemological Dualism

Metaphysical dualism is the thesis that there exist only two distinct

substances. This thesis originates with Descartes, and is the fundamental metaphysical

distinction that underlies all of modem thought since Descartes. Thinkers since

Descartes have tried to give an account of the relation between extensio and cogitatio.

Frege is committed to metaphysical dualism. In the same way that Descartes, and most

thinkers following him, recognized only two kinds of things: mind, intellectual or thinking

things, and material things which pertain to extended substance or body,370 Frege too

recognized two basic kinds of things. There is mind, or the mental activity and capacity

existing in persons to cognize, or ‘grasp’ in Frege’s term, and there are the basic objects

the mind has the capacity to grasp. Frege extends objects of cognition to include logical

concepts and objects, as well as physical objects. However, despite this distinction, all

objects, whether logical or physical, depend on representations of mind. Thus,

everything for Frege, like Descartes, is essentially either psychologically subjective or

objective. Metaphysical dualism is the underlying presupposition of the philosophy of

both Descartes and Frege.

388 Frege, Begriffsschrift, in van Heijenoort, 7. 370 Descartes, Ibid., 208.

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It might be objected that, for Frege, both concepts and objects are

‘objective’. However, for Frege the terms ‘object1 and 'concept' are technical terms, by

which Frege means ideas belonging to logic and which are objective in Frege’s technical

sense, and not ideas belonging to psychology, and, therefore, subjective in his technical

sense. Frege developed these technical terms to differentiate between subjective and

objective ideas to avoid the confusion stemming from Kant’s use of the term ‘idea’ in

both the subjective and objective sense.371 Whether they are subjective or objective in

Frege’s technical terminology, they are nonetheless essentially psychological notions,

since for us to have access to objective ideas, even in Frege’s technical use of the term,

we must be able to grasp an objective idea through the conscious awareness of mind.

Frege’s concept-object terminology clearly stands within the tradition of

Cartesian dualism. However, Frege is not concerned with providing an account of the

duality of substances, nor is he concerned directly with providing an account of

cognition. Frege is concerned with providing an account of the objectivity of the logical

relations between concepts and objects of cognition, which may be either physical

objects or objective mental representations, such as logical and abstract objects. Frege

has simply further refined the notion of representation, or ideas (or Vorstellung, to use

Kant’s term), as used in the tradition to differentiate subjective ideas from objective

ideas. In fact, objective concepts are the ’foundation-stones’ (together with

equinumerous relations) upon which he built his logical theory.372 Logical objects, or

abstract objects of cognition, are of particular interest to him, as they constitute the

fundamental subject matter, i.e. objects, of mathematics and logic.

371 Frege, Foundations, 37. 372 Frege, Basic Laws, 32.

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A theory of concept may be either viewed cognitively or ontologically.

Concepts are generally viewed by contemporary thinkers part of the theory of mind, as it

concerns thinking things, and epistemology, as it concerns what it means for thinking

things to be possessed of knowledge. The theory of object, or objects, is part of the

theory of metaphysics or ontology, as it concerns what things exist in the world. An

adequate theory of concepts must be able to give an adequate account of how concepts

are capable of picking out objects. Frege's theory of concepts attempts to give just such

an account.

Epistemological dualism is the thesis that we possess more direct access

to, and a clearer and more distinct idea of, our own minds than we do the external

physical world.373 This thesis can be fundamentally idealistic if it is interpreted to mean

that all we are aware of are representations of things, or ideas, and that nothing exists in

reality other than ideas or what is constructed of ideas. Idealism carries with it the

epistemological claim that each of us has only direct access to our own minds. From

this idealist standpoint, appearances given to us in the form of mental representations

are not distinguishable from separately existing things in reality. Realism is committed to

the view that there are actually things existing in the world outside of our own minds.

Such things that exist for the realist are physical objects. The extreme realist holds that,

in addition to physical things, there exist non-physical things, such as numbers and

relations. This view, known also as Platonism, is often attributed to Frege. I will argue

that the view of Frege as Platonist is incorrect.

373 Hamlyn, Metaphysics, 14.

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The Cartesian presupposition underlying Frege’s thought commits him to

only one possible relation between the intellect, or concepts, and objects of cognition.374

The intellect contributes or actually represents, through the formation of concepts and

thoughts, to the manner in which the objects reveal themselves as products of cognition.

Concepts, thoughts, relations, or eternal truths are constructed by the mind in the act of

thinking and grasping. All human minds, in virtue of their being human, have the innate

capacity to construct or grasp such ideas. Frege never provides a complete account of

how it is possible for the mind to form concepts or to ‘grasp’ thoughts, or for that matter,

to have access to abstract or logical objects. Frege is, however, fully committed to the

presupposition that minds have the innate capacity to do so.

The alternate Platonist view is that the intellect is a passive receptor of

objects of cognition that reside in a separately existing realm outside of the mind which

somehow reveal themselves to the intellect. In this view the intellect plays no role as

receptor of objects of cognition. This sort of relation between mind and objects of its

cognition is fundamental for Platonism. Abstract entities, e.g. truths, values, numbers,

etc., exist in a separate realm, and are somehow revealed to us in a form of internal

vision, or introspection. Frege often seems to vacillate between a Platonist version and

a Cartesian version of the relation between concepts and objects. However, he is tacitly

and firmly committed to the Cartesian outlook in which the mind is actively involved in,

constructs, or contributes in some way to, its representations precluding a Platonist view

of language, logic and mathematics as a metaphor of their objectivity.

374 Stanley Rosen, The Limits of Analysis (New Haven: Yale, 1985). 19. I am indebted to for the structure of this argument, but differ with him in the inferences I draw relating to Frege.

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The Platonist interpretation of Frege's view of language, logic and

mathematics to secure their objectivity must be ruled out on grounds of his acceptance

of dualism. Though Frege vehemently rejects psychologism, he implicitly accepts the

representational conception of mind. Frege’s claims for the non-subjective status of

thoughts, logical and abstract objects in order to secure their objectivity must be seem

as metaphorical. Since Frege never provides an adequate account of how it is possible

for the mind to access the realm of thoughts, as objective entities, there is a resulting

ambiguity in Frege’s arguments for the objectivity of thoughts, which is never adequately

reconciled.

From the traditional Cartesian stand-point there is no problem concerning

the communicability of thoughts. Thoughts (including, logical objects and abstract

objects) are ‘objective’ in the sense that they simply can be grasped by one or more

persons. However, they are still human mental constructions, or ’objective’ mental

representations, having no actual existence separate from the act of thinking by some

intellect or another. The reason the same thought can be grasped by one or more

persons is that idealism presupposes the very thing that it seeks to deny - the public

frame of reference.375 Despite its seeming egocentric, even soiipsistic, stand point,

epistemological dualism simply assumes that anything which holds for the subject also

for other persons.

From this perspective, Frege implicitly sees the mind as the ‘mirror of

nature'. The mind is the repository of images and conceptual representations of objects.

From this perspective, language becomes meaningful by being associated with

conceptual representations, without which there could be no communication. This is a

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conceptualist view that makes meaningful only those objects of thought that are held

before the mind. On this view of Frege, he is not a Platonist; rather, he is a

conceptualist.

Eptstemoloqtcat FoundatlonaHsm

Frege held a foundationalist view of human knowledge, a view that is also

found in the epistemology of Aristotle and Descartes. Descartes and Frege believed

that human knowledge is made secure from skeptical doubt if grounded in necessary

truths. Descartes did not always clearly distinguish necessary truths from intuition.

Frege wanted to ground mathematical knowledge in the necessary laws of logic, but he

held that geometry was grounded in intuitive truths. It is implicit in his thought that he

held a similar view of the grounding of causal, or natural, laws in synthetic a priori

knowledge. Aristotle’s, Descartes' and Frege's epistemological foundationalism was

distinguished by their acceptance of a limited class of basic instances of knowledge, or

truths, with privileged epistemic status. Foundationalist theories of knowledge exhibit a

two-tiered structure; some truths are basic, or foundational; others are non-foundational,

or inferential. Frege recognized the priority of basic truths (referring to them as axioms)

and the derivability of the latter (referring to them as theorems) in his axiomatized

system of proof designed to establish the validity of mathematical propositions. He was

concerned throughout his career in developing an axiomatic “gap-free” method of proof

in logic in order that non-foundational truths could be derived from basic truths.

375 Hamlyn, ibid.,16.

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Dummett has argued that Frege’s thought represents a revolutionary turn

in the history of philosophy; his emphasis on logic, and the primacy he gave to logical

laws, must be seen as a return to views espoused by the Scholastic thinkers who gave

central place to metaphysics and logic. Frege's philosophy is a continuation of

Descartes’ foundational view of human knowledge. They both rejected the obscurities of

the Scholastic metaphysical and logical principles, which he diagnosed as the “putting

forward as principles things of which they did not possess perfect knowledge."378 The

failure of Scholasticism was that it did not take seriously the need to push philosophical

inquiry back to clear and self-evident starting points. An example of Scholastic obscurity

often cited by Descartes was the explanation given of why bodies fall; ‘they possess the

quality of gravity, or heaviness’ or simply, ‘it is the nature of earthly matter to fall’.

Descartes proposed adoption of a new method of acquiring “perfect knowledge" defined

as knowledge deduced from first causes." According to Descartes, if we are to acquire

“perfect knowledge - and it is this activity to which the term ‘to philosophize strictly refers

- we must start with the search for first causes or principles." 377 By first causes and

principles he meant simple and self-evident starting points. According to Descartes,

“The whole method consists entirely in the ordering and arranging of objects on which

we must concentrate our mind’s eye; we first reduce complicated and obscure

propositions to simple ones, and then, starting with the intuition of the simplest ones of

all, try to ascend through the same steps to the knowledge of all the rest.”378

378 Descartes, Principles of Philosophy in The Philosophical Writings of Descartes, vol. i., eds. J. Cottingham, R. Stoothoof, and D. Murdoch, (Cambridge: Cambridge University press, 1985),182. 377 Ibid, 179. 378 Descartes, Rules for the Direction of the Mind in The Philosophical Writings of Descartes, vol. i., eds. J. Cottingham, R. Stoothoof, and D. Murdoch, (Cambridge: Cambridge University press, 1985), 20.

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The Scholastics studied the logical principles of the syllogism, which

originated with Aristotle. But the logic of the syllogism is closely related to the

metaphysics of Aristotle. Dummett’s association of Frege with the logic of the

Scholastics, tied as it was to Aristotle's syllogistic logic, is misleading and is in serious

need of emendation. As is well known, Frege rejected the traditional syllogistic logic of

properties, and replaced it with a modem logic based on relations.

Frege did hold a foundational view of knowledge originating in Aristotle’s

Posterior Analytics, distinguishing the ultimate starting-points of science. Like Arisotle,

these include the axioms - the propositions, which are true of anything whatever, such

as the Law of Contradiction, the Law of the Excluded Middle, and 'if equals are

subtracted from equals the remainders are equals' which I traceable to Euclid's 'common

notions’. Aristotle was willing to admit conventional understanding as an acceptable

starting point. But the extreme modem formulation of foundational knowledge, as self-

knowledge, is found in Descartes’ Meditations.379 In Mediations Descartes says, there

are some instances of knowledge, which we can hold to be necessary truths because

they are self-evident. Such a ‘truth’ is exemplified in Descartes dictum: "I think, therefore

I am", or cogito ergo sum in its Latin form, also known simply as Descartes' cogito. The

very act of thinking confirms that “I exist". This dictum is open to criticism for its

circularity and that it claims too much. It is circular if, as in Descartes formulation, in

order to gain certain knowledge of the external world, we must first assume the

existence and benevolence of God as guarantor of the certainty of our knowledge.

379 Moser, P.K., “Foundationalism" in The Cambridge Dictionary of Philosophy, 276-8.

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Putting circularity aside, Descartes' formulation of the cogito is not simply

a psychological question. It is reducible to ‘It is physiologically impossible to doubt that

one exists, if one thinks.’380 Thus, It is a logical question: ‘I think’ logically implies that ‘I

exist’. He wants to claim that ‘I think, therefore I am’ involves a logical certainty. Ayer

has pointed out that ‘I think' and 'I exist’ are not truths of logic. The logical truth is that 'I

exist if I think.' Ayer claims that what Descartes’ argument does is not make the

existential claim that he or anyone else knows that anything exists; it simply makes the

logical point that one sort of statement follows form another.381

But Frege makes an argument with striking similarity to Descartes'

aprioristic methodology in his essay “Thoughts". Frege says:

Not everything that can be the object of my acquaintance is an idea. I, being owner of ideas, am not myself an idea. Nothing now stops me from acknowledging other men to be owners of ideas, just as I am myself. And, once given the possibility, the probability is very great, so great that it is in my opinion no longer distinguishable from certainty. Would there be a science of history otherwise? Would not all moral theory, all law, otherwise collapse? What would be left of religion? The natural sciences too could only be assessed as fables like astrology and alchemy. Thus the reflections I have set forth on the assumption that there are other men besides myself, who can make the same thing the object of their consideration, their thinking, remain in force without any essential weakening.382

Thus, Frege, in “Thoughts,” makes exactly the same sort of claim found in

Descartes’ Cogito. Frege affirms the certainty of the existence of an independent

and external material world distinguishable from the thinking subject, yet

apprehensible through the self-evident ideas, or representations of the thinking

subject.

380 Ayer, The Problem of Knowledge, 45. 381 Ayer, The problem of Knowledge, 45. 382 Frege, “Thoughts" in Collected Papers, 367-8.

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Descartes built his entire theory of knowledge on the cogito. Self-evident

truths, for Descartes, are clear and distinct ideas. “I call a perception ‘clear’ when it is

present and accessible to the attentive mind • just as we say that we see something

clearly when it is present to the mind’s gaze and stimulates it with a sufficient degree of

strength and accessibility. I call a perception 'distinct' if, as well as being clear, it is

sharply separated from all other perceptions that it contains within itself only what is

clear."383 ‘Clear’ and ‘distinct’ ideas are the bases for eternal truths, which, so long

as they are entertained, clearly and distinctly, cannot be doubted, and have no existence

outside of thought.384 Eternal truths include propositions, such as: 'It is impossible for the

same thing to be and not to be at the same time,’ ‘He who thinks cannot but exist while

he thinks’, and ‘Nothing comes from nothing.’385 Eternal truths, for Descartes, are so

basic that they are self-evident to the ‘natural light of reason'. He means by natural light

of reason a quality that is innate in human reasoning.

In Frege there is the comparable cognitive notion of 'grasping a thought

and seeing at once that it is true.' The capability of grasping a thought is a natural

faculty of human reasoning, just as having clear and distinct ideas was a natural faculty

of human reasoning for Descartes. Frege believed that some truths, or axioms, are

basic, and others are provable from the basic ones by a chain of inferences.

"Traditionally, what is called an axiom is a thought whose truth is certain without,

383 Descartes, Principles of Philosophy, in The Philosophical Writings of Descartes, eds. J. Cottingham, R. Stoothoff, and D. Murdock. (Cambridge: Cambridge University Press, 1985), 207- 8. 384 Descartes, Principles of Philosophy, 208. 385 Descartes, Principles of Philosophy.

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however, being provable by a chain of logical inferences.”386 Frege divided all truths that

require justification into two kinds: “...those for which truth can be carried out purely by

means of logic and those for which it must be supported by facts of experience."387

Ultimately, all truths, whether logical or those that must be supported by empirical

evidence, are derivable from mental activity. For Frege goes on to say: “But that a

proposition is of the first kind is surely compatible with the fact that it could nevertheless

not have come to consciousness in human mind without any activity of the senses.

Since without sensory experience no mental development is possible in the beings

known to us, that holds of all judgments.”388

Frege's epistemology is in essential respects the same as that of

Descartes. Descartes and Frege held that rational knowledge is grounded in self-

evident truths of reason. According to Frege, epistemology is concerned with the nature

and grounds for truths already recognized by us, and logic is concerned with the chain of

problem-solving, or the laws of inference, in the same manner as Descartes' analytical

method. In an unpublished essay that he wrote between 1879 and 1891, Frege

explains:

Now the grounds which justify the recognition of a truth often reside in other truths which have already been recognized. But if there are any truths recognized by us at all, this cannot be the only form that justification takes. There must be judgments whose justification rests on something else, if they stand in need of justification at all.

And this is where epistemology comes in. Logic is concerned only with those grounds of judgment which are truths. To make a judgment because we are cognisant of other truths as providing justification for it is

386 Frege, On the Foundations of Geometry and Formal Theories of Arithmetic, trans. E.-H. W. Kluge (New Haven: Yale University Press, 1971), 23. 387 Frege, Begriffsschrift in van Heijenoort, 5. 388 Ibid.

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known as inferring. There are laws governing this kind of justification, and to set up these laws of valid inference is the goal of logic.389

Thus for Frege, epistemology concerns the grounds for the recognition

foundational truths, while logic concerns the laws of valid inference that give us the

justification to make judgments, or inferences, concerning second-tier truths that rest on

known foundational truths. Epistemology is concerned with the ultimate source, or

foundational truths. What Frege meant by ‘logic’ is laws of inference, or deductive logic,

which could be used to infer additional truths from foundational truths. Frege’s interest

in logic is to provide a gap-free logical methodology to guarantee certainty of inferences

drawn from foundational truths. In this sense Frege’s logic is an epistemology tool for

mathematical or scientific investigation.

Logic, or ‘deductive logic,' is concerned with the validity of inferences

whose premises cannot be true without the conclusion being also true. This is in

contrast to inductive logic whose premises can be true even if the conclusion is false.

Logic cannot be seen as replacing epistemology as the ‘foundation’ of philosophy. Logic

is concerned with the deductive validity of inferences of second-tier non-foundational

knowledge; and non-foundational instances of knowledge are themselves grounded in

foundational instances of knowledge. Descartes and Frege both adhere to the

foundational view of knowledge, and share a confidence in a deductive process of

reasoning that enables us to move step-by-step from basic foundational knowledge to

more complex deductively valid conclusions.

389 Frege, ‘ Logic" in Posthumous Writings, 3.

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Mathematico-Deductive Methodology

Frege and Descartes both believed that deductive methods modeled on

mathematics could secure the reliability of claims to knowledge. To be sure, Descartes

gave central place to epistemology. But logic held an equally important place as a

methodology and tool for logical inference in Descartes’ epistemology. Logic did not

vanish with the demise of scholastic philosophy, and the rise of Cartesian epistemology,

as Dummett and Kenny would have us believe. Logic to played a central role in modem

philosophy after Descartes, and in the rationalist tradition. There was indeed a decline

in the respect to which philosophers held the classical logic due to its association with

the Scholastic philosophy. But logic did not cease to exist with the advent of modem

philosophy. Descartes indeed challenged authority of Scholasticism, rejected many of

its metaphysical assumptions, questioned the legitimacy of the then traditional form of

logic, and gave central place to epistemology in his Meditations on First philosophy,

Rules for the Direction of the Mind and Discourse on the Method, and Principles of

Philosophy. Descartes never discarded logic in the deductive sense; rather, it was the

presuppositions of Aristotelian logic that Descartes challenged. In the his Rules for the

Direction of the Mind, He says:

...we should realize that, on the basis of their method, dialecticians are unable to formulate a syllogism with a true conclusion unless they are already in possession of the substance of the conclusion, i.e. unless they have previous knowledge of the very truth deduced in the syllogism. It is obvious therefore that they themselves can learn nothing new from such forms of reasoning, and hence that ordinary dialectic is of no use whatever to those who wish to investigate the truth of things.390

380 Rules for the Direction of the Mind, 36-7.

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According to Descartes, the syllogism was useful to systematize only the knowledge we

already possess, for what is stated in the conclusion of the syllogism is already stated

implicitly in the premises. The syllogism could only tell us something that we already

know; it is useless for the discovery of new knowledge. Descartes rejected the

categorical-deductive logic of Scholastic, or traditional Aristotelian logic, not the

usefulness of deduction as a method of scientific discovery. Thus, it is only in the

restricted sense of the traditional categorical-deductive logic that Descartes could be

said to have discarded logic. Descartes, like Frege, wanted to overcome the limitations

of Aristotelian syllogistic logic.

In this sense Frege, too, may be said to have discarded the traditional

categorical-deductive logic. Frege rejected only the restrictive adherence to a subject-

predicate logical form, and related quantification inadequacies. Both Descartes and

Frege advocated the replacement of the traditional categorical-deductive logic with the

hypothetical-deductive method. Despite criticism of Descartes and others, like Ramus

and Bacon, who also denounced Aristotelian logic as useless, it remained part of the

philosophical syllabus. It continued to shape metaphysical, logical and epistemological

concepts of philosophers until Frege's invention of the Concept-Notation at the end of

the nineteenth century. Frege’s crucial step was the further advance of analyzing

propositions into function and argument form, thus fully replacing Aristotelian syllogistic

logic’s reliance on subject-predicate analysis. The underlying framework of Frege’s

logistics remains hypothetical-deductive.

For Descartes, like Frege, mathematics is the model of a deductive

method. For both, the mathematical method consisted in breaking down a problem into

its simplest essentials, until we arrive at propositions that are simple and self-evident

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enough to serve as reliable starting-points, and from which the answers to more complex

problems may be deduced.

Descartes emphasized the importance of deductive inference, and

regarded arithmetic and geometry as models of reasoning in which there was hope of

certainty.391 The successes of mathematics and mathematical physics encouraged

Descartes to believe that truths in other fields of knowledge were obtainable though

deductive method. His expectations for a deductive methodology are made clear in his

Discourse on the Method:

The long chains composed of very simple and easy reasonings, which geometers customarily use to arrive at their most difficult demonstrations, had given me occasion to suppose that all the things which can fall under human knowledge are interconnected in the same way. And I thought that, provided we refrain from accepting anything as true which is not, and always keep to the order required for deducing one thing form another, there can be nothing too remote to be reached in the end or too well hidden to be discovered. I had no great difficulty in deciding which things to begin with, for I knew already that it must be with the simplest and most easily known. Reflecting, too, that of all those who have hitherto sought after truth in the sciences, mathematicians alone have been able to find any demonstrations - that is to say, certain and evident reasonings - 1 had no doubt that I should begin with the very things that they studied. From this, however, the only advantage I hoped to gain was to accustom my mind to nourish itself on truths and not to be satisfied with bad reasoning.392

Descartes, like Frege, saw deductive logic as a tool of research and the paradigm of

scientific methodology. For both Descartes and Frege, logic is a scientific method for

deducting one truth from another truth. Frege shares with Descartes the rationalist

mistrust of traditional forms of logic, a call for the reform of logical principles, the

preference for deductive methods of proof, the use of logic as a tool of scientific

research.

391 Rules for the Direction of the Mind.

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Descartes envisioned the application of mathematics, and mathematical

principles, as a methodology for everything within the scope of human knowledge. For

him, mathematics made use of the most general and simplest notions that could serve

as a starting point for any scientific study:

The exclusive concern of mathematics is with questions of order or measure, and it is irrelevant whether the measure in question involves numbers, shapes, stars, sounds or any other object whatsoever. This made me realise that there must be a general science which explains all the points that can be raised concerning order and measure, irrespective of the subject matter, and that this science should be termed mathesis universalis - a venerable term with a well-established meaning.393

By mathesis universalis Descartes intends a universal or general science with

application to other branches of science. Frege's Begriffsschrift Is a logical calculus

modeled on the conception of a universal mathematical language. The concept for the

logical calculus is derived from Leibniz’s lingua characterica and calculus ratiocinatur,

which in turn are directly derived from Descartes’ conception for a mathesis universalis.

Axiomatization of Knowledge

The core of Descartes method bears close similarity to Frege’s method.

For Descartes, and for Spinoza following him, as well as Frege, the paradigm of

scientific method was the axiomatization of knowledge represented by the methodology

of Euclid’s Elements on the Geometry. Axiomatic method means the formalizing of a

subject matter by using only the methods of formal logic in order to derive the truths of

the subject from a list of undefined terms and a list of axioms. Spinoza’s Ethics and

Principles of Cartesian Philosophy exemplify a geometrized style. In the latter work,

Spinoza uses a ‘synthetic’, or axiomatic and geometric style, i.e. progressing away from

392 Discourse on Method, 120.

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the axioms of a science to the desired result. The ‘synthetic’ method contrasts with

‘analytic’, deductive method progressing in the opposite direction away from a given

proposition until we reach the axioms that generate it.394 Spinoza gave preference to the

geometric method working from axioms, which were self-evident. In Spinoza’s view, all

truths would be self-evident to a perfect being; self-evidence in humans is relative to the

degree of attentive reflection on the concepts involved.385 For Spinoza, it is the purified

intellect that arrive at definitions which capture the essence of things; in the same way,

for Descartes, knowledge is based on intuition of eternal truths.

For both Descartes and Spinoza, self-evidence provides the foundation of

a deductive system. In their rationalism, we find the beginnings of a movement toward

the unification of knowledge through axiomatization that is found later in Frege. The

axiomatization of mathematics, in which all of mathematics is deduced from a few simple

concepts, is the ‘Cartesian ideal’398, the very model of a rationalist system. The

development of logic as a discipline expanding into mathematics is clearly part of the

geometrizing of knowledge, which began with Descartes, Spinoza leading to eventually

to Frege. Frege offers us a similar axiomatic account of how logical proofs in

mathematics ought to be performed in “Logic in Mathematics” (1914):

Now we make advances in mathematics by choosing as the premises of an inference one or two propositions that have already been recognized as true. The conclusion obtained from these is a new truth of mathematics. And this can in turn be used, alone or together with another truth, in drawing further conclusions. It would be possible to call each truth thus obtained a theorem. But usually a truth I only called a theorem when it has not merely been obtained as the result of an inference, but is itself in turn used as a premise in the development of the

393 Descartes, Rules for the Direction of the Mind, 19. 394 Cottingham, The Rationalists (Oxford: Oxford University Press, 1988). 395 Cottingham, 53. 396 Passmore, A Hundred Years of Philosophy, 149.

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science, and that not just for one but for a number of inferences. In this way chains of inferences are formed connecting truths; and the further the science develops the longer and more numerous become the chains of inference and the greater the diversity of the theorems.

But one can also trace the chains of inference backwards by asking from what truths each theorem has been inferred. As the diversity of theorems becomes greater as we go forward along the chains of inference, so, as we step backwards, the circle of theorems closes in more and more. Whereas it appears that there is no limit to the number of steps forward we can take, when we go backwards we must eventually come to an end by arriving at truths which cannot themselves be inferred in turn from other truths.

In “Logic and Mathematics" Frege shows that he closely followed the

rationalist principles of axiomatization, which originated in modem philosophy with

Descartes and his rationalist followers like Spinoza, in developing his own systematic

proof theory for application to mathematical problems. Like the method of Descartes

and Spinoza, in Frege’s system, the starting points, or axioms, are recognized self-

evident truths from which new truths are derivable.

The rationalist methodology followed by Descartes, and later in Spinoza,

is set forth in Descartes’ Rules for the Direction of the Mind and in his Discourse on

Method consisting of three fundamental principles are aptly described by John Schuster:

1. All rationally obtainable truths consist in a network of deductive linkages, and this is the meaning of the unity of the sciences.

2. As rational beings, humans possess two divinely given faculties for the attainment of truth: the power of intuiting individual truths, and the power of deducing valid links between them.

3. A single mind, exercising intuition and deduction, could in principle traverse the entire unity of knowledge.397

397 Schuster, “Whatever should we do with Cartesian Method?” in Essays on the Philosophy and Science of Rene Descartes, ed. S. Voss (Oxford: Oxford University Press, 1993), 200-1.

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Objectivity of Knowledge and Anti-Psychologism

One of the central problems that concerned Frege was the objectivity of

claims to knowledge. The theological outlook of the Scholasticism that dominated

philosophy prior to the seventeenth century provided the necessary metaphysical

objectivity for philosophical problems. Descartes' revolution which made epistemology

at the center of philosophy placed greater certainty in a person’s subjective experience

and self-evidence than in the external world, or in ontological sources, outside of a

person’s own ideas. After Descartes, knowledge was viewed as subjective in nature

and consisting of relations of ideas in the mind.

The subjective philosophical outlook was shared by both Continental

rationalists and British empiricists. It was due, in part, to the philosophical importance

placed on the subjectivity of knowledge by Descartes’ philosophical revolution, and, in

part, to the emphasis on sense experience connected with the revolution in scientific

methods.

It should not be assumed, however, that objectivity was totally lacking

after Descartes. The problem of objectivity was long recognized in the philosophical

tradition. To secure the objectivity of a concept, ‘objective reality’ was depicted or

represented by an idea in the mind. To exist objectively in the intellect simply meant to

exist representatively in the intellect.398 Similarly, prior to Descartes, the Scholastics

made a fundamental distinction between esse extra animam and esse in anima.399 To be

in the mind was not at all to be a subjective quality of some particular mind, but simply

398 Cottingham, 200. 399 Angelelli, 69.

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means to be in front of the mind as an ob-jectum.*00 However, The problem of objectivity

did not become a central concern for philosophy until the nineteenth century. That

Frege was concerned with questions of objectivity does not place him outside the post-

Cartesian tradition. On the contrary, Frege is deeply entrenched in a tradition that had

long since recognized the need for objectivity. However, Frege’s interest in the problem

of the objectivity of claims to knowledge is heightened by the renewed interest given to

objectivity in the later nineteenth century, and to the Neo-Kantian framework in which the

validity of knowledge is secured by its objectivity.

Though Descartes and Frege share a preference for a deductive

methodology, and both ground their deductive systems in basic, eternal or self-evident

truths, an important theoretical problem potentially divided Frege and Descartes. That

problem was the extent to which inferences are based on intuition. For Descartes,

inferences operate best and most soundly when based on intuition. For Frege,

inferences are most sound when all vestiges of intuition can be eliminated from

deduction. For Frege, the central question became: How to separate the logical from the

psychological, the objective from the subjective? While for Descartes, the distinction

between the subjective and objective content in inferences rests upon the relation of

subjective ideas within the mind and objective ideas before the mind. However, all ideas

are essentially in the mind, and may refer discriminately to concepts or objects, real or

abstract; and truths are given to intuitively. Frege distinguished the mental, or

subjective, aspect of a judgment from its objective content. He saw that logical

operations could be made to justify taking rules of inference as objectively valid.

400 Ibid.

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Frege challenged the subjectivist tradition’s inability to explain the

essentially objective nature of required of mathematical knowledge. Frege’s problem

was that mathematical ideas are formulated in subjective terms that neither provided a

firm foundation for mathematical knowledge, nor secured for it the required objectivity to

guarantee its truths. A fundamental aspect of Frege's problem was the inability of

subjective tradition to explain the objectivity of human knowledge in general; and the fact

that human knowledge can be communicated and understood by anyone other than the

subject. Ironically, despite his avowed anti-psychologism, and his ceaseless efforts to

remove subjectivity from mathematics, logic and language, Frege was “shackled by an

assumption endemic among his contemporaries and predecessors."401 That assumption

was that traditional Cartesian epistemology and its attendant problematic. Frege

“inherited a Cartesian picture of judgment as an epistemically private mental act, and of

assertion as an act expressing or manifesting such an act of judging."402 Frege never

adequately reconciled the distinction between the subjective acts of judgment and

logically objective thoughts. Though he argued for the objectivity of thoughts, the

problem of how we are to grasp an objective thought without involving ourselves in a

subjective mental act is never fully explicated by him. Thus, the distinction is always

blurred, and Frege never really extricates himself from the Cartesian epistemological

perspective. Frege dealt with the problems of objectivity and anti-psychologism from the

outlook of late-nineteenth century Neo-Kantian philosophy.

401 Baker and Hacker, Frege: Logical Excavations, 39. 402 Ibid.

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Freges theory of judgment

Frege held a theory of judgment routed in the representational theory of

mind, which stems from Locke and Descartes. Moreover, as I have argued in this paper,

Frege rejected empiricism, and instead affirmed a rationalist foundation for his

epistemology. His philosophical outlook was shaped by late nineteenth century Neo-

Kantianism, as evidenced by the technical vocabulary borrowed from Kant’s critical

philosophy. Thus, on my alternative account, Frege’s theory of judgment is more closely

linked to rationalism and idealism than to empiricism and realism. This view of Frege

runs counter to the standard interpretation of Frege advanced by Dummett and his

followers.

The standard interpretation treats Frege's account of sense and reference

as primarily concerned with the philosophy of language and semantics rather than, as it

ought to be viewed, as an appendix to Frege's philosophy of mathematics. By giving

Frege’s writings on sense and reference central place in his exposition of Frege's

thought, it makes it appear Frege was more interested in semantics than mathematics.

In fact, a semantic account of proper names involves important problems that have

vexed twentieth century philosophers, but these questions do not motivate Frege's

interest in sense and reference. Frege intended his theory of sense and reference as an

analysis of problems in the philosophy of mathematics concerning the question whether

informative identity-statements can ever be regarded as logically true, or analytic. There

is no evidence that Frege was fundamentally concerned with the semantic account of

proper names, as has been maintained by Dummett and others who uphold the

'standard interpretation’ of Frege’s thought. The 'standard interpretation' lifts Frege's

thought out of its proper historical context within his philosophy of mathematics, and

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gives it center place as a modem philosophical problem in semantics and philosophy of

language.

The emphasis placed on Frege's theory of sense and reference by

Dummett and other analytic philosophers has resulted in the proliferation of Fregean

expositions centering on language. However, this preoccupation with linguistic issues,

while of special interest to other philosophers of language, misrepresents Frege's

thought. Frege was not primarily concerned with matters of language at all. He was

actually concerned with semantic problems important only in the context of scientific

knowledge, which for Frege meant primarily mathematics. He was motivated by

epistemological problems concerning the foundations of mathematical knowledge, and

the semantic problems he dealt with were due to his primary interests in mathematics.

Frege’s Theory of Judgement

My interpretation of Frege's theory of judgement owes much to David

Bell’s, Frege's theory of Judgement. Where I differ from Bell is that I do not agree with

his suggestion that Frege translated Kant’s transcendental-psychological investigation in

the Critique of Pure Reason into a semantico-ontological one.403 I maintain that Frege

largely agreed with Kant’s transcendental method. Frege, as was Kant, was concerned

not so much with the ontological status of transcendental objects, than with the mode of

our knowledge of objects in so far as this knowledge is to be possible a priori*0* Frege

wholly adopted Kant’s transcendental method for his own purposes - the investigation of

analytic a priori judgements of mathematical knowledge, including the possibility of

defining abstract objects of number derived from them as a special kind of act of

403 David Bell, Frege's Theory of Judgment (Oxford: Clarendon, 1979), 71. 404 Kant, Critique of Pure Reason, A12.

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cognition expressed as an identity. Frege accepts Kant’s analytic and synthetic

distinctions, and agrees with Kant that geometry is synthetic a priori knowledge, but

wants to establish the analytic character of mathematical judgments. That is what Frege

meant where he says in the Foundations of Arithmetic: “Kant obviously as a result, no

doubt, of defining them too narrowly - underestimated the value of analytic

judgments.”405

The theory of judgement is of central importance to Frege’s entire

philosophy, and thus of primary importance to his conception logic and mathematics.

Throughout his philosophical career he was concerned to produce a theory of discursive

mental activity.406 His rejection of psychology has obscured his real concern with mental

activity. Frege was motivated to examine the working of discursive mental activity

because of his logico-mathematical investigations. He employed the logical tools to

solve essentially epistemological problems involving the foundations of mathematics.

Ironically, the significance of the contributions he made to the development of logical

tools distracts from his contribution to epistemology.407 It must be remembered why he

was motivated to invent the logical tools in the first place. He employed the logical tools

in the investigation of the logical foundations of mathematical knowledge.

Frege subscribes to a theory of judgement that derives directly from Kant.

Judgement provides the matrix for Kant’s entire philosophy, and each of the Critiques

concerns the analysis of a particular class of judgements: The Critique of Pure Reason

with theoretical judgements, the Critique of Practical Reason with practical judgements,

and the Critique of Judgment with aesthetic and teleological judgements. Frege is not

405 Frege, Foundations of Arithmetic, 99. 406 Bell, 11.

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concerned with practical, aesthetic or telelogical judgements, but confines his interest to

theoretical judgments of scientific, particularly mathematical knowledge.

At the core of the Critique of Pure Reason are Kant’s claims for

theoretical judgments: "we can reduce all acts of the understanding to judgments,” and

“all judgments are functions of unity among our representations."408 Kant applies a

technical term ‘function’ to describe the unity of the act of thinking. This use by Kant of

the term ‘function’ must have given Frege the notion of assimilating the mathematical

functions to concepts. “By ‘function’ I mean the unity of the act of bringing various

representations under one common representation."409

According to Kant, “Thought is knowledge by means of concepts.”410

Thinking is a form of cognition. Kant distinguishes the cognition of two kinds of objects:

“I must be able to prove its possibility, either from its actuality as attested by experience,

or a prion by means of reason." But “I can think whatever I please, provided only that I

do not contradict myself.”411 Not individual concepts, “but concepts, as predicates of

possible judgments, relate to some representation of a not yet determined object."412

Frege’s use of the term ‘context principle’ describes perfectly what Kant

meant by “Thought is knowledge by means of concepts.” Frege often said that what

distinguishes his logic from Leibniz was that he started, not from concepts, but from

judgements. When Kant said “thought is knowledge by means of concepts", he meant

concepts as predicates of possible judgments. Kant used the term ‘concepts’ in a wider

407 Ibid. 408 Kant, Critique of Pure Reason, A69/B94. 409 Ibid., A69/B93. 410 lbid.,A69/B94. 411 ibid., Bxxvi. 4,2 Ibid., A68/B94.

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sense than Frege's technical sense. Kant’s concepts of the understanding are

equivalent to Frege’s act of judgment, which for Frege is a psychological term. While for

Frege, ‘concept’ is a logical term dependent upon ultimately representations for its

sense.

The Context Principle

The context principle is one of the central doctrines unifying Frege’s

philosophy of logic and mathematics. The context principle, together with the Leibnizian

notions of a perfect language and the reduction of arithmetic and other sciences to logic,

constitute the guiding doctrines for his development of the Concept-Script.413 The context

principle was famously articulated by Frege in the Foundations of Arithmetic, where he

says: “never to ask for the meaning of a word in isolation but only in the context of a

proposition”.414 Simply stated, the context principle is the doctrine of the priority of

judgments over concepts. This principle underlies Frege's logical language,415 and

embodies his methodological strategy for conceptual analysis.416 The doctrine expresses

one of the many Kantian elements in his thought.417

The origin the context principle is traceable directly to Kant. Kant first

explicated the context principle in a pamphlet entitled The Mistaken Subtlety of the Four

Syllogistic Figures (1762). The relevant passage is quoted in Kemp Smith’s

Commentary to Kant’s Critique of Pure Reason?18

413 ibid. 414 Frege, Foundations of Arithmetic, x. 415 Currie, Frege: An Introduction to His Philosophy, 19. 416 Currie, 149, 417 Sluga, Gottlob Frege, 95. 418 Norman Kemp Smith, Commentary to Kant’s Critique of Pure Reason (Atlantic Highlands: Humanities Press, 1992), 181-2.

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It is clear that in the ordinary treatment of logic there is a serious error in that distinct and complete concepts are treated before judgments and ratiocinations, although the former are only possible by means of the latter. I say, then, first, that a distinct concept is possible only by means of a judgment, a complete concept only by means of a ratiocination. In fact, in order that a concept should be distinct, I must clearly recognise something as an attribute of a thing, and this is a judgment. In order to have a distinct concept of body, I clearly represent to myself impenetrability as an attribute of it. Now this representation is nothing but the thought, 'a body is impenetrable.' Here it is to be observed that this judgment is not the distinct concept itself, but is the act by which it is realised; for the idea of the thing which arises after this act is distinct. It is easy to show that a complete concept is only possible by means of a ratiocination: for this it is sufficient to refer to the first section of this essay. We might say, therefore, that a distinct concept is one which is made clear by a judgment, and a complete concept on which is made distinct by a ratiocination. If the completeness is of the first degree, the ratiocination is simple; if of the second, or third degree, it is only possible by means of a chain of reasoning which the understanding abridges in the manner of a sorites . . . Secondly, as it is quite evident that the completeness of a concept and its distinctness do not require different faculties of the mind (since the same capacity which recognises something immediate as an attribute in a thing is also employed to recognize in this attribute another attribute, and thus to conceive the thing by means of a remote attribute), so also it is evident that understanding and reason, that is, the power of cognising distinctly and the power of forming ratiocinations, are not different faculties. Both consist in the power of judging, but when we judge mediately we reason.

Kant’s logical thinking was dominated by the substance-attribute

character of traditional logic. It might be objected at this point that Frege rejected the

subject-predicate composition of propositions; thus Frege could not have had Kant’s

version of the context principle in mind when he formulated his own version of the

principle. But the substance-attribute character of traditional logic is mirrored in the

argument-function, object-concept, and sense-reference dichotomy of Frege’s theory of

meaning. Frege generalized the logical analysis of judgements when he assimilated the

mathematical notion of function to the logical notion of predicative concept. Kant and his

predecessors often spoken of concepts as subjects and predicates of complete

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judgments. In the passage quoted above, Kant refers to concepts as predicates, or

merely one element or constituent unifying element of a complete judgment. This

suggests that concepts are to be taken as incomplete, unless completed in the act of

judgment, thus paralleling Frege’s notion of ’saturated' and ‘unsaturated’ concepts. In

this passage Kant was moved to formulate a version of the context principle as early as

1762. Thus, Kant is claiming here that only in the context of the act of a judgment is a

concept made distinct. Further, a ratiocination is a chain of judgments wherein concepts

are made complete.

Moreover, Kant claims that all judgments are ’functions’ of the unity

among our representations that allow us to distinguish objects is at the core of Kant’s

Critique of Pure Reason.

besides intuitions there is no other mode of knowledge except by means of concepts. The knowledge yielded by understanding, or at least by human understanding, must therefore be by means of concepts, and so is not intuitive, but discursive. Whereas all intuitions, as sensible, rest on affections, concepts rest on functions. By ’function’ I mean the unity of the act of bringing various representations under one common representation. Concepts are based on spontaneity of thought, sensible intuitions on the receptivity of impressions. Now the only use which the understanding can make of these concepts is to judge by means of them. Since no representation, save when it is an intuition, is in immediate relation to an object, no concept is ever related to an object immediately, but to some other representation of it, be that other representation an intuition, or itself a concept. Judgment is therefore the mediate knowledge of an object, that is the representation of a representation of it . . . Accordingly, all judgments are functions of unity among our representations... Now we can reduce all acts of the understanding to judgments, and the understanding may therefore be represented as a faculty of judgment. . . thought is knowledge by means of concepts, as predicates of possible judgments, relate to some representation of a not yet determined object.419

419 Kant, Critique of Pure Reason, A69/B94.

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It is commonly accepted that Frege was the first to articulate the context

principle. This passage shows that the context principle, or a version very similar to the

one Frege gave, was previously given by Kant; thus the principle is not unique to Frege.

Frege does not give attribution to Kant for the context principle. However, he was

familiar with and accepted the Neo-Kantian philosophical outlook that includes the unity

of judgement and the Kantian epistemological framework. Thus, it is plausible to

conclude that Frege's use of the context principle was of Kantian origin.

Sluga has argued controversially that Frege may have acquired the

context principle not directly from Kant, but through Lotze.420 According to Sluga, in

Lotze we find the notions of objectivity, or validity, apply only to whole propositions; and

mistaken doctrines of concepts have heir origin in the separation of concepts from the

propositional context.421

It is generally the Foundations of Arithmetic to which most interpreters of

Frege refer when discussing the context principle. The reason for this is that it is in the

Foundations of Arithmetic best known, and it is here that Frege most clearly articulates

the principle. Thus the Foundations of Arithmetic is considered by most philosophers as

the locus classicus of Frege's views on the context principal. However, it is evident that

Frege accepted the context principle as a central doctrine in his Begriffsschrift, published

in 1879.

In Begriffsschrift Frege develops a logic, not as a purely technical or

pragmatic device, he also expressing a definite philosophical viewpoint.422 Following

420 Sluga, Gottlob Frege, 55. 421 Ibid. 422 Sluga, Gottlob Frege, 95.

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Sluga, we might say that it is only in the context of his philosophical views that the

context principle has any meaning.423

After Begriffsscrift and prior to the publication of the Foundations of

Arithmetic, Frege presented an early version of the principle in his essay “Boole’s logical

calculus and the Concept-script,” which appeared in 1881. He says:

And so instead of putting a judgment together out of an individual as subject and an already previously formed concept as predicate, we do the opposite and arrive at a concept by splitting up the content of possible judgment.424

Frege’s most famous articulation of the context principle is found in the

Introduction of the Foundations of Arithmetic, where he lays out three basic principles

that he says will guide his inquiry. The context principle is the second of the three

principles he presents:

Always to separate sharply the psychological from the logical, the subjective from the objective;

never ask for the meaning of a word in isolation, but only in the context of a proposition;

never lose sight of he distinction between concept and object.

In the very next paragraph, he attempts an explication of the principles

just given. He says, in part:

In compliance with the first principle, I have used the word “idea" always in the psychological sense, and have distinguished ideas from concepts and from objects. If the second principle is not observed, one is almost forced to take as the meanings of words mental pictures or acts of the individual mind, and so offend against the first principle as well.

423 Ibid. 424 Frege, Posthumous Writings, 17.

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The context principle is a methodology of conceptual analysis that

Frege uses to investigate (i) the relation between the concepts and the

judgements in which such concepts occur; and (ii) the relationship between

logical concepts and logical objects that fall under them. It enables him to show

that it is possible to assert the self-subsistence of numbers as abstract objects

without intending them to be subjective ideas or empirical objects. “We can form

no [subjective] idea of the number either as a self-subsistent object or as a

property in an external things, because it is not in fact either anything sensible or

a property of an external thing."425 The principle enables him to show that there

are abstract objects, which are logical and objective; thus avoiding any notion of

them as psychological or subjective concepts. If the principle is not used, the

inevitable consequence is that numbers are likely to be confused with

(subjective) ideas or empirical objects.

This interpretation is consistent with the later references to the context

principle in the Foundations of Arithmetic. In §60, he explains how the context principle

makes it possible to distinguish the meaning of a word without our having formed a

subjective idea of the word:

That we can form no idea of its content is therefore no reason for denying all meaning to a word, or for excluding it from our vocabulary. We are indeed only imposed on by the opposite view because we will, when asking for the meaning of a word, consider it in isolation, which leads us to accept an idea as the meaning. Accordingly, any word for which we can find no corresponding mental picture appears to have no content. But we ought always to keep before our eyes a complete proposition. Only in a proposition have words really a meaning426

425 Frege, Foundations of Arithmetic, 70. 428 Frege, Foundations of Arithmetic, 71.

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The context principle is again reiterated in the Foundations of

Arithmetic §62, where he lays out his reasons for defining cardinal numbers as

classes of concepts:

How then are numbers to be given to us, if we cannot have any ideas or intuitions of them? Since it is only in the context of a proposition that words have any meaning, our problem becomes this: To define the sense of a proposition in which a number word occurs.427

The context principle is the source of considerable disagreement

among contemporary interpreters of Frege. Their disagreements turn on

questions involving (i) the nature of the principle itself, and (ii) the scope of its

applicability to Frege's early and later works. The answers to these questions

has importance implications for our views concerning his philosophical outlook

on such matters, as whether his motivations were semantic or epistemological,

and whether he was a realist or objective idealist.

From the standpoint of Frege exegesis the role of the context principle is

related to Frege’s theory of meaning in the following way. During the early years, when

he wrote and published Begriffsscrift (1879) and the Foundations of Arithmetic (1984),

there are several clear references to the context principle. He is explicit in maintaining

the priority of judgments over concepts. However, after the Foundations of Arithmetic,

Frege wrote the series of papers “Function and Concept” (1891), “On Sense and

Reference" (1892) and “Concept and Object” (1892). In the papers, according to some

interpreters, Frege abandons the context principle in favor of a theory of meaning that

gives greater weight to the semantic power of words to determine the semantic value of

sentences. The semantic value of a word is its referent, and the semantic value of a

427 Frege, Foundations of Arithmetic, 73.

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sentence is its truth-value (i.e. its truth or falsity). The use of the terms semantic power

and semantic value have been used, respectively, by Evans428 and Dummett429 to

describe the workings of Frege’s theory of sense and reference. However, Dummett

goes farther than Evans in applying it to the context principle.

The context principle is widely understood among advocates of the

standard interpretation as a semantical principle. That Frege used the term Bedeutung

in stating the principle, a term that was naturally translated in English as ‘meaning’, led

many to conclude that the central concern of the context principle was meaning.

However, the term Bedeutung can just as naturally be translated as ’significance’.430 The

term ‘significance’, if used in translation, would have been more suggestive of Frege’s

actual epistemological motives.431

The semantical interpretation of the context principle is exemplified by

Dummett in his The Interpretation of Frege's Philosophy. In fact, for Dummett, the

context principle is a pair of semantical principles. Although Frege had not yet made the

sense-reference distinction at the time Foundations of Arithmetic was written, Dummett

has argued that both aspects of the sense-reference distinction were put to work

implicitly by Frege in the Foundations of Arithmetic.

As a principle concerning sense, the context principle singles out sentences as having a unique role in any account of the senses of expressions. The sense of any expression is its contribution to determining the condition for the truth of any sentence in which it occurs. More exactly, taking due account of the relation of sense to reference, the matter stands thus: the reference of an expression is, as we have seen, its semantic value, that feature of it which goes to determine the truth or falsity of any sentence containing it; and the sense of the expression

428 Gareth Evans, The Varieties of Reference, ed. J. McDowell (Oxford: Clarendon, 1982), 8. 429 Dummett, Frege: Philosophy of Language and The Interpretation of Frege's Philosophy. 430 Currie, 156. 431 Currie, 156-7.

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consists in the manner in which the speakers of the language apprehend its reference as being determined.432

The context principle is seen by Dummett as vindicating Platonism about

numbers; and thus marks Frege as an extreme realist. It asserts that once the sense of

sentences in which a singular term occurs has been fixed, so that we know in principle

at least how to set about determining their truth value, then no further philosophical

questions remains about whether that term has reference 433 This is so despite the

natural objection: that we do not know, and could have no possible means of knowing,

anything of such objects.

According to Dummett, the context principle was “let slip" by Frege in his

writings after Grundlagen. In Frege’s Philosophy of Language, Dummett explains it this

way:

.. .the plausibility of Frege's theory of meaning, as expounded in his later writings, is enhanced because we tend to read into it what is not actually there, what is in fact expressly denied - the acknowledgment so strongly emphasized in Grundlagen of the quite special role that sentences play within language. It is a correct insight which leads us to do this, because the apprehension of the central role of sentences for the theory of meaning was one of Frege’s deepest and most fruitful insights, indeed, which seem, once they have become a familiar part of our vision, to be so obvious that we can scarcely grasp how things looked before. Nevertheless, it was an insight which Frege let slip, one which cannot consistently be reconciled with the views he later held; if we do not hold this fact in mind in reading the post -Grundlagen writings, we shall ascribe to the system a tension to which it is not really subject.434

The reason why this interpretation has arisen is two-fold.435 First, in

Frege’s essay on “Function and Concept", Frege’s explanation of concepts as functions,

and sentences as names of truth-values, seems incompatible with his earlier claim in

432 Dummett, The InterpretatioOn of Frege’s Philosophy, 369. 433 Ibid. 434 Dummett, Frege: Philosophy of Language, 628-9.

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Grundlagen for the central role of sentences in the theory of meaning. Second, Frege’s

later sense-reference theory is primarily a theory of referring expressions (e.g. proper

names and definite descriptions), and so the problem of sentence meaning is subsidiary

to it. This suggests that Frege changed his position on the context principle in favor of a

semantic theory favoring the composition of sentences from words, rather than words

acquiring meaning only in the context of a proposition.

I maintain that the context principle is anchored deeply in Frege’s thought,

and thus it is implausible to conclude that in his later years Frege simply let it slip from

his mind.436 However, if it can be shown that Frege’s understanding of the relation of

judgments and concepts did not change around 1891 and he held to the context

principle, then his account of concepts and functions and of sense and reference must

be shown to fit into it. This can be done, if we take seriously Frege’s comments in his

various other writings.

The essay “On the Principle of Inertia” has been suggested by Sluga as

indicating that Frege’s logical views in the 1890’s, about the time he wrote “On Sense

and Reference, were still very consistent with acceptance of the context principle.437

In Frege's "Notes for Ludwig Darmstaedter” which was written and dated

by Frege in July 1919, Frege states explicitly that:

What is distinctive about my conception of logic is that I begin by giving pride of place to the content of the word ‘true’, and then immediately go on to introduce a thought as that to which the question ‘Is it true?’ is in principle applicable. So I do not begin with concepts and put them together to form a thought or judgment; I come by the parts of a thought by analysing the thought. This marks off my concept-script from the

435 Sluga, Gottlob Frege, 134. 438 Sluga, Gottlob Frege, 95; also, Currie, 148-66 and 177-8. 437 Sluga, Gottlob Frege, 134.0

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similar inventions of Leibniz and his successors, despite what the name suggests; perhaps it was not a very happy choice on my part.438

Thus, as Sluga has pointed out “Frege says that the sentence is

primary in his logic. The fact that sentences express thought and that these

thoughts can be true or false is to be considered logically fundamental. The

parts of the thought are reached only by analysis."439

Many modem interpreters of Frege are influenced in their interpretation

by Wittgenstein. Dummett is representative of interpreters who have attributed a

Wittgensteinian spin to Frege’s work, especially the theory of sense and reference. The

context principle so impressed Wittgenstein that he mentions, practically verbatim, in at

least two places in his writings. In the Tractatus, Wittgenstein says:

Only propositions have sense; only in the nexus of proposition does a name have meaning.440

Wittgenstein believed that the sense of the proposition is a unique

function of the meanings of its component words. He therefore held the exact

opposite view concerning the meaning of words and propositions than did Frege.

According to Wittgenstein,

The meanings of primitive signs can be explained by means of elucidations. Elucidations are propositions that contains primitive signs. So they can only be understood if the meanings of those signs are already known.441

A name means an object.442

In a proposition a name represents an object.443

438 Frege, Posthumous Writings, 253. 439 Sluga, Gottlob Frege, 134. 440 Wittgenstein, Tractatus, § 3.3. 441 Ibid.. §3.263. 442 Ibid., §3.203. 443 Ibid.. §3.22.

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An elementary proposition consists of names. It is a nexus, a concatenation, of names.444

Later interpreters of Frege assumed that the Frege’s context principle

shows that he accepted the same account of meaning that Wittgenstein espoused in the

Tractatus. After Wittgenstein abandoned the Augustinian view of language that he held

at the time of the Tractatus, he adopted a contextual view of word meaning, not merely

within a proposition, but attributes to Frege the notion of the meaning of a word in a

language-game. In the Philosophical Investigations, he explains:

We may say: nothing has so far been done, when a thing has been named. It has not even got a name except in the language-game. This was what Frege meant too, when he said that a word had meaning only as part of a sentence.445

This interpretation of Frege by Wittgenstein has presumably

influenced some interpreters of Frege, like Dummett, to suggest that Frege held

a nascent view of language games. In Frege: Philosophy of Language, Dummett

says, for Frege, “the sense of a word consists in a rule which, taken together with

the rules constitutive of the senses of the other words, determines the condition

for the truth of a sentence in which the word occurs.”448

The context principle is a methodology for conceptual analysis that is

prevalent throughout Frege’s early and later works. It is not a semantic principle.447 It is

a methodology that Frege never abandons in his later works. It is merely obvious in the

Foundations of Arithmetic where the principle is expressly stated. However, it is present

later in the essay “Thoughts” in his use of the metaphor ‘to grasp’ or ‘grasping’ a

444 Ibid., §4.22. 445 Ludwig Wittgenstein, Philosophical Investigations, §49. 448 Dummett, Frege: Philosophy of Language, 194. The italics is my own.

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thought. The analogy with the hand grasping a physical object makes it seem as though

Frege has a realist motives mind. Grasping a thought or the sense of a word is the act

of thinking, and by which the mind brings objects under concepts. It is analogous in all

essential respects with Kantian synthesis; the epistemic framework within which Frege’s

entire logical theory operates.

In conclusion, I maintain that the context principle is not original to

Frege's thought; his methodology is Kantian in origin. Frege’s acceptance of the

context principle shows he accepted the traditional account of judgement, as that

of the combining of concepts. The affirmation or denial of a judgment is the

recognition that one concepts falls under another. Properly understood, the

context principle is the rejection of the empirical model. Frege’s aim was to

establish a firm foundation for mathematics based on rationalist as opposed to

empiricist principles. By rejecting intuition, as the basis of knowledge of

mathematical objects, Frege was returning to Leibnizian, and thus rationalist

principles, thus, shifting the epistemic bases of mathematics from a posteriori to

a priori grounds, or ‘sources’ to use Frege’s term.

There is a tension attributed to Frege thought by Dummett and others

who believe Frege abandoned the context principle in favor of his mature theory of

sense and reference. Giving primacy to Frege’s later theory of sense and reference,

Dummett claims that the later theory is nevertheless implicit in the Foundations of

Arithmetic, and that the context principle is a semantic principle, not a cognitive principle.

The notion that Frege might have abandoned the context principle suggests that he may

have abandoned Kantian transcendental idealist principles, in favor of a form of realism

447 Ibid.,149.

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consistent with analytic philosophy. Since, as I have shown, Frege did not abandon the

context principle, it is plausible that Frege never abandoned transcendental idealism.

Subjectivism and Objectivism

In the Foundations of Arithmetic Frege tells us that one of his guiding

principles is "always to separate sharply the psychological from the logical, the

subjective from the objective.” According to the canonical interpretation, Frege means

by this maxim to distinguish between mind-independent objects and mind-dependent

states. This reading of Frege gives an ontological construal to his subjective-objective

distinction, and attributes a Platonistic metaphysics of meaning to Frege to explain how

linguistic statements may be determined to be true or false. This canonical

interpretation, which has been espoused most ardently by Dummett, sees Frege’s work

the prolegomena for twentieth century semantics and makes him the father of the

philosophy of language. The application of this interpretation enables us discover the

ontological presuppositions of language; thus establishing Frege as the father of

analytic philosophy. This reading of Frege makes ontological notions prior to notions of

judgment, assertion, logical inference and truth. This reading of Frege is inaccurate

and in need of revision. In fact, ontological notions are secondary for Frege.

The starting point for Frege is his theory of judgment. He says, "I start out

from judgments and their contents, and not from concepts."448 Frege rejected the

naturalism and empiricism that was rampant in nineteenth century Germany. His theory

of judgment owes much to the Neo-Kantianism and resurgence of interest in Leibnizian

philosophy that was current in his day. Judgments provide the matrix of Kant’s entire

448 Frege, “Boole’s logical Calculus and the Concept-script” in Posthumous Writings, 16.

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philosophy, and all three Critiques provide an analysis of a particular class of

judgment.449 Likewise, for Leibniz, all sound philosophy begins with the analysis of

judgments.450

Frege distinguishes between understanding or grasping a thought and

recognizing its truth. To recognize the truth of a thought is to make a judgment that it is

true. This distinction is manifested in the linguistic practice of asking questions and

answering them in the affirmative or the negative. We demonstrate that we understand

or grasp a thought when we ask a question. We demonstrate that we recognize it as

either true or false when we answer the question either affirmatively or negatively.

Thoughts are objective in the sense that several people can all grasp or

understand the same thought, and judge whether it is true or false. That the same

thought may be publicly accessible to several people demonstrates that thought are

objective, and not subjective as is the case with a person’s pain. Pain is subjective

because it is not accessible to anyone except the individual subject. It is not possible to

feel the pain of another person; this shows that pain is subjective, and not objective.451

Thus, Frege, unlike the later Wittgenstein452, rejects any notion that all language is

public.

The objectivity of thoughts does not entail a Platonistic

interpretation of thoughts as timeless mind-independent objects. Timelessness

and mind-independence are just ways of talking about thoughts to secure their

objective as opposed to their subjective status. Frege’s use of the subjective-

449 Caygill, A Kant Dictionary (Oxford: Blackwell, 1995), 267. 450 Russell, The Philosophy of Leibniz, 8. 451 Frege, “Thoughts’’ in Collected Papers. 452 Wittgenstein, Philosophical Investigations, §243-303.

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objective distinction is parallel to Kant’s. By objectivity, Kant did not mean either

derived from objects or derived from Platonistic ideas. The objective ground for a

judgment is derived from the subject. Kant expressly ruled out objectivity in the

Platonistic sense; objectivity is grounded in the order and regularity in the

appearance which we introduce ourselves. In the Critique of Pure Reason, Kant

did not clearly separate the subjective from the objective. Frege sets out to

clarify what Kant actually meant. Frege believed that he was following Kant’s

principles when he separates the subjective from the objective. Thus, Frege

believed he was operating within the Kantian framework.

What is objective, according to Frege, is something “that is exactly

the same for all rational beings, for all who are capable grasping it.”493 He also

says:

I understand objective to mean what is independent of our sensation, intuition and imagination, and of all construction of mental pictures out of memories of earlier sensations, but not what is independent of reason, - for what are things independent of reason? To answer that would be as much as to judge without judging, or to wash the fur without wetting it 454

Thus, what is objective for Frege is what is inter-subjectively accessible to all

rational beings in Kant’s sense. Thus what is objective, in Frege’s technical

sense, is the same as what is inter-subjective, in Kant’s sense.

In contrast to the objective, the subjective, according to Frege, is

whatever is not inter-subjectively accessible. The examples that he gives are

“sensations” and “mental processes,”455 and “sense impressions"456, as well as

453 Posthumous Writings, and7 105. 454 Frege, Foundations of Arithmetic, 36. 455 Frege, Foundations of Arithmetic, §26. 458 Frege, Foundations of Arithmetic, §27.

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“ideas” understood “in the psychological sense."457 Ideas are subjective

because they are like images or sensations “which we cannot know to agree

with anyone else’s.”458

Frege distinguishes between the use of the term “idea" in the

subjective or the objective sense. In an important footnote in the Foundations of

Arithmetic (§27), he says:

An idea in the subjective sense is what is governed by the psychological laws of association; it is of a sensible, pictorial character. An idea in the objective sense belongs to logic and is in principle non-sensible, although the word which means an objective idea is often accompanied by a subjective idea, which nevertheless is not its meaning. Subjective ideas are often demonstrably different in different men, objective ideas are the same for all. Objective ideas can be divided into objects and concepts.

Frege goes on to explain how his use of the term “idea" compares with Kant’s

use of it. Frege clearly considers himself to be using the term in the same sense as

Kant, but clarifying the distinction that he believes is implicit in Kant’s philosophy:

I shall myself, to avoid confusion, use ‘idea’ only in the subjective sense. It is because Kant associated both meanings with the word that his doctrine assumed such a very subjective, idealist complexion, and his true view was made difficult to discover. The distinction here drawn stands or falls with that between psychology and logic. If only these themselves were to be kept always rigidly distinct!459

Thus, Frege clearly considers his own use of the term “idea” to be a technical

clarification of what Kant’s true views were. Frege is here placing himself within

Kant’s orbit. Frege intends to make clear a distinction between what is

457 Frege, Foundations of Arithmetic, x. 458 Frege, Foundations of Arithmetic, §26 459 Frege, Foundations of Arithmetic, 37.

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accessible to only a subject and what is inter-subjectively (objectively in Frege’s

technical sense) accessible to all rational beings.

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REALISM OR IDEALISM IN FREGE’S PHILOSOPHY

Introduction

The standard interpretation of Frege is that he was a realist and ally of Russell

and Moore in the revolt against idealism. I have been describing an alternative view of

Frege consistent with the historical setting in which he found himself at the end of the

nineteenth century in Germany as more plausibly a Neo-Kantian. If I am correct, Frege

was not a realist at all, but rather a transcendental idealist, in the Neo-Kantian sense. If

Frege was a Neo-Kantian, it is likely that he was not a Platonist, and not concerned with

Platonic entities at all. The mathematical entities that concerned him must be

conceptual constructions of the mind.

It is not sufficient to show that Frege was in an historical position to have

been a Neo-Kantian, or even that he could have been influenced by Neo-Kantians with

whom he had close associations. It is necessary to demonstrate through textual

references in his works that he either advocated Neo-Kantian doctrines or views

substantially in conformity to those views actually held by other Neo-Kantians. Since

there are no statements of explicit acceptance of such views, I will show that a

consistent interpretation of his writings can be made to demonstrate his implicit

acceptance of Neo-Kantianism.

The familiar questions for metaphysics concern the materialism-idealism

dichotomy. Materialism claims that there are only material objects. For the materialist,

all mental entities are all reducible to material objects. The idealist, on the other hand, 186

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believes that there are only mental entities, i.e. that everything is reducible to minds or

mental states. Dualism claims that there are both kinds of entities. As have argued,

Frege was a metaphysical dualist. In most of his writings, which dealt primarily with

logical and mathematical topics, Frege was not concerned with metaphysical questions

regarding the status of familiar objects in the spatiotemporal world. He was concerned

with the status of abstract or logical objects, consisting of numbers, concepts, functions,

and value-ranges and thoughts. His concern was to distinguish logical objects from

spatiotemporal objects. Logical objects are not cognizable by the senses; they are

known only to reason. Frege held a representational theory of mind. The cognition of

logical objects relies upon mental representations for meaning. However, he explicitly

rejects any notion that logical objects are cognizable either directly or indirectly through

the senses. Frege, thus, rejected empiricism and embraced a rationalist epistemology.

The reason Frege is often thought of as a realist by modem philosophers

is that many of the statements he made concerning, for example, the spatial and

temporal independence of thoughts, numbers, and classes indicate his belief in a mind-

independent realm of abstract objects. In addition, the vast majority of modem

twentieth-century scientists, philosophers of science and adherents of common sense

share acceptance of metaphysical realism. They share the similar views. First, that

there are real objects in the spatiotemporal sense. Second, that such objects exist

independently of our experience or knowledge of them. And, third, they have properties

and enter into relations independent of the concepts and language that we use to

understand them.

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Frege advocated a similar status for logical objects. Logical objects are

supposed to be independent of our knowledge of them, and they have properties and

relations that are discoverable by, but not constructed by the mind. Most

mathematicians think of numbers and other mathematical objects and relations as

possessing a kind of reality that is discoverable by the human mind and not invented by

it. Thus, it seems natural to think of him as realist. In the light of the influence that

Frege is known to have had on some of the central figures of modem analytical

philosophy, which has developed largely within a an empiricist epistemological and

realist ontological framework, it seems natural to think of Frege as a realist.

However, there is a tension in Frege’s thought, which belies the orthodox

realist interpretation of him. The alternative interpretation of Frege, as idealist, is rather

more likely. I maintain that this interpretation of him is more likely true, especially given

the historical problem-situation, which I elaborated earlier.

The realist view of Frege is appealing to those philosophers who are

committed to a realist ontology concerning the general categories existence. Frege is

seen as a Platonist or extreme realist who believes in the existence of abstract objects

like numbers, abstract objects, functions, concepts, and value-ranges residing in an

objective Third Realm’ reminiscent of Plato’s Forms. However, it is my thesis that Frege

was not primarily concerned with the ontological status of numbers, abstract objects,

functions, concepts, value-ranges, or in problems involving their existence. He was a

conceptualist who held a view of logical objects as essentially abstract constructs of the

mind. He was concerned with epistemological problems in mathematics and logic.

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Frege’s views concerning abstract objects, and his alleged realism, must be also seen in

light of his concern with the objectivity.

Realism

It is first important to get clear on what is meant by the term realism, or

Platonism, as has been attributed to Frege. Characteristic are the claims which have

been made by Dummett regarding Frege’s alleged realism. Dummett has claimed that

“Frege himself was not only a realist concerning the external world but a Platonist in

mathematics; this tendency provides further justification for the practice of characterizing

a philosopher, as I think it right to characterize Frege, simply as a realist. ’,46° According

to Dummett, “Platonism is the doctrine that mathematical theories relate to systems of

abstract objects, existing independently of us, and that the statements of those theories

are determinably true or false independently of our knowledge.”461 “Likewise, a realistic

view of mathematics, which is usually called a Platonistic view, involves that the truth of

a mathematical statement does not depend upon our having, or ever coming to have, a

proof of it: it may be true even though it lies beyond our ability to prove it; and, again it

must either be true or not."482

Many contemporary writers use the term ‘abstract object’ when referring

to indications of Platonism in Frege's thought. This is because Platonism is the view

that numbers are ‘abstract objects’. An ‘abstract object’ object is neither an idea nor a

physical object. Curiously, it seems that Frege never used the term ‘abstract object’,

480 Dummett, “Realism” in Interpretation of Frege’s Philosophy, 433-4. 481 Dummett, Frege: Philosophy of Mathematics (Cambridge: Harvard University Press, 1991), 301. 482 Dummett, “Realism” in Interpretation of Frege’s Philosophy, 434.

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except once in reference to Cantor in §86 of his Grundgesetze der Arithmetik.463 There

Frege uses the term “abstract conceptual things"484 This is not surprising. Cantor often

expressed the concept of numbers in terms with Scholastic and realistic distinctions.485

He did not think of numbers as creations of the human mind. Thus, Cantor rejected any

notion of numbers as a universal principle of human knowledge, or intuition. Fore

Cantor, numbers required a metaphysical grounding. Numbers were real in a Platonistic

sense. For Cantor the concept of set was the metaphysical grounding for numbers. The

plurality of existing objects in sets is given metaphysically, not sensually, and that is

where the grounding for the existence of numbers, as abstract objects. From the

metaphysical conception of set followed logically. Cantors concept of number was

extensional because numbers were abstracted from the concept the set of clearly

differentiated things.488

Russell, too, believed that the concept of number was inextricably related

o the concept of set, for which he used the technical term ‘class’. Numbers were the

classes of classes. The number two, for example, is the totality of ail existing pairs. The

number three is the totality of all existing triads, and so on. Thus, Russell held an

extensional definition of class. He regarded classes as only the aggregate of single and

independent elements.487

483 Weiner, Frege in Perspective, 177n3 and 178. 484 Frege, Grundegetze der Arithmetik, Vol. ii, §86, in Translations of the Philosophical Writings of Gottlob, 182. Translated by Max Black. 485 Cassirer, The Problem of Knowledge, New Haven: Yale University Press, 1950), 63. 488 Cassirer, 64. 487 Russell, Principles of Mathematics, chapter vi.

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Frege’s notion of number derives from the assimilation of concept with

numbers. His approach is purely conceptual without reliance upon metaphysical

presuppositions. His methodology is thus conceptual, as opposed to metaphysical.

Frege is a conceptualist because he locates generality in the mind, and points to human

ability to subsume things under concepts, which perform a generalizing and

classificatory role.488 Frege’s view of numbers is opposed to Cantor’s and Russell’s

realistic notion of numbers that asserts there are entities of a general kind that exist

independently of the human mind and ways of thinking or speaking about the world.469

Frege also rejected nominalist notions of number that was formalism, in which numbers

were associated with words and the technical symbolism, and mathematics viewed as

the manipulation of the symbols. Generality is secured only by its representation in

words of the language or symbolism of mathematics.

The standard interpretation holds that Frege is an extreme realist, or

Platonist. The evidence for Frege’s realism stems from several textual references in his

work. Notably in the Foundations of Arithmetic and in his later essay “Thoughts” there

seems to be good reason to attribute a realist view to him. In Chapter IV of the

Foundations of Arithmetic, the subtitle reads: “Every individual number is a self-

subsistent object."470 In “Thoughts” he speaks of a “third realm," in which “the thought

we have expressed in the Pythagorean theorem is timelessly true, true independently of

488 Hamlyn, Metaphysics, 95-6. 469 Hamlyn, Metaphysics, 95. 470 Frege, Foundations of Arithmetic, 67.

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whether anyone takes it to be true.”471 Such explicit statements seem to subject that

Frege held a Platonistic view.

There is a tension in Frege’s works suggesting that he may not be

classified as a Platonist in the traditional sense. Thus, Resnick has proposed to classify

Platonists according to three fundamental types. The ‘methodological platonists’

endorse non-constructive mathematical methods, such as the use of the law of the

excluded middle, impredicative definitions, sets, and similar abstract entities. There is

no doubt, according the Resnick, that Frege’s position presupposes a picture of

mathematics as dealing with a mind independent infinite domain of such abstract

entities. This is to be distinguished from ‘ontological platonists’ who recognize the

existence of numbers, sets and the like as being on a par with ordinary objects, but who

do not attempt to reduce them to physical or subjective mental entities. And, further to

be distinguished are ‘epistemological platonists’, who believe that our knowledge of

mathematical objects is based, at least in part, upon a direct acquaintance of them

analogous with our perception of physical objects.

Resnick further distinguishes as a realist, one who believes that the

objects of the physical sciences and mathematics exist independent of our mental lives.

Realists are opposed to subjective idealists and to transcendental or objective idealists,

like Kant. According the Resnik non-realists might endorse one, or more, or even all of

the three versions of Platonism, all the while maintaining that the mind possesses a

‘perceptual faculty’ which constructs the world of mathematical objects in a deeper level

of analysis prior to our experiencing it. In effect, such Platonism would create an

471 Frege, “Thoughts” in Logical Investigations, 17.

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objective world of mathematical objects prior to our experiencing it. Thus, the objects of

such a world would be “independent of our sensation, intuition, and imagination, and ail

construction of mental pictures out of memories of earlier sensations, but not what is

independent of reason."472 In effect, Resnick’s classification distinguishes Platonism from

realism, where Platonism becomes a kind of abstract reasoning.

According the Resnick, Frege was an ontological platonist because he

believed that mathematical objects are neither spatio-temporal nor mental existing in a

mind-independent realm, and that the statements of mathematics are true or false

depending on whether they describe such objects and their relationships correctly.

Frege was also an epistemological platonist because he maintained that we can know

mathematical objects through a kind of perception analogous, but distinct from the

faculty which enables us to perceive ordinary physical objects. Moreover, Frege was a

methodological platonist because he used impredicative definitions, the law of excluded

middle473

Resnick concludes that, if his interpretation of Frege in correct, “then the

distinction between Platonic realist and a Platonic objective idealist is not a crucial one

for current philosophy of mathematics." The reason for this is that the focus in

contemporary philosophy is on methodology and semantics, and either form of

Platonism would lead to the same conclusion. Frege is not easy to classify even with

Resnick's terminology since he is not consistent in describing his philosophical position.

However, the nature of Frege’s Platonism is important for a clear understanding of

Frege.

472 Frege, Foundations of Arithmetic, 36.

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In Grundlagen there are many instances where Frege suggests that

numbers are not independent of the mind. Notably in § 26 of Foundations of Arithmetic,

where Frege says:

I understand objective to mean what is independent of our sensation of mental pictures out of memories of earlier sensations, but not what is independent of reason, - for what are things independent of the reason?" To answer that would be as much as to judge without judging, or to wash the fur without wetting it.

LdealLsm

Some evidence for Frege’s idealism is to be found in §26 of the

Foundations of Arithmetic where Frege says: “I distinguish what I call objective from

what is handleable or spatial or actual."474 Frege goes on to acknowledge Kant’s

epistemological framework: "Space, according to Kant, belongs to appearance...

everyone recognizes the same geometrical axioms, even if only by his behaviour, and

must do so if he is to find his way about the would.475 Thus, Frege accepts Kant’s view

of geometry as synthetic a priori knowledge.

In the footnote to §27 of Foundations of Arithmetic, Frege gives us

another reason to believe that he holds an idealist view of numbers. He says there that

we wishes to distinguish between "idea in the subjective sense" and "idea in the

objective sense":

An idea in the subjective sense is what is governed by the psychological laws of association; it is of a sensible pictorial nature. An idea in the objective sense is belongs to logic and is in principle non-sensible, although the word which means an objective idea is often accompanied by a subjective idea, which nevertheless is its meaning. Subjective ideas

473 Resnik, Frege and the Philosophy of Mathematics, 16. 474 Frege, Foundations of Arithmetic, 35. 475 Ibid., 35.

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are often demonstrably different in different men, objective ideas are the same for ali. Objective ideas can be divided into objects and concepts.476

In other words, Frege believes there are “ideas" in the “objective sense", which are "in

principle non-sensible” [my italics]. Frege goes on to clarify that it is his intention to

make clear Kant’s “true view” that Kant intended to distinguish between ‘subjective

ideas’ and ’objective ideas'; but because Kant uses the term 'idea' both in the objective

and subjective sense that Kant’s true view was not understood.

It is because Kant associated both meanings with the word (’idea’) that his doctrine assumed such a very subjective, idealist complexion, and his true view was made so difficult to discover477

The footnote in the Foundations of Arithmetic from which I have quoted

above defines Frege’s distinction between the psychological and logical. The

psychological refers to "subjective ideas" and the logical refers to "objective

ideas”, as used by Kant. Frege says; “The distinction here drawn stands or falls

with that between psychology and logic."478 This shows that Frege accepted

Kant’s objective idealist framework.

In §55 through §59 of Foundations of Arithmetic, Frege argues that

numbers are “self-subsistent objects”. He says, “Every individual number is a self-

subsistent object"479 “We can form no idea of a self-subsistent object or as a property in

an external thing, because it is not in fact either anything sensible or a property of an

external thing.”480 The term ‘self-subsistent object’ here used by Frege suggests

476 Ibid., 37. 477 Ibid., 37. 478 Ibid., 37. 479 Ibid., 67. 480 Ibid., 70.

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something which has a spatio-temporal location outside of the mind. What Frege means

is that numbers are not subjective ideas. Frege does not want to use the term objective

idea due to the possibility of confusion with the term subjective idea. Hence he avoids

the use of the term idea altogether. Numbers are self-subsistent objects because they

are abstract objects. The term self-subsistent is used to distinguish them form physical

objects. Physical objects are spatio-temporal objects known to us through our sense

perceptions as subjective ideas. Numbers are self-subsistent “independent of our

sensation, intuition, and imagination, and all construction of mental pictures out of

memories of earlier sensations, but not what is independent of reason."481 Thus numbers

are self-subsistent, or abstract, or objective ideas, known to us through reason in Kant’s

sense.

For Frege, numbers, or self-subsistent objects, are known to us through

reason, and not through sensations. We can have knowledge of self-subsistent objects

in the context of a proposition.

That we can form no idea of its content is therefore no reason for denying ail meaning to a word, or for excluding it from our vocabulary. We are indeed only imposed on by the opposite view because we will, when asking for the meaning of a word consider it in isolation, which leads us to accept an [subjective] idea as the meaning. Accordingly, any word for which we can find no corresponding mental picture appears to have no content. But we ought always to have before our eyes a complete proposition. Only in a proposition have words really a meaning. It may be that words float before us all the while, but these need to correspond to the logical elements in a judgement. It is enough if the proposition taken as a whole has a sense; it is this that confers on its parts also their content.482

481 Ibid., 36. 482 Ibid.,71.

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In the passage just quoted, Frege means subjective idea when he uses the word

'idea'. Subjective ideas can have meaning for us in isolation; and they need not

be used in a proposition to have sense. However, Frege claims here that

objective ideas of numbers can also have meaning even though we have no

subjective idea of them.

There is additional praise for Kant, and further evidence that

Frege was an idealist in the Kantian sense, in the Foundations of Arithmetic. In

§3 Frege refers to Kant’s epistemological distinctions of a priori and a posteriori,

and analytic and synthetic analytic, judgments. For Frege, these distinctions

have to do with “not the content of the judgement but the justification for making

the judgement."483 In the accompanying footnote, he explains that “By this I do

not, of course, mean to assign a new sense to these terms, but only to state

accurately what earlier writers, Kant in particular, have meant by them."484 What

is significant here is that Frege clearly believes that he is using these terms in the

same sense that Kant meant them. His accepted of not only the Kantian

epistemological framework, but also, by extension, Kant’s transcendental

idealism.

Frege's reverence for Kantian idealism is borne out, again, by his

explicit endorsement of Kant in §89 of the Foundations of Arithmetic:

I consider Kant did great service in drawing the distinction between synthetic and analytic judgements. In calling the truths of geometry synthetic and a priori, he revealed their true nature. And this is still worth repeating, since even to-day it is often not recognized. If Kant was wrong about arithmetic, that does not seriously distract, in my opinion, from the

483 Ibid., 3. 484 Ibid., 3.

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value of his work. His point was, that there are such things as synthetic judgments a priori; whether they are to be found in geometry only, or in arithmetic as well, is of less importance.485

Sluga has proposed that there is strong evidence suggesting that Frege was an

objective idealist, and associates him with the philosophical tradition of Leibniz, Kant and

Lotze.488 He has pointed to the likely exposure of Frege to Lotze’s ideas, particularly the

similarity of Frege’s distinction between the objective and the real and Lotze’s distinction

between the objective, or valid, and the real, or existent. If seen as an objective idealist,

Frege’s philosophy is not genuinely platonic.487 Resnik, who has argued for the view that

Frege was methodological platonist, also concedes that Sluga’s interpretation of Kant as

an objective idealist is “extremely plausible" and “most persuasive.”488

I might be objected that there are references in some of Frege’s writings

in which he is explicitly opposed to idealism. On closer inspection, however, these

remarks are seen to refer to the subjective idealism of Berkeley and empiricism of

Locke. For example, in a draft of his essay “On Concept and Object" Frege says:

Indeed would not Locke’s empiricism and Berkeley’s idealism, and so much that is tied up with these philosophies, have been impossible if people had distinguished adequately between thinking in the narrower sense and ideation, between the parts of content (concepts, objects, relations) and the ideas we have? Even if with us men thinking does not take place without ideas, still the content of a judgement is something objective, the same for everybody, and as far as it is concerned it is neither here nor there what ideas men have when they grasp it.489

485 Frege, Foundations of Arithmetic, 102. 488 Sluga, Gottlob Frege, ‘ Frege as Rationalist", and “Frege’s Alleged Realism" 487 Currie, Frege: An Introduction to His Philosophy, 177. 488 Resnik, Frege’s Philosophy of Mathematics, 163-164. 489 Frege, Posthumous Writings, 105.

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In his unpublished essay, entitled "Logic", written about 1897, in reference to the

idealist theory of knowledge, Frege says:

If the idealist theory of knowledge is correct then the sciences would belong to the realm of fiction. Indeed one might try to reinterpret all sentences in such a way that they were about ideas. By doing this, however, their sense would be completely changed and we should obtains quite a different science; this new science would be a branch of psychology.490

In the same essay he says:

Psychological treatments of logic arise from the mistaken belief that a thought (a judgement as it is usually called) is something psychological like an idea. This view leads necessarily to an idealist theory of knowledge; for if it is correct, then the parts that we distinguish in a thought, such as subject and predicate, must belong as much to psychology as do thoughts themselves. Now since every act of cognition is realized in judgements, this means the breakdown of every bridge leasing to what is objective. And ail our striving to attain to this can be no more than an attempt to draw ourselves up by our own bootstraps. The most we can do is to try to explain how it comes to seen that there is such a thing as what is objective, how we come to assume the existence of something that is not part of our mind without, however, our thereby having any justification for this assumption.491

In his unpublished essay, entitled "Logic in Mathematics” published in 1914, Frege says:

Let us take for comparison the sentence ‘Etna is higher than Vesuvius’. With this sentence we associate a sense, a thought; we understand it, we can translate it into other languages. In this sentence we have the proper name ‘Etna’, which makes a contribution to the sense of the whole sentence, to the thought. This contribution is a part of the thought, it is the sense of the word ‘Etna’. But we are not making a statement about this sense, but about a mountain, which is not part of the thought. One who holds an idealist theory of knowledge will not doubt say ‘That is wrong. Etna is only an idea in your mind.’ Anyone who utters the sentence ‘Etna is higher than Vesuvius’ understands it in the sense that it is meant to assert something about an object that is quite independent of the speaker. Now the idealist may say that it is wrong to hold that the name ‘Etna’ designates something.492

490 Ibid., 130. 491 Ibid.. 143-4. 492 Ibid., 231-2.

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The idealism Frege has in mind when he criticizes it in these

passages is the subjective idealism that Kant rejected. In the Critique of Pure

Reason, Kant rejected the subjective idealism of Berkeley. Frege challenged the

same kind of idealism, and like Kant, did not consider himself to be an idealist in

the sense of subjective idealism. The kind of idealism that Kant was concerned

to challenge doubted the reality of external objects. For Berkeley’s subjective

idealism, space and the things in it are “merely imaginary entities."493

Kant proposed instead a transcendental idealism, which was also

an empirical realism. Transcendental idealism holds that "objects of experience .

.. are never given in themselves, but only in experience, and have no existence

outside it."484 Experience of reality is given to individual subjects in the form of

intuitions, and reason is not possible without experience. However, the forms of

intuition and the concepts of understanding originate in the subject, and may thus

be described as 'idealist', but the way in which they organize experience is

objectively valid. By objectivity Kant did not mean derived from objects, nor from

Platonic ideas. The objective ground is derived from the subject. Objectivity is

grounded in the order and regularity of the experiencing subject.

Frege was closely associated with several prominent Neo-

Kantians. Although he never explicitly associated himself with Neo-Kantians, he

nevertheless held views resembling at least two Schools of Neo-Kantianism:

Southwestern or Baden School and the Marburg School. These facts are

493 Kant, Critique of Reason, B275. 494Kant, Critique of Reason, A492/B521.

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significant for an understanding of Frege’s metaphysical views. Frege believed,

as did these Neo-Kantian Schools, in an ‘anti-psycholgistic’ theory of human

consciousness as the source of objectively valid truths. He held an axiological

theory of values. He believed there is a realm of truth-values possessing a

transcendent reality but not actually existing, where ‘thoughts’, ‘senses’ and other

logical objects obtain logical validity. Thus, Frege’s work was closely associated

with Neo-Kantianism. He was not an extreme realist or Platonistic. His

metaphysical views are more properly described as transcendental idealist.

Frege’s views are similar to the contemporary anti-realist, who

does not deny that there are things in themselves, but who adopts a view similar

to Kant’s transcendental idealism. According to the modem anti-realist, our

conception of the world rests on our perceptual and conceptual faculties,

including our language. What separates Frege from the modem anti-realist is his

belief in the primacy of thought over language. Frege held a conceptualist view

of the primacy of thought over language. Language, for Frege, was imprecise; at

most it could only express a thought. ‘Thoughts’, in Frege’s technical sense, are

primary contributors of meaning. For Frege, there are no universals existing in a

reality of their own. Universals are ‘thoughts’ that possess objective validity. But

‘thoughts’, which are objective ideas, acquire their meaning only through their

association with mental representations, which are subjective ideas.

Frege rejected the nominalist view that universals acquire their

significance through association with general words or uses of words in

language. He also rejected the psychologistic view that universals acquire their

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significance from association with subjective ideas. Frege never totally

overcame the Cartesian perspective. He attempted to secure the objectivity of

scientific knowledge in logical laws accessible to reason. But his notion of

objective truth was grounded in the subjectivity of human consciousness.

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CONCLUSION

In the preceding Chapters, my purpose has been to demonstrate the

plausibility of the position taken by Sluga, as against Dummett and other adherents of

the 'standard interpretation', that Frege's intellectual development cannot be understood

outside of the broader historical intellectual developments of his times. To make Frege

a compatriot of twentieth- century analytic philosophers is to remove him from the

historical setting in which his thought developed. Frege is not an analytic philosopher in

the twentieth-century sense of that term. His intellectual development is shaped by Neo-

Kantian ideas. He is not a compatriot of Moore and Russell in the revolt against

idealism. While Moore and Russell were motivated to reject their intellectual inheritance,

the Neo-Hegelian idealism of Bradley, McTaggart, Bosanquet, and Green, Frege did not

reject his own Neo-Kantian intellectual heritage. Thus, while Frege is motivated to place

his ideas on the foundations of arithmetic within the context of Neo-Kantianism and

within the rationalist and transcendental idealist tradition, Moore and Russell, and their

followers in the analytic tradition were moving rapidly away from idealism, including the

presuppositions of its Neo-Kantian variants.

Frege was first and foremost a mathematician who was not in the

mainstream of his field. He was not concerned with practical applications of

mathematics, as were most mathematicians of the nineteenth century. He was

concerned with demonstrating the logical source of mathematical knowledge. The

logical source was reason. In demonstrating the objectivity of mathematical knowledge,

203

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ideas, as distinguished from subjective ideas. He placed mathematical knowledge

within the scope of objective ideas. He was concerned to give a modem account of

judgement regarding mathematical and scientific knowledge within the Kantian

framework, and not concerned with giving an account of meaning of natural language.

Frege explicitly rejected the correspondence theory of knowledge. Thus,

we must disassociate him from the tenets of positivism, empiricism and linguistic

theories of meaning of twentieth century analytic philosophy. Frege was likely a Neo-

Kantian, holding as he did a notion of objective validity rather than correspondence with

reality.

Frege's anti-psychologism is spurious. In fact, he held a wholly

psychologistic account of human knowledge. This is evident when we recognize that

Frege held a representational view of mind. Despite his avowed anti-psychologism,

thoughts and the senses of words, in Frege’s technical terminology, are made

meaningful ultimately only by association with subjective ideas in the mind. Frege's

clandestine psychologism obscures his actual association with the mainstream of

modem philosophy.

Frege’s rationalist epistemology becomes evident when his thought is

examined in light of his reliance upon self-evident axioms of the laws of logic to secure

the foundations of knowledge, and his axiomatic view of knowledge. He wanted to

develop a universal or philosophical language, a vision first articulated but left

incomplete by Leibniz, but with roots in the Cartesian mathesis universalis. His project

and philosophy is best understood in association with the rationalist philosophy of

Descartes, Leibniz and Kant.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY

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