ABSTRACT

Author's Name Jack Glazbrook

Title of Thesis Berkeleyts Analysis of Science

Department Philosophy

Degree M.A.

Summary The purpose of this dissertation is to examine Berkeley's philosophy of science in the context of his general philosophy (Part One) and to trace the influence of his analysis of science on later ~hought (Part Two). Part One begins by reviewing the influence of other think­ ers - Locke, Newton and r~lebranche in particular - after which his rejection of abstraction is taken up as a prelude to an examination of his metaphysics. The opening discus­ sion of Part Two concludes that Berkeley's philosophy of science is well integrated into his philosophic system. His two main critiques of Newtonian theory, the doctrine of motion and the calculus, are examined as part of his theory of scientific methodology and his concept of nature. The influence of Berkeley's analysis of science is pre­ sented less in its direct impact on individual thinkers than as a contribution to the general intellectual climate of later scientific thought. Short Title

BERKELEY'S ANALYSIS

OF SCIENCE BERKELEY'S ANALYSIS

OF SCIENCE

by

Jack Glazbrook, B.A.

A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfilment of the requirements for the degree of ~~ster of Arts.

Department of Philosophy, McGill University, ...... r1ontreal • March, 1970

, (e) Jack G1azbrook 1970 1 TABLE OF CONTENTS

Preface i

Part One. Berkeley's Philosophy in General

Chapter 1. The Context of His Philosophy l Chapter 2. His Rejection of Abstraction 12 Chapter 3. On Physical Objects 22 Chapter 4. On Spirits 33

Part Two. Berkeley's Philosophy of Science

Chapter 5 • The Relation of His Philosophy of 45 Science to His Philosophy in General Chapter 6. His Critique of Absolute Space, 56 Time and r1otion Chapter 7. His Critique of IvIathematics 73 Chapter 8. Scientific r1ethodology 83 Chapter 9. The Influence of His Analysis of 92 Science

Bibliography i

PREFACE

The purpose of this dissertation is to examine Berkeley's philosophy of science in the context of his general philosophie position and to trace the influence of his analysis of science on later thought. Part One provides an account of his philosophy in gen­ eral and Part Two offers a detailed analysis of his philosophy of science. Time has been kind to Berkeley. The origi­ nality of his thought and the freshness of his style are revealed in his works as much today as when they were written over two centuries ago. Nor has the large volume of commentary dimmed his light. On the contrary, l have found even those interpretations with which l take exception to be valuable and stimulating. Without ignoring Locke, l have presented Berkeley in terms of a Newton-Malebranche axis: from Newton, the new science, from Malebranche, a divine inspiration. This cornes out in his life, guided by a sense of divine purpose, but influenced by a feeling ii

of concern for his fellow man. It is reflected in his philosophy with its respect for science in its study of God's world for the benefit of mankind. Berkeley appears as a very human person, who must, incidental­ ly, have been deeply wounded by the attacks of his contemporaries and especially by their reluctance to even try to understand him. An account of Berkeleian philosophy can con­ veniently begin with his critique of abstraction, from which there are many strands leading in particular to his philosophy of science. His metaphysical system is divided, as iS customary, between his treatments of

physical objècts (~ is percipi) and spirits (~ is percipere). Professor Bracken's "intentional tie" thesis has proven helpful here as it permits an expla­ nation of Berkeley's linguistic approach to metaphy-, sical problems that does not make him a phenomenalist. Bridging the gap between the general philo­ sophy and the philosophy of science at the beginning of Part Two poses little difficulty since Berkeley himself integrated his analysis of science well into his whole system despite, and even perhaps because of, his careful separation of science from metaphysics.

1 iii

Further, there is no need to complicate the matter by talk of development in his writings because Berkeley reached his conclusions early in scientific theory and stuck with them. Central to Berkeley's analysis of science is his criticism of Newtonian physics. In retrospect, we can recognize Newton and Berkeley as the two great protagonists in scientific theory in the early eigh­ teenth century. Protagonists they were, but not an­ tagonists. B8rkeley, a more enthusiastic supporter of the new science in its results and even in its theory than could be justified today, criticized Newtonian physics in order to make its foundations philosophically impeccable. In kinetic theory, he accepted the value of Newton's laws of motion, but rejected the notions of absolute space, time and motion as illegitimate and unnecessary. His critical arguments are now substan­ tially accepted, and new positive doctrines have been developed to preserve the first and second laws of motion - the status of the third law is more debat­ able - in the more restricted context made necessary by the introduction of relativity theory. His criti- iv

cism of the notion of the infinitesimal in calculus is generally agreed to be correct as far as the New­ tonian or Leibnizian formulations are concerned. How­ ever, subsequent mathematical theory has found an answer to Berkeley in a revised formulation in terms of a theory of limits that preserves the value of the calculus as a method. Berkeley's scientific methodology clearly represents an early reaction to the essentialist view of science. To what extent he contributed to the views of science which replaced essentialism is more questionable. Certainly, he anticipated Mach in the rejection of essences and of infinitesimals, but it does not follow from this that Berkeley anti­ cipated ~~chean instrumentalism, positivism or phe­ nomenalism. Further, when recent research has raised question on the influence of even the "crucial" Michelson-Morley experiment on Einstein, any claim that Berkeley through Mach influenced Einstein should be subjected to very careful re- . examination. The valuable contribution of Berkeley's analysis of science seems to me to be best regarded as an influence on the general intellectual climate PART ONE

BERKELEY'S PHILOSOPHY

IN GENERAL

1 l

Chapter 1. The Context of His Philosophy.

In this outline of Berkeley's philosophy in general as a prelude to an examination of his analysis of science, it will be useful to examine his general philosophie position in its contexte To do this, we will consider in order: (1) the influence of other thinkers on his philosophy (2) the connection between his life and his philosophy (3) the response of his contemporaries to his philosophie proposals. During his years at Trinit y College, Dublin, Berkeley became well read in philosophie works in Latin, Greek, French and Hebrew, and became especially familiar with Plato's Dialogues, Malebranche's Recherche de la Vérité (1674-5) and Locke's Essay Concerning Human Understanding (1690). He had also studied the Newtonian science and the mathematical calculus which dominated the scientific thought of the early eighteenth century;l that Berkeley gained a thorough gasp of these disciplines will become apparent when we turn in Part Two to his analysis of science. His attitude to earlier thinkers is best summarized by two remarks recorded in his early notebooks, written in 1707 and 1708 and not then intended lG.J. Warnock, Berk\eley ("Pelican Books"; Harmondsworth, 1953), p. 15. 2

for publication, but published first in 1871 by Professor A.C. Fraser under the title Commonplace Book of Occasional Meta­ physical Thoughts and in revised forro in 1948 by Professors A.A. Luce and T.E. Jessop as the fhilosophical Commentaries:

Entry 266: Mem : that l was distrustful at 8 years old and Consequently by nature dis­ posed for these new Doctrines. Entry 682: l must acknowledge my self behold­ ing to the Philosophers have gone before me. They have given good rules tho perhaps they do not always observe them. Similitude of Adventurers who tho they them selves attained not the desir'd Port, they by their wrecks have made known the Rocks & sands, whereby the Passage of aftercomers is made more secure & easy. Pref: or 1ntrod: 2

This combination of respect mixed with criticism is most apparent in Berkeley's response to Locke, who is the sub­ ject of over seventy of the ' entries in the Philosophical Com­ mentaries, most of them sharply critical. Locke's influence on Berkeley has been so frequently recorded by commentators that Professor Frederick J.E. Woodbridge claims it to be exaggerated,3 and Professors G.J. Whitrow and Jessop insist

2George Berkeley, The Works of George Berkeley, Bishop of Cloyne, ed. A.A. Lüëë and T.E: Jessop (London, 1948 ), 1-,-33, 83. (All references to Berkeley's works are to this edition. Subsequent footnotes refer to Works and indicate the shortened title and Berkeley's section numbers, if any). 3Frederick J.E. Woodbridge, "Berkeley's Realism," in Studies in the History of 1deas, ed. Department of Philosophy of Columbia University (New York, 1918), 1, 188. 3

that Newton's influence was at least equal to Locke's.4 Despite sorne reservations - as to the nature of space, for exarnple 5 - Locke substantially accepted the Newtonian science and atternpted, with a good rneasure of success, to formulate

a philosophy co~patible with that science. As a result, both the strengths and weaknesses of Newtonian science are reflect- ed in Lockean philosophy. While Berkeley acknowledged these strengths, he concentrated on tllose weaknesses which his contempories seemed ready to overlook, his attack being di­ rected against Newton when the views of scientists or rnathe­ mati cians were primarily in question and against Locke when the philosophers were the target. If the philosophico-scien­ tific tradition in general held the doctrine which Berkeley opposed, he would attack Newton and Locke equally, as in his criticism of the notion of a space independent of experience, by which both Newton's absolute space and Locke's pure space were rejected. The Cartesian tradition represents another interest- ing influence on Berkeley. Although he studied Descartes and noted sorne criticisms in his notebooks, Berkeley appeared for the most part to accept the contemporary view which regarded the experimental methods of the new scientists to be in direct

4G.J. Whitrow, "Berkeley's Critique of the Newtonian Analysis of Motion," Hermathena, 82 (1953), 90 and T.E. Jessop, "Berkeley and the Conternporary Physics," Revue Internationale de Philosophie, VII (1953), 87-90. 5Richard I. Aaron, John Locke, 2nd ed. (Oxford, 1963), pp. 156- 1 160. 4

opposition to the ~ priori methods of the Cartesians, who stood therefore sufficiently refuted.6 Although he frequently attack­ ed positions which were held by the Cartesians, he did not often mention the Cartesians themselves in his published works, the exception being Malebranche. Being familiar with the views expressed by Malebranche, whom he probably met in Paris in 1713 or 1714, Berkeley was vexed to find that sorne readers of the Principles mistook him for a fullower of Malebranche. In fact, as Berkeley took the opportunity te demonstrate in the Three Dialogues, their epistemological positions were radically opposed. To cite one contrast only, Malebranche regarded our sensations, being mere modifications of finite minds, to be inherently deceptive whereas Berkeley made the ideas in our minds one of his basic realities.7 Despite the gulf which separates Berkeley from Malebranche in epistemology, Professor Luce has established a connection between the two thinkers,S a connection taken up by Professor J.O. Wisdom in his psychologically oriented examina­ tion of Berkeley.9 Certainly, there is more than a verbal similarity between Malebranche's statement in the heading to

6Mary Shaw Kuypers, Studies in the Eighteenth Century Back­ ground of Hume's Empiricism TNew York, 1958), pp. 14-6. 7Works, II, 213-5; Three Dialogues, II. SA.A. Luce, Berkeley's Immaterialism (London, 1945), pp. 4-5. 9J.O. Wisdom, The Unconscious Origins of Berkeley's Philosophy (London, 1953);-Pp. 4-5. 5

Chapter Six of his Recherche de la Vérité that "we see aIl things in God" and Berkeley's favourite quotation that in God "~ live, and ~, and have ~ being."lO Their differences reflect, in a sense, their divergent interpretations of the term "in" appearing in the two quotations whereas their com­ mon ground lies in the shared concept of a universe wholly dependent on the will of God. Their respective philosophies were at the same time derived from and inspired by this con­ cept. If Locke taught Berkeley, it was Malebranche who inspired him. From a too· casual reading of the biographies of Berkeley, one might picture him as a rather worldly man of religion, devoting his youth to the development of a system of philosophy to justify his faith, his early mature years to the missionary attempt to educate the American native and his later years to the seeking and the enjoyment of eccle­ siastical preferment. If not inaccurate, such a view is in­ complete. To reach a fuller understanding towards an exami­ nation of his philosophy of science, it is necessary to begin with a brief review of his life. Simplifying the chronological outline given by Professor Turbayne,ll we can divide his life, somewhat arbitrarily, into three main periods:

10Works II, 109, 214; Principles, S. 149, Three Dialogues, II. llColin Murray Turbayne, ed. "Introduction," Principles, Dialogues, and Philosophical C0rrespondence: George Berkeley (Indianapolis, 1965), pp. xl-xli. 6

First Period - Education, creativity, continental tours. 1685-1720. Second Period - The American Dream. 1720-1731. Third Period - Awaiting preferrnent, bishopric. 1731-1752. Berkeley's American Dream was the idealistic project to found a university in Bermuda for the Christian education of co1onists and natives from the mainland of America. Although fina11y unsuccessful, his enthusiasm for the project as weIl as his absence of rancour and scrupulous financial arrangements when it failed gained him respect. Whi1e in Rhode Island, he enter- ed into a correspondence with Samuel Johnson, an earnest, but not overly perceptive enquirer, which offers an insight into Berkeley's character. Whereas he might have dismissed Johnson's enquiries on the excuse of i11ness or profited from the occasion to demonstrate his own bri11iance, instead, by deprecating himself _nI do not therefore pretend that my books can teach truth,,_12 he first tactfully encouraged Johnson to resolve most of his difficulties by his own efforts and then responded cordially on those few difficulties which remained. This same concern for others, whether as individuals or in groups, is equally in evidence during the third period of Berkeley's lire. He secured his appointment as Bishop of Cloyne in 1734 largely on the strength of the impression created by his publication of A1ciphron in 1732 and The Analyst in 1734, both Christian apologetics against free-

12Works II 282. ~~~, , 7

thinkers and mathematicians respectively. It would have been in full accord with the standards of the time to have treated the bishopric as a well-earned reward for past services to the church and in return for which no further effort wa~ required. Instead, he left London, where his grace and charm made him a popular figure, to live for eighteen years in Cloyne in a remote part of south-west Ireland, where he be­ came active in attempting to alleviate the poverty and sick­ ness of his parishioners, as weIl by direct practical action as by the publication of the economic proposaIs of The Que­ rist {1735-1737} and the medical proposaIs of Siris {1744}. This latter work is open to the criticism that the curative qualities of the tarwater which Siris promotes are today considered to be negligible.13 Nevertheless, the writing of Siris makes clear a readiness to devote his energies to the study of the rudimentary medical science of his day, at a time when his own health was failing, to attempt an ad­ vance in medical knowledge which would be of benefit to mankind. That he met with only limited success, both in America and Ireland, does not diminish the importance he placed on the betterment of human life.14 With this evidence of a concern for his fellow man, it is helpful to consider Berkeley's philosophie writings in the light of this philanthropie purpose. This is not to

13Wisdom, Unconscious Origins, pp. 78-9. 14Turbayne, "Introduction," pp. xiii-xiv. ignore his fundamental religious faith that the world and everything in it are manifestations of the divine will. Cou­ pIed with this religious faith, his philanthropic purpose was responsible for a philosophy that is not only theocentric, but designed to justify and defend religion and in particular to show "the use and benefit of the Christian religion" to mankind. 15 In addition to being the source of aIl things, Berkeley's God is remarkably useful to man. This philanthro­ pic purpose, when properly subsumed under his religious faith, contributes to an understanding of his philosophy of science. To Berkeley, as to most of his contemporaries, the whole of learning is of value only to the extent that it is of use to man. His application of this principle to natural science had been anticipated by others, but his originality shows in extending this principle into the fields of mathematics (see Chapter 7) and language. The chief end of language is not communication, but "the influencing our conduct and actions, which may be done either by forming rules for us to act by, or by raising certain passions, dispositions and emotions in our minds."16 What distinguishes him even more noticeably from his contemporaries is his insistence that, if the value of learning lies in its use, errors must be purged from the­ ory, not as a pedantic exercise, but as a service to mankind. To his end, Berkeley dedicated much of his philosophic

15Works , III, 117-8; Alciphron, V, s. 4. 16Ibid• , III, 291-2; AlciEhron, VII, s. 5. 9

effort, especially in the philosophy of science. Although it will be clear in what sense he was a philosopher of the common man, it remains to ask whether his was a cornrnonsense philosophy. He considered both Locke and himself as philosophers of commonsense; in this Berkeley seems to have been right about Locke, but wrong about himself. Professor Harry M. Bracken points out that it is for Berkeley a philosophical necessity that his principles should accord with cornrnonsense since to separate reality from sensible appearances opens the way to scepticism.17 While a study of the effects of this on Berkeley's episttmological princi­ pIes can be left until Chapter 3, it is relevant to the pres- ent discussion to note that this scepticism poses a threat to the faith in a divine being and the belief in the corporeal world on which the ordinary man depends. In remarking in his notebook:

Entry 405: AlI things in the Scripture wch side with the Vulgar against the Learned side with me îsso. l side in aIl things with the Mob, he rnay have been referring not so much to the content of his philosophy as to its purpose. And in the purpose of his phi- losophy, there is, as we have seen, a mixture of divine inspi­ ration reminiscent of and possibly influenced by Malebranche l7Harry M. Bracken, The E(T~Y Reception of Berkeley's Irnrnaterialism, l7l0-I733 e Hague, 1965T, pp. 47-8. l8Works, l,51. 10

with concern for the welfare of mankind. In attempting a balanced account of Berkeley's philosophy, one should ack­ nowledge both his philanthropic and his religious motives. It has been stated that Berkeley was lucky to be born in a tolerant age when a book like An Essay Towards ~ New Theory of Vision (published in 1709), in which Berkeley as a young man of not more than twenty-five attacked the whole traditional structure of optics, attracted no more than a few polite pamphlets and reviews in response.19 Such a statement can hardly be maintained since the publication of the careful research of The Earl} Reception of Berkeley's Immaterialism 1710-1733 in which Professor Bracken concludes that "Berkeley had been accused of scepticism, egoism, idea­ lism and atheism long before 1733" and remarks of one review of Three Dialogues Between Hylas and Philonous (1713) that it took Berkeley's philosophy seriously and refrained from ridicule "unlike the vast majority of criticisms published during Berkeley's life.,,20 In fact, Berkeley was most un­ fortunate in his early critics, who granted. him neither courtesy nor a fair hearing. The reasons lie partly in the turbulent intellectual climate of the times, which made it advisable to take sides and treat an independent thinker such as Berkeley as an enemy. The Baylean Pyrrhonists could not

19A•D• Ritchie, George Berkeley: A Reappraisal (Manchester, 1967), p. 1. 20Bracken, Early Reception, pp. 5-11. Il

ignore his attacks on scepticism nor the Newtonians his attacks on the mathematicians in A Treatise Concerning The Principles of Human Knowledge (1710) whereas the Jesuits treated him as a Malebranchean and hence an enemy. Perhaps most surprising in view of the announcement of his opposi­ tion to scepticism and atheism in the title pages of both the Principles and the Three Dialogues are the accusations of supporting the very evils which his philosophy was designed to overthrow. Other reasons for the harshness of this early criticism lie in the difficulties in his philosophy, to which we now turne 12

Chapter 2. His Rejection of Abstraction

In this outline of Berkeley's philosophy in general as a prelude to an examination of his analysis of science, we can conveniently begin with the rejection of abstraction which occupies an important position in his philosophic system. Al­ though it has been seen as the basis of his whole philosophy,21 the rejection of abstraction is perhaps best described by Professor Jessop's reference to it as one of the two discov­ eries - the other is the immaterialism contained in the axiom "esse is percipi" - believed by Berkeley to be the keys to aIl sound knowledge. 22 In this paper, the treatment of the rejection of abstraction follows Professor H.B. Acton's recom­ mendation that we treat Berkeley's writings "as a continuing and developing critique of abstraction.,,2) The most comprehensive statement of his rejection of abstraction is found in the Principles. The doctrine of abstraction is presented as a two-fold process: 24

21Whitrow, "Berkeley's Critique of Newton," 82, 107. 22Works, II, 6. 2)H.B. Acton, "Berkeley," The Encyclopedia of Philosophy, 1967, 1, )0). 24Works, II, 84; Principles, s. 99. 1 13

First degree of abstraction. From the perception of an object a8 extended, coloured and moved, motion, to take one of Berkeley's examples, is analysed out mentally from the other sensible qualities of extension and colour in order to be considered in isolation. Second degree of abstraction. Motion is then abstracted from its being perceived by leaving out of consideration not only the body moved, but also such qualities of the motion as the particular figure described, direction and velocity. The abstraction of motion thus arrived at refers equally to aIl particular cases of perceivable motions. Similarly, the abstract idea of animal would be constituted of what is com- mon to aIl men, birds, beasts, fish and insects, namely body, life, sense and spontaneous motion. But body as here under­ stood would have no particular shape or figure since there is no one shape or figure common to aIl animals. 25 Berkeley's critique is based on a contrast drawn bet­ ween a legitimate and a non-legitimate model of abstra~tion.~6 He admits the first degree of abstraction as a legitimate use of abstraction since, to use the same example, although motion is isolated from the other sensible qualities of an object, it still depends on the direction, velocity and other qualities of the motion of a particular objecte The second degree of

25Ibid., II, 27-9; Principles, Introduction, SS. 6-9. 1 26 R1"t Ch" le, p. Xll."" 14

abstraction, by which motion is abstracted from its own perceivable qualities, is clearly independent of aIl sensible qualities of particular objects and cannot thereby gain legitimacy. However, the abstraction of motion arrived at in this manner may be legitimate if it can serve as a useful mathematical operator. It is important to stress at this point that the legitirnacy of this abstraction of motion depends solely on its usefulness in quantifying motion and making it more precise. Having a merely pragrnatic justifi­ cation in the field of mathematics, such hypotheses as motion, space and time can have no ontological status. He consis­ tently attacked the Newtonian motions of absolute space, time and motion as hypostatizations of mathematical hypotheses, representing at the same time an illegitirnate use of abstrac­ tion and a dangerous error in the foundations of natural science. Berkeley admits that we can sometimes consider one quality of an object as separate from its other qualities, but denies that we can legitimately abstract from the other qual­ ities of an object a quality which cannot exist separately, or that we can form a general notion by abstracting from particular instances signified by that notion. The example he uses - as a nkilling blown27 - is Locke's general idea of a triangle formed by abstraction and resulting in a triangle which has aIl and yet none of the qualities of particular

27Works, I, 84; Philosophical Commentaries, Entry 687. 15

triangles. Such an abstract general idea with its inconsis­ tent qualities is, Berkeley insists, both impossible and unnecessary. It is true that we use general ideas in dis­ course to stand for all parti~ular ideas of the same sort, but the meaning of a general notion lies in its relation to the particulars for which it stands and not in any entity forrned by abstraction. 28 It will be helpful at this point to refer to Pro- fessor G.J. Warnock's linguistic interpretation of Berkeley, which suggests that the issue of abstract ideas derives from two rival theories of meaning. 29 Locke's theory requires that we be able to frame abstract ideas to account for the meaning of general terrns. The main point of Berkeley's crit- icism of Locke, who is also accused of vagueness in his presentation, is that it is both logically and psychologically impossible, whether by abstraction of any other method, to frame an abstract idea with inconsistent qualities. The result is that abstract ideas, being deprived of "their basis of meaning, become incomprehensible. Berkeley, who is as concerned to assert general terrns as to deny abstract ideas, must give an alternative theory of meaning of general terrns. A geometer draws a triangle on the board to demonstrate, say, the theorem that the surn of the angles of a triangle is two right angles. Locke's geometer would then frame the abstract

28Ibid., II, 29-35; Principles, Introduction, SS. 10-16. 29Warnock, pp. 60-76. 16

idea of a triangle - which "mùst be neither oblique nor rec­ tangle, neither equilateral, equicrural, nor scalenon, but aIl and ~ of these at once" - to prove that the theorem is universally true. Berkeley's geometer would proceed by demonstrating that none of the qualities of the particular triangle - for example, being right-angled or isosceles or of a certain size - is used in the proof so that the theorem holds good for the general t.erm "triangle" and is universally true .30 Berkeley's rejection of the doctrine of abstract ideas was designed to expose the mistake of supposing that every noun stands for sorne one thing or, as he himself ex­ pressed it, "that every general name stands for a general abstract idea.,,31 Nor, although he is the only philosopher quoted in this connection, was Locke alone in holding this view. The attack is directed at both the Schoolmen, "those great master of abstraction,,,3 2 and at the materialists, who use abstractions to explain everything. There is in fact ample justification for Berkeley's suggestion that the doctrine of abstract general ideas in an error that runs "through most parts of learning.,,33 It is no doubt his acumen in detecting the flaw in this influential and widely held view as much as

30Works , II, 32-5; Principles, Introduction, ss. 13-16. 31Ibid. , IV, 135; Defence, s. 47. 32Ibid. , II, 35; Principles, Introduction, s. 17. 33Ibid. , IV, 136; Defence, s. 48. 17

the able statement of his arguments which led Hume to pro- nounce Berkeley's rejection of the doctrine of abstract ideas "to be one of the greatest and most valuable discoveries that has been made of late years in the republic of letters.,,34 Hume's evaluation has endured, and, despite qualification and changes in terminology and presentation, contemporary philosophy substantially follows Berkeley's rejection rather than Locke's acceptance of the doctrine of abstraction. There is considerable evidence in his texts to support the contention that Berkeley maintained his rejection of the doctrine of abstract ideas consistently throughout both his general philosophy and his philosophy of science. His major statement in the Principles is anticipated by the following remarks from his early notebooks, recorded in their probable order of composition:

Entry 318 - Qu. is it not impossible there shou'd be General ideas? •• Entry 401 - No general Ideas, the contrary a cause of mistake or confusion in r~thematiques etc. this to be intimated in y e Introduction. Entry 524 - General Ideas Cause of much Tri­ fling & Mistake. Entry 666 - All our knowledge is about partic­ ular ideas according to Locke. All our sensa­ tions are particular Ideas as is evident. Wt use then do we make of general Ideas, since we neither know, nor perceive them.35

34David Hume, A Treatise on Human Nature, ed. T.H. Green and T.H. Grose (London, 1874);-1, 325. 35Works, 1, 39, 51, 65, 81; Philosophical Commentaries. 18

This early view is echoed in Berkeley's first important pub­ lication, the Essay ~ Vision, a work on optics which dif­ ferentiates between objects of sight and those of touch in order "to shew the manner wherein we perceive by sight the distance, magnitude, and situation of objects." In addition to this main purpose, the Essay ~ Vision serves as a prelude to the statement of Berkeley's general philosophie position in the Principles by introducing selected parts of his doctrine. The rejection of abstraction is introduced in the context of an unsuccessful search for ideas common to the senses of both sight and touch, restricted here to the abstract-ideas of extension or figure,36 but extended in the Principles to a general attack on abstraction.

The Essay ~ Vision also condemns, in passing, "the idea of motion in abstract" as unintelligible with a hint to­ wards the future treatment of motion in De Motu (published 1721).37 This latter work opens with a criticism of the use in contemporary physics of such obscure terms as "solicitation of gravity , urge, dead forces, etc," based on Berkeley's rejection of abstraction. "Abstract terms (however useful they may be in argument) should be discarded in meditation, and the mind should be fixed on the particular and the concrete, that is, on the things themselves.,,38 Later, this argument is

36Ibid., l, 171, 220-3; Essay on Vision, SS. l, 122-7.

37Ibid., l, 226-7; Essay ~ Vision, SS. 137-8. 38Ibid., IV, 31-2; De Motu, SS. 1-7. 19

applied to Newton's notion of absolute motion, Berkeley's refutation of which will be considered in Part Two. This leads to Berkeley's three rules for

determining the true nature of motion: (1) to distinguish mathematical hypotheses from the natures of things; (2) to beware of abstrac­ tions; (3) to consider motion as something sensible, or at least imaginable and to be content with relative measures.3~

The first rule brings attention to the intimate, bu.t frequent­ ly mis-interpreted relationship of mathematics to physical science. The subject of his first published works at the age of twenty-two, Arithmetica Absgue Algebra and Miscellanea Mathematica, mathematics retained its interest for Berkeley, as evidenced by his participation in the controversy occa- sioned by the appearance of The Analyst (published 1734) in his mature years. Although a Christian apologetic designed to defend the Christian faith from the attacks of contemporary mathematicians, this work also represents an acute analysis of the foundations of Newton's differential calculus and, in particular, of the notion of fluxions, dismissed by Berkeley as "the ghosts of departed quantities.,,40 Of interest to us is the assumption of the rejection of abstraction implicit in The Analyst, for example, in one of the queries:

39Ibid., IV, 49; De Motu, S. 66. 40Ibid., IV, 89; Analyst, S. 35. 20

TNhether the notions of absolute time, abso­ lute place, and absolute motion be not most abstractedly metaphysical? ~Vhether i t be possible for us to measure, compute, or know them?, 41 an assumption made explicit in A Defence of Free-thinking in Mathematics (published 1735), a response to Berkeley's critics which adds nothing to the mathematical issues, but which reit­ erates his stand against the doctrine of abstraction and makes clear that he regards the key concepts of the doctrine of fluxions as abstract ideas.42 Berkeley maintains his philosophic rejection of abstraction in works intended for a more popular audience. In the Three Dialogues, published in 1713 in an attempt to pop­ ularize the philosophy of the earlier Principles, Philonous denies that we can frame abstract ideas. 43 In Alciphron, written similarly in the dialogue form and published in 1732 as part of the antitheistic controversy, the doctrine of abstraction is considered and again rejected.44 His last work, Siris (1744), has been interpreted as an abandonment of the earlier rejection of abstraction in favour of the accep­ tance of a world of Neo-Platonic terms.45 Despite its diffi-

41Ibid. , IV, 96; Anal;y:st, Qu. 8. 42Ibid. , IV, 136; Defence, S. 49. 43Ibid. , II, 192-4; Three Dialogues, 1. 4·4Ibid. , III, 291-6; AlciEhron, VII, SS. 5-7. 45John Daniel 1/'lild, George Berkele;y:: A Stud;y: of His Life and PhilosoEh;y: (New York, 19 2), pp. 424-5. ~l

culties, the text of Siris seems to contain ample grounds for the refutation of this interpretation. One need merely cite the references to absolute space as IIthat phantom of the mechanic and geometrical philosophers" and to abstract ideas "in the modern sense" and "as sorne moderns understand abstrac­ tion,,;46 in addition to the negative context of each reference, there is a pejorative connotation associated with the mention of contemporary science and philosophy in a work laudatory of ancient learning. There seems, in fact, to be solid evidence in Berkeley's texts for Professor Luce's conclusion that Berkeley, throughout his life, "stood over every detail of his early doctrine of abstraction. ,,47

46Works, V, 127, 153, 148; Siris, SS. 271, 335, 323. 47Ibid., IV, 106. 22

Chapter 3. On Physical Objects.

Although his denial of abstraction was fundamental to his philosophy, Berkeley was willing to abandon neither general nor particular ideas. The meaning of a general idea lies in its relation to certain particular ideas. But what does the term "idea" mean for Berkeley? Locke used "idea" as a blanket term for any kind of mental content or, in his own words, to stand for "whatsoever the mind perceives in itself, or is the immediate object of perception, thought, or understanding.,,48 Berkeley sharpened Locke's rather blunt concept to make "idea" stand for any representation or content of the mind in the sense of an object of experience, that is, an object of the senses whether perceived, remembered or imagined. Hardness, softness, colour, taste, warmth, figure and similar qualities are aIl ideas for Berkeley and as such they exist only in the mind which perceives them. "The exis- tence of an idea consists in being perceived"; no idea is unperceived at any time and talk of unperceived ideas becomes unintelligible. 49 Vlhen "idea" is used without qualification

48John Locke, An Essay Concerning Human Understanding, ed. John W. Yolton, revised ed. (London, 1965), l, 104. 49Works, II, 56-7, 42; Principles, S3. 38, 2. 23

in this thesis, it will, of course, refer to this Berkeleian concept of idea. Physical objects are merely collections or combina­ tions of ideas. To give Berkeley's own example, if a certain colour, taste, smell, figure and consistence are regularly noted to go together, we conclude that we are observing a distinct thing which we signify by the name "apple." Since

physical objects as we know them are co~posed of ideas, what is true of ideas is also true of physical objects. They, too, exist only in the mind, their exi:tence consists in being perceived, and talk of unperceived objects becomes unintelli­ gible. In Berkeley's famous dictum, "their ~ is Eercipi.,,50

Before we leave this accou~t of physical objects, it will be helpful to examine a little further the relation between things and their properties. One traditional view, now usually associated with phenomenalism, considers the rela­ tion of properties to things as analogous to the relation of the part to the whole. Locke, who is in general agreement with this position, writes:

So also, finding that the substance, wood, which is a certain collection of simple ideas so called, by the application of fire is turned into another substance, called ashes, i.e. another complex idea, consisting of a collection of simple Idëas.5l

50Ibid., II, 41-2; Principles, SS. 1-). 5l Locke, l, 271. 24

At first sight, it might appear from Berkeley's frequent description of things as collections of ideas52 that he accepted this Lockean view. However, he spoke more often of things as combinations of ideas than as collections. 53 The linguistic connotations of the term "combination" along with other considerations have lead Professor Bracken to identify the relationship between a thing and its properties in Berkeley's philosophy as an intentional tie, meaning roughly that the properties, which we know by our ideas, function as signs from which we learn the meaning of the terms used to name things. 54 The impl,i'cations. of the inten­ tional tie thesis are not confined to the thing-property relationship and we will again refer to this doctrine later in consideriI1g the connections between things and material substance and between ideas and mind. To turn now to sorne consequences of the doctrine of "esse is percipi," we rnight first ask how Berkeley accounted for illusion. Clearly, an imaginary fire - as dreamt, imag­ ined or remembered_would consist of a combination of ideas of certain colours, smells, sensations of warmth and so on in the mind just as would a real fire. We distinguish the

52Works, l, 24, II, 41, 109; Philosophical Commentaries, Entry 179 and Principles, SS. l, 148. 53Ibid., II, 52, 56, 107, 195; Principles, SS. 26, 38, 145 and Three Dialogues, 1. 54Harry M. Bracken, "Substance in Berkeley," in New Studies in Berkeley's Philosophy, ed. Warren E. Steinkraus (New York, 1966), pp. 93-4. 25

imaginary from the real fir.e since the former set of ideas is less strong, lively, distinct, orderly and coherent than the latter set. 55 As Berkeley stated the criteria for distinguishing the imaginary from the real in relative terms, it has been suggested that he used the term "reality" in a comparative sense. 56 l would rather say that he stated the grounds for the making of what are substantially linguistic judgments in such cases of perception, permitting him to account for our correct judgments as weIl as our occasional erroneous judgments, when we mistakenly take the imaginary for the real thing or vice versa. If the argument from illusion poses no serious problem for Berkeley, it does lead us to the philosophically more interesting distinction between commonsense objects and scientific objects. To see how this distinction can arise, let us consider the treatment by the ordinary man and the scientist of one quality of physical objects, colour. The ordinary man uses colour names to distinguish differences in colour visible to the naked eye. The experimental phys­ icist studies the colour of an object by measuring the wave­ lengths and intensities of the reflected light with a spec­ troscope; he can identify an indefinite number of different colours, "naming" each mathematically by the recording of certain wavelengths and intensities in its spectrum. From

55Works, II, 53-5; Principles, ss. 30-3. 56Luce, Berkeley's Immaterialism,tP. Ill. 26

the particular problem raised by this example of the rela­ tionship between the colour names (strictly, what is named) of the ordinary man and the measurements of wavelengths and intensities of the physicist, first, to each other and, secondly, to the coloured object, there arises the general problem of how to account for this apparent difference be­ tween the objects of cornrnonsense and the objects studied by the scientiste Galileo was the first thinker to apply the distinc- tion bet't"leen primary and secondary qualities to the solution of this problem. On the one hand are the primary qualities, those inherent qualities which are conceived as inseparable from their objects, for example, extension, figure, motion; on the other hand are the secondary qualities, such as colours, sounds, tastes, smells, which are conceived as being separable from their objects and appear to depend rather on the perceiver. Galileo expelled the variable secondary qualities from physics, which he construed as dealing with the constant prirnary qualities, that is, with observable data capable of measurement. 57 Galileo's distinction between primary and secon- dary qualities was accepted by later philosophers, notably the Cartesians and in particular Descartes and Male~ranche, and by scientists through Robert Boyle down to and including

57T.E. Jessop, "Berkeley as Religious Apologist," in New Studies in Berkeley's Philosophy, ed. Warren E. Steinkraus (New Yor~ 1966), p. 101. 27

Newton. 58 One exception among the minor Cartesians was Simon Foucher, whose Critique de la Rt.rcherche de la vérité (publish­ ed 1675), an attack on Malebranche's Recherche de la Véritf, gives the essential points of Berkeley's later criticism of the distinction between primary and secondary qualities. Although there is no evidence that Berkeley read Foucher's work, both Berkeley and Hume studied Pierre Bayle's Dictio­ nnaire, which appeared in 1697 and which, under "Pyrrho, " Remark B, surnrnarizes Foucher's argument, accurately although in radical forro. 59 Despite Foucher's objections, the doc­ trine of primary and secondary qualities became firmly established and had won virtually universal acceptance by Berkeley's time. In a touch of mild irony, it was Locke, one of the few men of the day known to be familiar with

Foucher's own writings,60 whose Essay Qg Human Understanding (published 1690) gave the doctrine of prirnary and secondary

qual~ties its fullest and most influential statement. Although the credit for originality belongs to Foucher, it waS Berkeley who integrated this critical argu­ ment into the framework of a coherent philosophic system in an attack on the distinction between primary and secondary

58Works II 152. ~~;;;;.' , 59Richard H. Popkin, "L'abbé Foucher et le ... problème des qua­ lite"'s premi~res," Bulletin de la Société d'Etude du XVIIe Siècle, 33 (December, 1956)--,633. 60Richard A. Watson, ed. "Introduction," Simon Foucher's Cri­ tique de la Recherche de la Vérité (unpublished), p. 3. 28

qualities introduced in the Principles and elaborated three years later in the Three Dialogues.61 Briefly, Berkeley first agreed with his opponents' argument and with their conclusion that the ideas of secondary qualities are rnerely contents of the rnind and not properties of physical objects without the mind, but then took issue with his opponents by arguing from the same grounds to a similar conclusion for such primary qualities as extension, figure and motion. If the secondary qualities are Berkeleian ideas, so then are the prirnary qualities. There are no grounds to accept the evidence of the senses for spatial properties, but to reject this evidence for colour. This argument from Berkeley's theory of perception was supplemented by an appeal to the rejection of abstraction to show the irnpossibility of for­ ming an idea of a primary quality such as motion indepen­ dently of such secondary qualities as colour and sound which go to make up the perception of the moved objecte This collapse of the distinction between primary and secondary qualities had important implications for the Newtonian science of the early eighteenth century. Berkeley recognized the value of the results being gained by the new science and was as enthusiastic a supporter of the experi­ mental method as his contemporaries.6~ Unlike his conternpo- ries, however, he insisted that, for its own sake, the

6lWorks, II, 44-7, 174-194; Principles, ss. 9-15 and Three Dialogues, 1. 62Kuypers, p. 16. 29

foundations of the new science be philosophically respectable according to its own empirical principles. One of Berkeley's several criticisms of these foundations arises from his rejec­ tion of the distinction between primary and secondary qualities. To put it roughly, the scientist measures certain aspects of the world such as volume, weight, motion in isolation as a part of the experimental method, the value of which Berkeley fully recognized. But, just as the common man wants a real stone to kick, the scientist wants a real object to measure. Berkeley balked at this. Although in ordinary discourse we may speak of real stones or external objects, in strict phi­ losophie discourse the stone is a combination of ideas in the mind and does not exist outside of the mind. Similarly, what the scientist measures is a combination of ideas and not an external object. Nor is it a primary quality inde­ pendent of mind since it has been shown that primary qual­ ities, like secondary qualities, are ideas and as such dependent on the mind of the perceiver. A hint of the value of this observation may be gained by again taking up the example of the measurement of colour. At the times of both Galileo and Berkeley, colour was not scientifically measur­ able and was generally considered as a secondary quality in contrast to a primary quality such as motion which was then measurable. With the development of the spe~troscope, colour has become scientifically measurable so that, if the primary­ secondary distinction were still current, we would today 30

have to class colour as a primary quality along with sound, smell and so on, traditionally treated as secondary qualities, but which can now be measured objectively. The collapse of the distinction between primary and secondary qualities and other considerations led Berkeley to distinguish sharply between science on the one hand and meta­ physics and theology on the other. 63 The value of science lies in its examination of certain measurable phenomena in order to discover uniformities in nature from which predic­ tions about the behaviour of other phenomena can be deduced. 64 Science ignores its own empirical principles when it strays beyond the boundaries of its own province as, for example, when scientists assert the independence of primary qualities, a metaphysical and not a scientific problem. One effect of such excursions is to obscure the scientific issues.65 A further consequence of Berkeley's theory of perception is his rejection of material substance or matter, again in opposition to both the Cartesian tradition and the contemporary science of his day. Locke's conception of material substance - "an unthinking and unknowable somewhat that is endowed with inherent powers to produce sensations in us,,66 - is sufficiently typical of the view which Berkeley

63G. Hinrich, "The Logical Positivism of De Motu," Review of Metaphysics, III (1950), 498. 64Works, II, 87-8; Principles, SS. 105-7. 65Ibid., IV, 52; De Motu, S. 72. 66Locke, 1, 244-6. 31

was attacking. Locke postulated substance as a logical correlate of qualities, as a merely formaI concept based on the supposition that qualitiee must be "of" something. In addition to rejecting it as an abstract idea, Berkeley attacked this concept of matter interpreted as an inacces­ sible substratum of groups of qualities beyond perception as self-contradictory, unnecessary and non-explanatory.67 It is self-contradictory as a concept since it is at the same time passive (an unthinking somewhat) and yet active in the causation of our ideas. Being self-contradictory in concept, it is also impossible in existence. Material substance introduces unnecessary duplication in its distinction between the real nature of things and what we actually perceive. It follows from "~ is percipi" that our ideas of colour, hardness, shape and so on are the only corporeal realities; the real world is the one known to aIl men directly by their senses and it has no hidden nature.6S Finally and perhaps most dangerously, material substance is non-explanatory. In postulating both material and spiritual substances as un­ knowable, Locke had to admit that they could be the same, an admission which could lead to the abandonment of spiritual substance in favour of a thorough-going materialism. As

67Works, II, 47-51; Principles, SS. 16-24. 6SRichard H. ?opkin, "The New Realism of Bishop Berkeley," University of California Publication in Philosophy, 29 (1957), 8. -- -- 32

Berkeley early remarked: "Matter once allow'd. l defy any man to prove that God is not matter.,,69 This threat te spir­ itual substance is one which Berkeley, who is most concerned to assert spiritual substance, was at pains to answer.

69Works, l, 77; Philosophical Commentaries, Entry 625. 33

Chapter 4. On Spirits.

Berkeley's doctrine of ideas permits him to account for our knowledge of the corporeal world. We perceive colour, figure, motion, extension and so on as sensations in the mind or as ideas; a certain set of ideas constitutes a tree, and similarly for all other sensible things. To suggest that sensible things include something beyond what is perceived or to posit material substance, primary qualities, external objects or archetypes inde pendent of the perceiving mind is to invite scepticism by introducing unknowable real qualities or entities into the world of experience. 70 Our ideas, Berkeley insists, are entirely adequate to account for our knowledge of the corporeal world. At the same time, our ideas, being "inert, fleeting, dependent beings," are incapable either of producing them­ selves or of existing independently of our minds. Ideas stand in contrast to minds - also referred to as spirits or spiritual substances or souls - which Berkeley describes as "active, indivisible substances" entirely distinct from their ideas.7l The doctrine of ideas is dealt with in detail in the Principles.

70Ibid., II, 78-9; Principles, SS. 87-8. 1 71Ibid., II, 79-80; Principles, S. 89. 34

However, the Principles is only Part l of a projected work in three or four parts; the manuscript of Part II to be called "Moral Philosophy" was lost in Italy and Part Illon "Natural Philosophy" and, probably, a Part IV on "Mathematics" were, for sorne reason, never written, at least in the form origi­ nally intended.72 Since the lost Part II was to deal with the distinction between the corporeal and the mental and with the nature of God, it is natural that the Principles should give less attention to the doctrine of spirits than to that of ideas, although an adequate view of the former doctrine can be gained from the Principles supplemented by the Three Dialogues. Given the fundamentally different natures of ideas and spirits, we cannot know spirits by ideas since (active) mind cannot be known by (inert) ideas. How then do we know spirits, that is, our own minds, the minds of others and the infinite mind of God? Berkeley's answer begins with one's own mind; spirit or spiritual substance means "what l am my self, that which l denote by the term 1." A spirit is "that which thinks, wills and perceives," thinking, willing and perceiving being activities which l meet with in myself as, for example, when l will my arm to move and observe that it does in fact move. It can be said that l have knowledge of my own mind or, in other words, that l have a notion of my own mind. From this notional knowledge of my own mind, l make the

72Ibid., II, 5-7. 35

inference to the minds cf others. l observe the arm of an- other human body to move as my arm moves when l will it to do so. This informs me that there are other agents like my­ self, capable of an act of willing and, by analogy to my own mind, also capable of acts of thinking and perceiving. Hence there are other minds. However, man is not capable of pro­ ducing everything in the world with the result that the natural world, being independent of man, must have its cause in sorne spirit greater than man, namely, infinite spirit or the Author of Nature or God. Berkeley thus bases the existence of God on the argument from causality and goes on to derive the nature of God from observation of the regularities in nature. Con­ centrating rather heavily on the orderliness, beauty and other attractive aspects of nature, Berkeley derives the attributes of God as "one, eternal, infinitely wise, good, and perfect." Berkeley explicitly states: "My own mind and my own ideas l have an immediate knowledge of" whereas "the knowledge l have of other spirits is not immediate," but depends on "the inter­ vention of ideas, by me referred to agents or spirits distinct from myself." Nevertheless, we have a certain knowledge of other spirits and especially of God, "every thing we see, hear, feel or any wise perceive by sense, being a sign or effect of the Power of GOd.,,73 Tt was noted early in this chapter that ideas, being inert, cannot produce themselves or each other. How

73Ibid., II, 231-2, 103-9; Three Dialogues, III and Prin­ ciples, SS. 135-148. 36

then are ideas produced? With ideas themselves ruled out as a possible cause, the answer must lie in spirits, the only other reality recognized by Berkeley. Ideas of memory or imagination can, we find, be produced in the mind at will, that is, by a power of our own finite minds which we calI will. In contrast, we find by experience that the ideas of sense are not dependent on our will for we cannot will our­ selves not to see particular objects within our: range of vision when we open our eyes. The distinctness, steadiness and coherence of the ideas of sense as opposed to those of imagination require that the former be produced by an infinite spirit or cosmic mind, namely God. 74 It is possible to reformulate Berkeley's whole epistemological doctrine in terms of a philosophy of language. As Professor Jessop states, it is for Berkeley a contradiction in terms to speak of: (1) anything corporeal which is neither perceived nor capable of being perceived, or (2) anything mental which is not actively perceiving,75 the novelty of which view is recognized by Berkeley in his early comments recorded in the Philosophical Commentaries.76 A linguistic interpretation is also proposed by Professor Bracken, who suggests that the Berkeleian doctrine of notions

74Ibid., II, 51-4, 56; Principles, SS. 25-30, 36. 75Ibid., II, 9. 76Ibid., l, 34, 61-2; Philosophical Commentaries, Entries 279, 491. 37

depends on a language metaphor and extends his intentional tie account of the thing-property relation to the relation of ideas to mind. In giving his reasons for preferring the term "idea" to "thing," Berkeley makes clear that ideas are related to the mind necessarily.77 Against those who would base this necessary relationship on either the inherence or the part-who1e pattern of traditional ontologies, Professor Bracken describes the relation of ideas to mind as an inten- tional tie, by which certain sets of ideas are signs meaning something to the mind of the perceiver, who learns to calI, say, a certain set of ideas a tree. In effect, Berkeley relies on the ordinary use of language rather than on any philosophical argument to justify his commonsense axiom that ideas are necessarily connected to the mind.7$ That much of Berke1ey's philosophy depends at least implicitly on a theory of language receives textual support in his treatment of spirits, where he equates having a notion of spirit with understanding the meaning of the word, and later remarks: "1 have sorne knowledge or notion of my mind, and its acts about ideas, inasmuch as l know or understand what is meant by those words. il79 As a linguistic interpretation, the intentional tie thesis is valuable in considering Berkeley's view of the order

77Ibid., II, 235-6; Three Dialogues, III. 7$Bracken, "Substance in Berkeley," pp. $$-97. 79Works, II, 105-6; Princip1es, SS. 140,142. of nature as God's language to men. Let us first review Berkeley's arguments for the existence of God. The argument in the Principles80 for God as the cause of our perception of things is supplemented by a second argument, introduced in the Principles and elaborated in the Three Dialogues, for God as a kind of permanent perceiver of aIl sensible objects, thereby guaranteeing their "esse" and accounting for the continuous existence of the corporeal world.81 These two theistic argu- ments, which are not incompatible, are typical of the a posteriori proofs, deriving the existence of God from the physical world, which were current in the natural theology of Berkeley's day.82 He buttresses hisposition by an argument for the benevolence of God. The first published statement of the argument appears in the Essay ~ Vision, in which Berkeley, after distinguishing sharply between the objects of sight and the objects of touch, proposes a kind of divine visual language. A benevolent God, who provides us with orderly collections of ideas of sight, arranges also that certain ideas of sight act as signs:

whereby we are instructed how to regulate our actions in order to attain whose things that are necessary to the preservation and

80Ibid., II, 56; Principles, s. 36. 81I bid., II, 43, 61, 80-1, 212; Principles, ss. 6, 48, 91 and Three Dialogues, II. 82Jessop, "Berkeley as Religious Apologist," p. 103. 39

well-being of our bodies, as also to avoid o whatever may be hurtful and destructive of them. 83

Professor Luce has suggested that in the Principles this doctrine is "quietly" extended by adding the objects of touch and the other senses to the objects of sight to form a divine sensible, rather than merely visual, language. 84 l would suggest, rather, that this move may be implicit in the orig­

inal statement of the doctrine in the Essay ~ Vision, but that neither the Principles nor later works, notably Alciphron in which Berkeley continues to refer to "this optic language" and "this Visual Language," makes this move explicit.85 In fact, the only noticeable change in presenting this doctrine occurs in the 1732 edition of the Essay on Vision in which the earlier reference to "the universal language of nature" becomes "an universal language of the Author of nature.,,86 There may be a hint here of a desire to emphasize the role of God in the explanation of the corporeal world, but no evidence of any significant change in the view expressed in the Prin­ ciples of an order of nature .. in' which combinations of our ideas functions as signs of natural phenomena or things signi­ fied much as in language letters combined into words signify

83Works, 1, 231; Essay on Vision, S. 147. 84Ibid., 1, 153. 85Ibid., II, 58-9, III, 149-162; Principles, S. 44 and AlëIPhron, IV, SS. 7-15. 86Ibid., 1, 231; Essay ~ Vision, S. 147. 40

what is meant by the word. These signs in nature are provided by God as a divine language for the bene fit of the human race so that the natural scientist who interprets these signs serves at the same time the needs of mankind and the glory of GOd. 87 As the sensory data are clearly not signs of which the meaning is the whole as would be required by the inherence pattern of traditional ontologies, it seems preferable to adopt the intentional tie thesis by which it can be said that to learn what sensory data signify is to learn God's language. Use of this thesis also permits a response to the assertion that Berkeley adopted Locke's account of things as collections of powers to produce our sensations, but transferred these powers from matter to God. Professor Luce argues that Berkeley later abandoned reference to combinations of powers in favour of a rather subtle interpretation of God's powers as sustaining causes. 88 A more natural reading results from the intentional tie thesis which would have permitted Berke­ ley to eliminate talk of powers of God by appealing to a lin­ guistic theory whereby meaning can be said to be "in" GOd. 89 Berkeley's concept of God has been carefully exam- ined and sometimes criticized by commentators. Professor J.D. \Vild concludes, from a study of aIl of the writings, that

87Ibid., II, 69-70, 88-9; Principles, SS. 65-6, 108-9. 88A•A. Luce, The Dialectic of Immaterialism (London, 1963), p. 154. 89Bracken, "Substance in Berkeley," pp. 93-4. 41

Berkeley came to recognize existence as being who11y phenom­ enal and to accept God as a mere1y logica1 abso1ute.90 This view is opposed exp1icit1y by Professor G. Hinrich, primari1y on the evidence of De Motu,91 and imp1icitly by Professor Warnock, in his acknow1edgement of the one exception to the extreme empiricism of Berkeley's philosophy, namely, the belief thatthe proposition that every part of the universe necessari1y and eternally exists in the mind of God is demon­ strably true.92 To this let it be added that aIl the refer- ences to God throughout the texts appear to be adequately interpreted as a series of attempts by Berkeley to clarify, elaborate and justify a concept of God which remains unchanged. The concept and role of God as considered above has been referred to as Berkeley's Deus ~ Machina, a viewagainst which Professor J.D. ~~bbott argues.93 That the ~ ~ Machina charge is unfounded is rendered most evident by considering Berkeley's criticism of Newton's notions of abso1ute space and time. Although at times the bishop is less theological than the physicist, Berkeley is close to the Newtonian position on the relation of God to phenomena. Berkeley cou1d agree with Newton both that the world process

90Wild, pp. 253-279. 9lHinrich,III,494. 92\'larnock, p. 19. 93J .D. f.'Iabbott, "The Place of God in Berkeley' s Phi1osophy," in Locke and Berkeley: A Collection of Critica1 Essays, ed. C.B. Martin and D.M. Armstrong (London, 1968), p. 364. 42

is metaphysical and that its actual course is ascertained only by its effects on observable phenomena. 94 However, when Newton went on to base his concept of the universe on absolute space-time, Berkeley objected that positing Newto­ nian absolute space or Lockean pure space would result in the dilemma "of thinking either that real space is God, or else that there is something beside God which is eternal, uncreated, infinite, indivisible, immutable.,,95 Had Newton and Locke followed their view of the universe as based on absolute space-time though to its logical conclusion, they, like Berkeley, would have found both of these alternatives to be theologically unacceptable. In pointing this out, Berkeley's procedure was philosophically perfectly respectable. We can admit that his criticism of Newtonian absolute space was impelled by theological considerations and also that his a posteriori arguments from the physical world to God fail to provide a wholly satisfactory connection between his philo­ sophy and his theology. But these admissions relative to his purpose do not grant the ~ ex Machina charge since the attack on absolute space-time is not only soundly based, but, as we will see in Part Two, is developed into a valuable and eventually influential criticism of Newtonian physics. It remains for us to consider Berkeley's view of

94G•J • Whitrow, "Berkeley's Philosophy of Motion," British Journal for the Philosophy of Science, IV (~~y, 1953 - Fe- bruary, ~4r;-37-9. -- 95Works, II, 94; Principles, S. 117. 43

relations, one of the few references to which is this remark in histreatment of notional knowledge:

It is also to be remarked, that all rela­ tions including an act of the mind, we cannot so properly be said to have an idea, but rather a notion of the relations or habitudes between things.96

Although such a brief description would make a detailed expo­ sttion of the Berkeleian view of relations largely a matter of conjecture, it is possible to trace his view in general terms. In the discussion of the dual relationships of things to their properties and of ideas to minds, it has been earlier suggested that he envisages these relationships as aspects of a the ory of meaning in the manner made clear by the introduc­ tion of the intentional tie thesis. This is not to minimize God's role as cause of our ideas and of the orderliness of their combinations. Roughly speaking, the answer to how ideas are related necessarily to minds (or how properties relate to things) lies in a theory of meaning, but the answer to why they are related lies in the divine will. The quotation given above refers more strictly to relations between things. Such relations can be divided into two types: relations which can be fully specified in terms of Berkeleian ideas and those which cannot. An example of the former type of relation would be the motion of a particular body, which can be fully specified in terms of observations

96Ibid., II, 106; Principles, S. 142. 44 of the moving body and at least one other body to serve as a frame of reference.97 To be legitimate, the general idea of motion must, Berkeley insists, be similarly based on empirical observation. ~otion as thus considered is passive and, being known by our ideas, falls within the province of physics. However, it forms no part of notional knowledge and, being passive, cannot serve as a cause or principle of anything. In saying that we have notions rather than ideas of relations, Berkeley may have been ruling this empirical type of relation out of consideration. Alternatively, he may have been drawing attention to the fact that the meaning of even the purely empirical relations, as exemplified by the motion of a partic­ ular body or the relation of one object being on top of ano­ ther, depends on a perceiving mind. An example of the latter type of relation would be causality, which cannot be specified in terms of Berkeleian ideas. The prototype of causality is my own will as encountered in my activity. Causality is active, revealed as notional knowledge and falls within the province of metaphysics and theology, but not science. Berkeley clearly has the relation of causality in mind when he refers to us having a notion rather than an idea of relations. The very different accounts of motion and causality which emerge will be taken up in the treatment of the separation of science from metaphysics in the next chapter.

97 Ibid., II, 47; De Motu, S. 58. PART TWO

BERKELEY'S PHILOSOPHY

OF SCIENCE 45

Chapter 5. The Relation of His Philosophy of Science to His Philosophy in General.

Before undertaking a detailed examination of Berkeley's analysis of science, we will find it helpful to establish three basic, but not particularly controversial, points: (1) that he was an admirer as well as a critic of the ex-

perimental and mathematical methods of Ne~conian science (2) that, in his philosophy of science as in his general philosophy, he reached his conclusions early in his philosophie career without subsequent change of any great consequence (3) that his analysis of science formed an integral part of his whole philosophie position. "One of my earliest inquiries was about Time," Berkeley wrote to Samuel Johnson in 1730, and many of the earliest entries in his notebooks, probably written in 1707, deal with space, time and motion.98 These references to fun­ damental scientific concepts reflect Berkeley's interest in the new physics and its mathematical method, an interest supported by his early studies in this field and maintained

98Ibid., II, 293, 1, 9-20. throughout his writings. Since his significant contributions to the philosophy of science are all vigorous attacks on aspects of scientific or mathematical theory, it will be helpful to set these criticisms in their context. vvith the exception of the traditionalists, almost all of his contem­ poraries admired without question the Newtonian physics, which came to dominate scientific thought from the early eighteenth century to late in the nineteenth century. Berke- ley shared this admiration of the new physics as a mode of research and felt Newton's experimental method to be far superior to the a priori methods of traditional thought. He had no sympathy with those traditionalists who favoured a return to Cartesianism or Aristotelianism. He fully approved of the application by physicists of Newton's empirical method to observations of phenomena in order to discover laws of nature which "direct us how to act, and teach us what to expect.,,99 The value of physical science lies in its power cf prediction, which in turn permits men to lead better lives. Berkeley, in harmony on this point with his own society, but not perhaps with ours, accepted physical science with its empirical method without reservation for its results, the correctness or value of which he did not question. lOO How­ ever, he felt that physicists of his day, including Newton,

99Ibid., V, 112; Siris, S. 234. lOOKarl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (New York, 1963), p. 168. 47

were prone at times to overlook their own rigorous principles as to boundaries and methods. His criticisms were designed to reassert these principles and in effect to use the tools of physics against itself not to destroy it, but to make its philosophical foundation more secure. Being sceptical of the metaphysical superstructure used by physicists, whether this was represented by the conscious structure of a Locke or Newton or the unthinking assumptions of lesser scientists and thinkers, Berkeley attempted with a fair degree of success to evolve a new rationale for physics which preserved intact its valuable experimental method, but excised those theoretical errors which threatned other kinds of knowledge or undermined the viability of physics itself.lOl On the question of the development of Berkeley's thought, the earlier view that there was sorne progressive change102 has now been largely abandoned. Let us look at this question in relation to his general philosophie position before turning to his philosophy of science. It has been argued above in Chapters 2 and 4 respectively that neither his rejec­ tion of abstraction nor his concept of God were changed substantially throughout his writings. In support of the earlier view of a progressive development in Berkeley's philo-

101G.W.R. Ardley, Berkeley's Philosophy of Nature (Auckland, 1962), p. 9. 102A. Campbell Fraser, Berkeley (Edinburgh, 1881), pp. 30-1. sophy, Professor J.D. Wild proposed that, after introducing a Platonic system of archetypes in the Three Dialogues, Ber­ keley moved to a form of transcendentalism in Siris under the influence of Neo-Platonism.IOJ No doubt Berkeley devoted much time to Greek philosophy and Neo-Platonism in the last twenty years of his life, but so did he also at Trinit y College, where he was appointed junior Greek lecturer at the age of twenty-seven. Although he eulogizes Greek philosophy and especially Plato in Siris, there and throughout his writings he maintained his early rejection of the èoctrine of abstraction, a corollary of which is his rejection of archetypes.. In the Principles he denies the possibility of archetypes existing outside a mind on the grounds of his doctrine of "~ is percipi"; since such archetypes cannot be perceived, they cannot be said to existe In the Three Dialogues he acknowledges the possibility of archetypes existing independently of my mind provided that they exist in the mind of God. This i~volves no contradiction of his earlier statement in the Principles since "~ is percipi" does not apply to the contents of the mind of God which are known by notional knowledge and not by ideas.104 Whether or not Berkeley accepted a Neo-Platonic system of perfect forms - and the point is open to debate - this would not be incompatible with his earlier writings since at least sorne

10JWild, pp. 169-170, 424-5, 442. 104Works, II, 59, 248; Principles, S. 45 and Thr~ Dialogues, III. 49

of the Neo-Platonic Forms could be Berkeleian notions in as weIl as qualities of the mind of God, a possibility left open in his correspondence with Samuel Johnson.l05 There seems to be reasonable evidence for the view, shared by Professors Woodbridge, Jessop and Wisdom among others, that Berkeley's considered view remained stable throughout his works despite changes in his attitude, mood and interest.l06 This stability is reflected in his philosophy of science, to which his treatment of motion is central. His early views on space, time and motion are maintained without substantial change throughout his writings up to the publica­ tion of his last work, Siris, in 1744. His first philosophie

publication, Essay Qg Vision (1709), contains a reference to motion and hints at a future work in this field while the Principles, which appeared in the following year, elaborates his views on motion to sorne extent.l07 His main work on mo- tion, De Motu (1721), is who11y in the spirit of the earlier works and repeats and elaborates the main argument from the Principles, an argument reiterated by the references to space, motion and force in Siris.lOB It is reasonable to claim that

105Ibid., V, 17, II, 26B-9, 292. 106Woodbridge, l, 214; Works, II, 7; Wisdom, Unconscious Origins, pp. 54-5. 107Works, I, 226-7, II, B9-93; Essay ~ Vision, SS. 137-B and Principles, SS. 110-6. 10Blbid., IV, 45-50, V,119; De Motu, SS. 52-65 and Siris, SS. 249-250. 50

in Berkeley's philosophy of science we are faced with a stable set of doctrines rather than a continuing development of his thought. Another type of development is implicit in the com­ ment in one of his letters: "I could wish that aIl the things l have published on these philosophical subje~ts were read in the order wherein l published them"I09 Berkeley sometimes found it desirable, apparently for didactic reasons, to post­ pone the presentation of certain parts of his philosophy until later publication. For example, the Essay 2.!!. Vision·, in which Berkeley prepares the way for the Principles by removing the objection to immaterialism that bodies and space exist away from us, contains no mention of his conclusion that no sensi- ble thing could exist without the mind even though he had already reached this conclusion before writing the Essay 2.!!. Vision.IIO In this sense of didactic purpose only can there bé said to be a development of thought throughout Berkeley's wri tings in general philo.sophy and the philosophy of science. That Berkeley's philosophy is "a strange and unstable combination of theses that MOSt other philosophers have thought do not belong together"lll is not apparent when his general philosophie structure is considered in the light of his analysis of science, which is weIl integrated into his

I09Ibid. , II, 294. IIOActon , l, 295-6. IIIIbid. , l, )0) • 51

whole philosophie system. His two realities of spirits and their ideas are the basis of an epistemology summarized by the dicta "~ is percipi" applying to the physical world and "~ is percipere" to the world of spirit. As a result, he sharply differentiates physical science, dealing with ideas and hence natural phenomena, from theology and meta­ physics, both dealing with spirits.112 The value of theo­ logy rests in its concern with religious faith - identified by Berkeley with the Christian religion - both in its in- trinsic purpose as "a principle of happiness and virtue" and in its pragmatic purpose to satisfy the needs of the ordinary man for an abiding religious faith and belief in a benevolent God. 113 Metaphysics (dealing with finite spirits) to sorne extent reflects this value of theology (dealing with infini te spirit of God) so that the conclusions of metaphysics con­ tribute to the support of theology by offering philosophical justification of religious faith. He wished to preserve this value of theology and metaphysics from the competition im­ plied by the new physics. When interpreted as proof of the power of man to discover the secrets of the world of reality unaided by relevation, Newton's theory represented a threat to religious faith.114 At the same time, Berkeley wished to preserve the value of the Newtonian physics as a method of

112Works, IV, 52; De Motu, S. 72. 113 Ibid., III, 177-8; Alciphron, V, 4. 114Popper, p. 98. 52

research of great use in the guidance of our future actions. He therefore insisted that physicists restrict themselves to the boundaries and methods imposed on them by the rigorous empirical principles established but not always practised by Newton. Physicists should in their work neither claim to discover metaphysical causes or principles nor posit such occult qualities as the non-empirical motion of gravita­ tional force. In a sense, a dualism is proposed: empiricism in physical science, supernaturalism in theology and meta­ physics.115 It was noted at the end of Chapter 4 that Berkeley's theory of relations allocates the study of motion, which is known by ideas, to physics and the study of causality, known notionally, to metaphysics. As a typical example of the errors perpetrated by scientists when they go beyond the boundaries of their own field, the breakdown of the distinc­ tion between primary and secondary qualities gives support to this separation of physics from metaphysics. Berkeley's rejection of abstraction has important implications for his philosophy of science as for his whole philosophy. ---De Motu opens with an attack on occult qualities in physics broad enough to include not only the gravitational forces of the Newtonians, but also the atomic particles of more recent physical theorists.116 He would certainly have rejected as illegitimate any attempt to posit electrons,

115Kuypers, p. 58. 116Popper, p. 266. 53

protons and neutrons (let alone such controversial particles of matter as the neutrino) as entities existing in this or sorne other world. While he denied such concepts of physics any ontological status, he did not rule out their use com- pletely provided they were treated merely as useful mathe­ matical hypotheses. He fully recognized the usefulness of mathematics as a tool essential to a physical science based on measurement. After refuting the Lockean notion of the general idea of a triangle formed by abstraction, Berkeley immediately offered his alternative general idea of a triangle in order to maintain the validity of trigc.lometry. He objected not to the use of mathematical hypotheses, but to the setting up of these theoretical abstractions as inde­ pendent entities. When the whole of mathematics is seen through his eyes as an artificial process remote from nature, any attempt to hypostatize the quantification of nature becomes a dangerous error. 117 The rejection of abstraction also gives rise to a refutation of the Lockean doctrine of material substance along with Locke's account of the thing-property relation based on the inherence pattern of traditional ontology. This calls for a new explanation of the relationship of things to their prop­ erties as weIl as of the relationship of ideas to minds, given by Berkeley in terms of a theory of meaning. (See Chap­ ter 4.) The effect of this is to close the gap, opened up

117Ardley, p. 24. 54

by Locke's use of rnaterial substance, between real objects and the objects of commonsense. Professor G.W.R. Ardley expresses clearly the contrast between these two opposing views. In accepting that physicists deal with the real constitution of the universe, Locke implied that the common- sense view of the world was a mere appearance. Being con- cerned at the effect of this world model on the commonsense view, Berkeley compared the physicists and their laws of nature to grammarians and their rules of language. For Berkeley, the world is substantially as it appears, and the physicist and the ordinary man both deal, although in dif- f eren t ways, Wl'th the same na t ura l'unlverse. 118 In his rejection of matter, Berkeley's reasons are partly theological in removing the threat to religious faith implied by the introduction of another substance which might come to be identified with God. It should be emphasized that the theocentricity of Berkeley's philosophy permeates also his philosophy of science. The physicist, who in his application of the empirical method to natural phenomena serves his fellow men, also serves the God who wills these phenomena. The theologian, by use of different methods in a different field, also aids rnankind while contributing to the glory of God. And Berkeley clearly saw his own role of a metaphysician, attacking the theoretical errors of natural science, as a service to both God and man. While physics l18Ibid., pp. 9-10. 55

must be separated from theology and metaphysics in the matter of method, it should be remembered that for Berkeley all is ultimately dependent' on God "who works all in all, and !2.r whom all things consist.,,119 Before turning to a detailed analysis of his criti­ cism of the concepts and methodology of physical science, we should refer briefly to his views on chemistry and physiology, which appear only in his late work, Siris. In contrast to the modernist spirit of his writings on physics, his expressed views on chemistry and physiology seem often embarrassingly out-moded. This is not due to any failure on his part to study the latest information available in all branches of science. It is simply that Newton had brought about a great advance in physics whereas at the time of Berkeley chemistry and physiology, still awaiting their Newton, were confined for the MOst part to the theories and techniques of the Renaissance.120 The result, nevertheless, is that his writ­ ings on chemistry and physiology hold no more than historical interest and do not represent a contribution to the philoso- phy of science.

119Works, II, lOg; Principles, S. 146. 120Jessop, "Berkeley and Contemporary Physics," VII, 90. 56

Chapter 6. His Critique of Absolute Space, Time and Motion.

From this general view of Berkeley's philosophy of science, we now turn to a detailed examination of one of his most important critiques of the contemporary natural science in which he attacks Newtonian absolute motion and the notions of absolute space and absolute time on which it depends. Al­ though most of his philosophic writings contain sorne reference to his theory of motion, we may reasonably focus our attention on De Motu (1721), which elaborates the argument in detail and is wholly in the spirit of the other works. In De Motu the rejection of the doctrine of abstract ideas is applied to a number of terms in the contemporary phy­ sics, among them solicitation of gravit y, urge, dead force and attraction, which are used in such a way as to lead to obscu­ rity. To take gravitational force as an example, we become aware of this in our own muscular effort and fatigue as we support a heavy objecte We observe the fall of a heavy object in accelerated motion towards the centre of the earth and pop­ ularly refer to this phenomenon as gravity. So long as we restrict the terms of reference to the motion and other ob­ servable qualities of the falling object, Berkeley has no objection to this employment of the expression "gravitational 57

force" é.,S a legitimate and useful general idea, descriptive of certain motions of objects and fully explainable in terms of the measurement of those motions and of other observable qualities of the objects. However, the physicists of his day, Berkeley insisted, did not limit themselves to this sensible iàea oî gravitational force, but posited force as a cause or principle of the fall of objects towards the earth's centre. When thus used to stand for an unobservable cause, force ceases to be a legitimate general idea based on sensible qualities and becomes an abstract idea or occult quality, independent of sensible qualities and hence inca­ pable of explaining any natural phenomena.121 An adequate account of motion, as of other physical phenomena, must be based on the senses and not derived from abstract terms. After this rejection of the use of abstract terms in physical science, De Motu turns to absolute motion, con­ centrating on Newton's exposition. In the Scholium to Book l of his Mathematical Principles of Natural Philosophy Newton distinguished "Absolute, True, and Mathematical Time," which "of it self, and from its own nature flows equably without regard to anything external, and by another name is called Duration" from "Relative, Apparent and Common Time" which fris sorne sensible and external (whether accurate or unequable) measure of Duration by the means of motion." He

121Works, IV, 31-5; De ~~otu, SS. 1-17. went on to distinguish Absolute Space, which "in its own nature, without regard to any thing external, remains al- ways similar and irnrnoveable" from Relative Space, which Iris sorne moveable dimension or measure of the absolute spaces; which our senses deterrnine, by its position to bodies." Place is lia part of space which a body takes up" and motion is rrthe translation of a body" from one place to another; both motion and place may be absolute or relative depending on whether the space is absolute or relative.122 It is important to note that Newton was not alone in this view of absolute space, time and motion. Professor Jessop traces this view back by way of Copernicus to the Pythagoreans123 while Berkeley attributes the distinction between absolute and relative space to Democritus.124 The Swiss mathematician and physicist, Leonhard Euler, and the English mathematician and divine, Isaac Barrow, are typical of the irnmediate predecessors and contemporaries of Newton who accepted this doctrine. By the early eighteenth century, almost all philosophers as well as scientists were ready to accept, expound and elaborate the Newtonian doctrine of ab­ solute motion with its underlying notion of gravitational force, often without the qualifications which Newton himself imposed. l22Sir Isaac Newton, Mathematical Princi~les of Natural Science, transe Andrew Motte (London, 19 8), ~ 9-10. l23Jessop, "Berkeley and Contemporary Physics," VII, 93. l24Works, IV, 47; De Motu, S. 57. 59

Berkeley was not unaware of Newton's qualifications on the use of the notion of gravitational force. In the definitions with which he began his work, Newton remarked in reference to gravitational ("centripetal") forces, which nwe may for brevity's sake calI by the names Motive, Accel­ erative and Absolute forces": "For l here design only to give a Mathematic notion of those forces, without consider­ ing their Physical causes and seats.,,125 Later in this work, Newton attacked the use in physics of hypotheses, which he defined as "whatever is not deduc'd from the phenomena.,,126 While the followers of Newton generally ignored these caveats, as when they hypostatized forces, thereby earning Berkeley's uncompromising opposition, Berkeley's reaction to Newton was more complexe Tt can be roughly summarized by saying that Berkeley accepted the theorems of the Mathematical Principles of Natural Philosophy, but not the scholia.127 He did not argue with Newton's empirical method, which lim­ its physics to the mathematical, that is, to measurement, or with its implication that the whole of physics is express- ible in terms of space, time,motion, mass and force. He simply claimed that this valuable method did not depend on absolute space or time, the excision of which would rem ove

125Newton, l, 7-8. 126Ibid., II, 392. 127J. Myhill, "Berkeley's De Motu: An Anticipation of Mach," University of California Publications in Philosophy, 29 (1957), 145. 60

a source of obscurity from scientific thought. As Berkeley early noted, "Sir Isaac owns his book could have been de­ monstrated on the supposition of indivisibles,,12$ or, in other words, without positing absolute space or time. Ber­ keley could wholeheartedly attack any attempt by physicists to establish a rival to the infinite mind of God in the form of a system of absolute space or time, confident that this would be as harmful to science as to theology. How­ ever, although Berkeley denied any ontological significance to gravitational force and like terms, he was ready to grant them a pragmatic significance as mathematical hypotheses. Berkeley's examination of Newton's doctrine of absolute motion introduces an entirely new criticism of the notion of absolute space. This, being defined as "infinite, immovable, indivisible, insensible, without relation and without distinction," comprises only privative or negative attributes and "seems therefore to be mere not~ing." Abso­ lute space, being by definition insenSi~hence beyond experience, cannot be known to our senses or lmagination by ideas. Nor can it be known to our intellect by notions since absolute space is not mind or spirit. He therefore dismisses the abstract idea of absolute space as impossible and removes the danger that this tnfinite and eternal unknown may come to be equated with God. With Newton's absolute space - and also Locke's pure space - refuted, absolute place and abso-

12$Works, I, 44; Philosophical Commentaries, Entry 374. 61

lute motion similarly lose their significance.129 The effect of the application of the doctrine of ~ is percipi is that absolute space, which is introduced to account for per­ ceived space yet is in effect defined as unperceivable, is both psychologically and ontologically impossible.130 Being unnecessary as weIl as impossible, absolute space should be excluded from scientific theory. Further, space cannot be infini te or infinitely divisible since it is never thus ex­ perienced.131 To sum up Berkeley's views on space, he felt that both the scientist and the ordinary man could operate satisfactorily with the empirical concept of relative space only and rejected the notion of absolute space as both im- possible and unnecessary. Let us turn from these observations on space to his treatment of time. Berkeley identifies time with "the succession of ideas in our minds" and later remarks in a letter to Samuel Johnson in 1730: "A succession of ideas l take to constitute Time, and not to be only the sensible mea­ sure thereof, as Mr. Locke and others think.,,13 2 Tying time to ideas, that is, to events as thought, willed or felt, re­ sults in a concept of time as 1ived or experienced similar to Berkeley's concept of space as perceived or experienced.

129Ibid., IV, 45-7, V, 146-7; De Motu, SS. 52-8 and Siris, S. 318-.- ---

13 0Jessop, "Berkeley and Contemporary Physics," VII, 93-4. 13 1Works, II, 98-101; Princip1es, SS. 124-9. 13 2Ibid., II, 83, 293; Princip1es, S. 98. 62

In common with space, real time is always relative, never ab­ solute and, being a series of particular indivisible ideas, time is neither infinite nor infinitely divisible. From his very limited attention to the question of time, it is clear that Berkeley rejected as impossible abstractions Newtonian absolute time, Lockean pure time - distinguished by Locke from the succession as this merely measures time - and any similar notion of a time independent of experienced time. This leads us to enquire into the consequences for both Berkeleian philosophy and Newtonian science of the ack­ nowledgement of relative or individual or psychological time at the expense of absolute or public or physical time. For sorne commentators there is no problem here. Professor Luce states that Berkeley admits a public time in providing for the move from one's own mind to the minds of others.133 Ber- keley seems to be asserting a public time both implicitly in his account of how we can know other minds and explicitly in his illustration of the appointment with one's servant at an agreed time and place to the complete understanding of both parties.134 However, he appears nowhere to give an adequate account of a public time, and the possibility of such an ac­ count may be ruled out by his admission that ideas may succeed one another twice as fast in one mind as in another as well as by his denial that time in one mind can be measured by the

133Luce, Berkeley's Immaterialism, p. 139. 134Works, II, 83; Principles, S. 97. succession of ideas in another mind.135 It appears equally difficult to accept Professor G.A. Johnston's suggestion that 'Berkeley justifies the shift from "Each man's time is private" to God's absolute tirne.136 Berkeley asserts two states: one in time, the other eternal in God; nowher8 does he explain the nature of their relationship beyond implying in Siris that God gives a normal rate of succession to ideas in our minds. Indeed, since time is the succession of ideas in a mind and there is l'no change, variation, or succession" in God's mind, it is difficult to see howa connection bet­ ween God and Berkeleian time is possible and how, therefore, God can provide Berkeley with any guarantee of a public time.137 In disagreement here with Professors Luce and Johnston, l can find no indication in the texts that Berkeley goes beyond the mere assertion of a public tirne. From the conclusion that Berkeley offers no satis- factory account of a public time, we now consider the conse- quences of this for his critique of Newton's theory of motion. In identifying tirne with the succession of ideas in our minds, he offers a relative or individual or psychological view of time, adequate to explain the temporal ordering of phenomena in everyday experience. However, he then fails l35Ibid., II, 190, 293; Three Dialogues, I. l36G.A. Johnston, The Development of Berkeley's Philosophy (London, 1923), pp. 239-242. l37Works, II, 254, 293, V, 120, 136; Three Dialogues, III and Siris, SS. 252, 293. to relate this psychological tirne to the concept of public or physical tirne as ernployed in natural science to account for the possibility of rnetrical cornparison of different in­ tervals of tirne.138 The feature of physical tirne of great- est significance to scientists is its uniforrnity or regular­ ity, which renders possible the exact rneasurernent of tirne in physics. Berkeleian tirne - rneasured like Newton's relative tirne in hours, days, rnonths or years - perrnits no such exact measure of tirne since slight variations in the motions of the earth, moon and sun introduce variations in the length of, say, the natural day. The traditional solution to this problern of the uniforrnity of physical time was to posit a uniforrn physical tirne in sorne sense independent of psychological tirne. Here, as with the distinction between prirnary and secondary quali­ ties, Galileo was the innovator in his description of tirne as "an objective reality independent of the perception of it," a view adopted by the early modern scientists in oppo­ sition to the psychological interpretation of tirne by the philosophers of this period.139 Isaac Barrow took a sirnilar view of tirne as inde pendent of the world and, in reducing time essentially to a mathematical concept, influenced Newton

13 8G. J • Whitrow, The Natural Philosophy of Time, (London, 1961) pp. 49-50. 139Cecil Currie, "Time, Continuity and Contiguency: An Histo­ rical Study," Masters dissertation, McGill University, Mon­ treal, 1933, pp. 21-3. in the introduction of absolute time.140 There have been many attacks on Newton's doctrine of time since Berkeley, but, although Newtonian absolute time is now generally acknowledged to be unsatisfactory, the concept of a time in sorne sense inde pendent of experience still has its supporters. For example, after rejecting New­ ton's notion of absolute time, partly on Berkeley's ground that it reifies time, partly because the function of flowing attributed to its is meaningless, and partly because on New­ ton's definition the notion can have no practical use, Pro­ fessor \\Thitrow goes on to propose a "unique basic rhythm of the universe" to explain why all time scales which we en­ counter in experience are identical. To give one illustra­ tion of this, the time scale for the decay of the Uranium 235 atom is identical with the time scale from Newton's first law of motion.141 Possibly Professor \fuitrow's proposed "basic rhythm of the universe" succumbs to Berkeley's power­ ful argument against abstraction since contemporary philo­ sophers have sought alternative solutions to the problem of the measurement of time in physics that do not require the positing of a time inde pendent of experience. It would not be relevant to our present purpose to pur sue this question further beyond drawing attention to one proposed solution in Professor Adolf Grunbaum's rigorous explanation of the rela-

0 14 \Vhitrow, Natural Philosophy of Time, pp. 130-2. 141Ibid., pp. 33-46. 66

tiol!ship between psychological and physj.cal time .142 Let us attempt a summary of Berkeley's concept of time. In his psychological time identified with the succes- sion of ideas in the mind, he adopted a radically empiricist theory of time, which is simple and sticks closely to ~he facts, but is incomplete in its omission of any account of the uniformity of time.143 In raising objections to Newto­ nian absolute time similar to his objections to absolute space, Berkeley introduced an original and telling argument, which is now substantially accepted in its conclusions on both space and time. But in adopting a similar approach to the problem of time as to the problem of space, Berkeley of­ fered a naive doctrine of time, which failed to do justice to the problems peculiar to time and in particular to the uniformity of time basic to physical science. He fell into the common error of assuming that time, having only one di­ mension, could be treated as analogous to, but simpler than three-dimensional space.144 In a striking example of his a bili ty as a. cri tic, he disposed brilliantly of Newton' s ab­ solute time. However, his positive doctrine is not wholly successful since the concept of psychological time, although properly derived from his doctrine of space and motion,

142Adolf Grunbaum, "The Nature of Time," in Frontiers of Sci­ ence and Philosophy, ed. Robert G. Colodny (Pittsburgh, 1962), pp. 149-188. 143Jessop, "Berkeley and Contemporary Physics," VII, 95-6. 144C.D. Broad, Scientific Thought (New York, 1923), p. 53. 67

failed to provide an adequate account of physical time and hence to give an alternative base for the physical science which he desired to support. In addition to fulfilling the need in principle for an ideal rate-measurer, natural days being unequal, absolute time was also posited by Newton as essential to absolute mo­ tion. Absolute motion, Newton felt, was supported by the empirical evidence of the bucket experiment, Professor W.A. Suchting's excellent account of which is as follows:

A bucket is suspended by a cord, rotated so that the cord is strongly twisted, and then filled with water. Now (1) the bucket is released. The torsion of the cord rotates the bucket in a direction opposite to that in which the cord was twisted. For a time the water does not rotate with respect to the walls of the bucket. During this period the surface of the water is plane, as before the bucket began to move. Then (2) the water acquires rotary motion from the bucket and eventually has the same angular velocity as the bucket, so that it is at rest relative to the sides of the bucket. During this time the water gradually recedes from the axis of motion and ascends the sides of the bucket, so that the water surface is concave. In stage (3) of the experiment the bucket's rotary motion is suddenly stopped. The water continues to rotate for a time and thus is in motion relative to the bucket. The surface of the water continues to be concave for a while until the water ceases to move and is once more at rest relative to the bucket, when the surface is again plane. Newton's interpretation is as follows. The change in the shape of the water surface manifested in stages (2) and (3) is the result of the occurrence of centrifugaI forces- "forces of receding from the axis of motion." There is no dependence between the occurrence of these forces and the relative motion of water and bucket, for in stage (1), 68

when the "circular motion purely relative" is at maximum, the water surface is plane, whilst in stage (2), when the relative motion of water and bucket is zero, the water surface is con­ cave. Therefore, there must be a dependence between the occurrence of these forces and a motion of the water with respect to absolute space: during stage (2) the water gradually acquires "true and absolute circular motion," which is preserved in stage (3); and the degree of this motion may be measured by the degree of concavity of the water surface, being in fact greatest when the bucket and water are at rest relative to each other.:45

Newton regarded the bucket experiment as a powerful argument for absolute rotation and hence for absolute motion. Unfor- tunately Berkeley, in launching the first attack on this in- terpretation, presented his argument in an elliptical form which is not easy to follow. According to Professor Such­ ting's interpretation, Berkeley denied that in stage (1) the water is really moving since to say that a body moves re- quires "first, that it change its distance or situation with regard to sorne other body: and secondly, that the force or action occasioning that change be applied to it,,,146 and the second condition - and possibly the first - is not met. He acknowledged that in stages (2) and (3) the water is in motion. However, while the "natural" motion of each particle is along the tangential component of this motion, its change of direc-

145W.A. Suchting, "Berkeley's Criticism of Newton on Space and Motion," Isis, 58 (1967), 190-1. l46~vorks, II, 9~; Principles, S. 115. 69

tion is along the radial component only so that, by Newton's second law of motion, there is a radial force present, but no tangential force, as Newton supposed. Hence the change in shape of the water surface can be explained solely by re­ ference to features of the bucket system without having re­ course to the notion of absolute motion.147 Although his account is neither clear nor perhaps entirely satisfactory, Berkeley's purpose was clearly to remove the empirical evidence of the bucket experiment in support of absolute motion, which becomes a mere abstraction. The essence of motion lies, not in translations in unper­ ceived space as Newton claimed, but in variation in perceived distance in space relative to sensory objects. If there are in the universe only two spheres, certain motions, for ex­ ample, the circular motion of the two spheres about a common centre, cannot be conceived by the imagination. However, if the fixed stars are introduced, the circular motion can be adequately conceived by the motions of the spheres rela­ tive to the fixed stars. Since we cannot know whether the fixed stars are moving relative to absolute space, it be­ cornes pointless to posit such a notion of space.148 Berkeley would have supported Ernst ~~ch's later statement that the motion of a body K can only be estimated by reference to bodies A, B, C, but that we cannot determine by experiment

147Suchting, 58, 192-5. l481Morks, IV, 47-9; De Motu, SS. 59-65. 70

what part A, Band C play.149 The current scientific view is that absolute motion,

and hence absolute space and time, are not n~cessary for New- ton, whose laws of motion can in general employas a frame of reference an inertial system, which can be defined relation­ ally in the way which Berkeley requires. One difficulty with this view is expressed by Professor Nagel in this way: for Newton, kinetically all motion is relative, but dynamically, that is, in terms of forces, motion is referred to absolute space as a frame of reference. To identify this difficulty more exactly, let us review Newton's three laws of motion. The first law states:

Every body perseveres in its state of rest, or of uniform motion in a right line, un­ less it is compelled to change that state by forces impressed thereon.

If our only instrument for measuring time were, say, the pendulum clock, which depends on Newton's first law, then this first law of motion would be no more than a definition of "the equality of temporal periods - two times being de­ fined as equal if during them a body moving under the action of no forces covers equal distances along a straight line." In fact, however, alternative instruments for measuring time have been developed, the most recent being the atomic clock,

149Ernst Mach, The Science of IViechanics, tranSe Thomas J. McCormack (La Salle, 1960),-pp. 281-3. 71

which depends on the very high degree of regularity in the decay of certain radio-active material. In the atomic clock, equality of time is defined in terms of the physical laws concerning rates of decay of radio-active materials and hence independently of Newton's first law of motion. As a result, the independent measurement of time by an atomic clock may provide experimental evidence in support of the first law of motion.150 The second law reads:

The alteration of motion is ever propor­ tional to the motive force impressedj and is made in the direction of the right line in which that force is impressed.

Here also the key notion, mass, can be measured without ref- erence to the rate of change of rnomentum, that is, indepen­ dently of the second law. As a result of this inde pendent support of the empirical validity of these first two laws provided by the availability of alternative methods of mea- surement, we are justified in retaining them in the absence of any absolute frame of reference. The difficulty previ­ ously referred to becomes apparent in the third law:

To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

There is in principle no way of measuring these forces inde-

150Ernest Nagel, The Structure of Science (New York, 1961), 1 pp. 158-9, 179-18~207. 72

pendent1y of their forces of reaction, that is, independent- 1y of the third 1aw of motion. As a resu1t this 1aw ho1ds universa11y on1y for Newtonian force and requires absolute motion, space and time for its frame of reference.151 The notion of force in the third 1aw of motion wou1d appear c1ear1y to be subject to Berke1ey's strictures against ab­ stract terms in science whereas the key notions of time in the first 1aw and m~ss in the second 1aw appear to escape these strictures. To the extent that Berke1ey's critique of Newton's kinetic theory is based on the rejection of ab­ stractions, it may be conc1uded that the effect of this cri­ tique is 1imited to Newton's third 1aw of motion. This is not, of course, intended to deny the va1uab1e contribution to the phi1osophy of science represented by Berke1ey's cri­ tique of Newtonian theory.

151Broad, pp. 161-176. 73

Chapter 7. His Critique of Mathematics

Berkeley regarded aIl branches of learning includ­ ing mathematics to be of value only to the extent that they were of use. As a result, he showed little interest in pure mathematics - the "trifling subjects" of mathematicians dis­ missed in his early notebooks152 and concentrated his atten- tion instead on applied mathematics. It will be convenient to consider the traditional mathematical branches of algebra, geometry and arithmetic in this order before turning to the new mathematics of his time, the differential calculus. From his first publication, Arithmetica Absgue Algebra (1707), which denies that algebraic demonstration precedes arithmetic demonstration, Berkeley never really took algebra serious- ly.153 Greater attention is given to geometry. The early Essay on Visionodeals with optics, considered by Berkeley to be a stronghold of the mathematicians, and attempts in an important section to refute Descarte's influential doctrine of an innate geometry to account for our judgment of distances

152Works, l,52; Philosophical Commentaries, Entry 409. 153Philippe Devaux, "Berkeley et les mathé"'matiques," Revue Internationale de Philosophie, VII (1953), 110. 74

by sight.154 In brief, Berkeley's refutation first radically separa tes objects of sight from objects of touch and then as­ serts that we judge distances by tangible extension, which is three-dimensional, and not by visual extension, which has only two dimensions. Since our geometry is three-dimensional, and even plane geometry calls for t~e manipulation of rulers and compasses, geometry must be concerned with three-dimensional tangible extension.155 It is not surprising that this attempt to base geometry entirely on the space of experience has been called a "disastrously empirical view of geometry.,,156 Never­ theless Berkeley does make provision for a universal, neces­ sary geometry in the claim that the particular triangle con­ sidered "doth equally stand for and represent all rectilinear triangles whatsoever, and is in that sense universal.,,157 A framework for Berkeley's views on arithmetic can be derived from three entries in the Philosophical Commen- taries:

Entry 758 - Algebraic Species or letters are denominations of Denominations, therefore Arithmetic to be treated of before Algebra. Entry 763 - Nurnbers are nothing but Names, never Nords.

154Works, 1, 171-2; Essay on Vision, SS. 4-5. 155Acton, l, 298. 156Warnock, p. 220. 157Works, II, 34; Principles, Introduction, S. 15. 75

Entry 766 - In Ari thmetical Problems IllIen seek not any Idea of Number. they onely seek a Denomination. this is aIl can be of use to them.1 58

For him arithmetic occupied sorne fundamental or privileged position in mathematics.159 Since by his rejection of the doctrine of abstraction arithmetic cannot depend on any ab­ stract idea of unit y or number, arithmetic is based on num­ bers ("denomination"), understood as signs of "particular numerable things" \'Tith no existence outside of the minds of men.160 Numbers being analogous to names or nouns in lan- guage, arithmetic and hence mathematics become a kind of language, invented by men for their use in counting and mea­ suring.161 His view of arithmetic is very different to his vieN of geometry. Arithmetic is a logical system, invented by men, arbitrary and necessary; its value lies in its appli- cation to counting and measuring, pure arithmetic being a pointless exercise. Geometry is based on particular trian­ gles and other figures as imagined or drawn and gains its necessity from the taking of these particular figures to re­ present general ideas of triangles and other figures as em­ ployed in geometrical theorems. Since the justification of geometry lies in this empirical base, which is construed in

158Ibid., l, 92-3. l59Devaux, VII, 110. 16 0'i'Jorks, II, 95-7; Principles, SS. 119-122. 161Acton, l, 303. 76

terms of Newtonian (relative) co-ordinates and hence in terms of Euclidian geometry, it does not appear that Berkeley could admit the possibility of the construction of other geometric systems than the Euclidian. This view of geometry had implications relevant to Berkeley's critique of the differential calculus to which we now turne Berkeley admired only Newton as a mathema,ticianl62 and his admiration extended to Newton's calculus so far as concerned the utility of the calculus and the validity of its results. However, Berkeley found fault with the logical structure of the calculus as weIl as with the reluctance of Newtonians even to acknowledge these faults, let alone at­ tempt to rectify them. His response to the Newtonian cal cu- lus is in general similar to his response to Newtonian ki- netic theory. From Berkeley's claim that geometry deals with the concrete space of experience, it follows that this space is not infinitely divisible or, in this own words, that "no fini te extension contains innumerable parts, or is infinitely divisible." Finite extension consists of Berkeleian ideas and as such falls under the doctrine of ~ is percipi. A line one inch in length cannot be divided into ten thousand parts since it would be impossible to see or touch or imagine each part. Similarly, a finite line is not infinitely divis­ ible since each part would be in principle incapable of being

162Works, 1, 44; Philosophical Commentaries, Entry 372. 77

seen, touched or imagined. In addition, he appea1s to his rejection of abstraction to refute the infinite divisibility of a finite line.163 This denial of infinite divisibi1ity leads Berkeley to reject the notion of the infinitesimal and to introduce, or perhaps adapt from the indivisibles of Cavalieri, the con­ cept of the minimum sensibile (visibile, tangibile), beyond which it is in principle impossible to perceive.164 Unfortu­ nate1y, he did not elaborate this positive aspect of his doc­ trine although he developed the negative aspect contained in his rejection of infinitesimals into an important criticism of the differential calculus in the formulations of both New- ton and Leibniz. Newton, who treated motion as a flowing quantity, based the calculation of rates of change of motion on the method of fluxions, which Berkeley dismissed as "the ghosts of departed quantities," being "neither finite quant­ ities, nor quantities infinitely small, nor yet nothing.165

~Vhen thus trea ted as fini te in one part of Newton' s method and as zero in another part, the notion of the infinitesimal becomes self-contradictory. Leibniz, whose theory of motion was close to Eerkeley's relative view of motion and who was therefore precluded from fo11owing Newton in treating motion

163Ibid., II, 97-101; Principles, SS. 123-9. 164Ibid., II, 101-2,1,42,191, 204-6; Principles, SS. 130-1, Philosophical Commentaries, Entry 346, Essay on Vision, SS. 54, 80-7. 165Ibid., IV, 89; Analyst, S. 35. 78

as a flowing quantity, based the calculation of rates of change of quantities on the notion of the limite Berkeley interpreted a limit as a mathematical point which cannot, without self-contradiction, be said to function at one time as an indivisible point and at another time as an incompa­ rably small yet finite quantity.166 Thus Berkeley criti- cized both the Ne~~onian and the Leibnizian formulations of the calculus for treating the infinitesimal in a self-con- tradictory way, sometimes as a negligible quantity and some­ times as a quantity sizeable enough to be taken into account. Nor is the criticism blunted by the tendency noted in New- ton's later work to favour the Leibnizian concept of the limit or by the converse tendency of Leibniz to favour the

"Jre wt onlan° concep t 0 f th e ln° fOlnl ° tOIeSlma • 167 It may reasonably be asked why, if this criticism is valid, the calculus is nevertheless capable of yielding correct results. To explain this, Berkeley introduced his doctrine of compensating errors by illustrating how in a geometrical problem two separate errors can compensate for each other to yield a true result.168 This doctrine of com­ pensating errors was intended not as a justification for the calculus, but merely to explain why the calculus can in prac-

166Wild, pp. 373-5. 167Devaux, VII, 107. l68Works, IV, 76-84; Analyst, SS. 20-9. 79

tice lead to correct results.169 For Berkeley, the neces­

sity of ~Bthernatics could be grounded only on its own rig­ orously logical structure and not on the pragmatism of the doctrine of compensating errors or of his own attitude to­ wards mathematics as a useful discipline. From this there arose the need for a clear structure of meaning in every branch of mathematics and especially in a recent addition such as the calculus. What, then, is the value of Berkeley's critique of the Ne,rtonian calculus? One criticism, that many of the con­ cepts used in the calculus, in particular the notion of suc- cessive fluxions, are incomprehensible, is dismissed by Pro- fessor vfuitrow as mere prejudice. Seeing his own philosophy as founded on commonsense, Berkeley made the cornrnonsense as-

sl~ption that the variables of analysis are connected to de­ finite physical concepts. This is not necessarily the case, as mathematicians came lat8r to realize, and Berkeley's charge of incomprehensibility loses it point. The second main criticism, claiming that Newton's method is self-contra­ dictory in its reliance on the idea of the infinitely divis­ ible and in the positing of the infinitesimal, is more prof­ ound and has had a much greater influence on the later philo­ sophy of mathematics.170 There is general agreement with

169J.O. Wisdom, "Berkeley's Criticism of the Infinitesimal," British Journal for the Philosophy of Science, IV (May, 1953 - February, 1954),~-~ -- 170T,fui trow, "Berkeley' s Critique of Newton," 82, 92-4. 80

Professor Karl Popper's view that Berkeley was fundamentally right in his critique of the differential calculus as applied to the formulations of Newton, Leibniz and their irnmediate successors.171 Despite this, Berkeley's second criticism of the calculus is based on a mistake in his interpretation of the concept of the limite The answer to this criticism lies in a more precise formulation of the calculus based on the modern concept of the limit as a boundary. He interpreted the limit as a math­ ematical point and failed to recognize that it could function as a boundary. Newton and Leibniz also failed to give a clear exposition of the concept of the limit although Newton showed sorne awareness of this possibility. The resolution of this problem belongs to the history of mathematics in the development and refinement of an adequate theory of limits, which still stands in sorne need of clarification, but A.N. Whitehead's simplified explanation172 will be adequate for our purposes. In determining the rate of increase in a func­ tion, one must choose a period long enough to permit measure­ ment, yet short enough to provide accuracy in case the rate of increase is not uniforme The positing of infinitesimals, correctly rejected by Berkeley as self-contradictory, was an unsuccessful attempt to solve th!s dilemma. The problem re-

171Popper, p. 70. 172A. N. Whitehead, An Introduction to rlTathematics (London, n.d.), pp. 217-235. 81

mains, "how to keep an interval of length h over which to calculate the average increase, and at the same time to treat h as if it were zero.,,173 The solution is to intro- duce the modern concept of the limit as a boundary as in this definition of limit:

A function f (x) has the limit l at a value a of its argument x, when in the neighbour­ hood of a its values approximate to l with­ in every standard of approximation.174

The expressions "neighbourhood" and "standard of approxima­ tion" remain to be defined, but this can be done in terms of an adequate theory of functions so as to permit us to abandon the self-contradictory notion of infinitesimals in favour of the mathematically intelligible notion "that corresponding to any standard of approximation, ~ interval with such and such properties can be found.,,175 It remains to add that Berkeley failed to do justice to Newton's concept of continu­ ity, in which Newton may weIl have seen the modern concept of the limit as boundary. Berkeley's contributions to the philosophy of mathe- maties can be summarized under three headings: first, his very powerful criticism of the self-contradiction implicit in the treatment of infinitesimals, secondly, his less effect-

173Ibid. , p. ~;(~. 174Ibid.--' p. 2~9. 175Ibid. , p. 234. ive criticism of such notions as fluxions on the grounds of incomprehensibility and,· thirdly, his doctrine of compensa~ tion of errors, introduced almost incidentally, but later adopted by Vaihinge~ as a principle of scientific method.176 Turning to the relationship of his philosophy of mathematics to his philosophy in general, we note that Berkeley's insis­ tence that the value of mathematics rested in its usefulness lead him to concentrate on applied rather than pure mathema- tics. The necessity of mathematics was derived from its own logical structure; hence it was important that the logical structure be rigorously correct so that the results achieved would be universal and necessary. Here, arithmetic occupied a fundamental positit '1 since its concern with measurement could contribute to the necessity of geometry and calculus - algebra was ignored - to the extent that these branches relied on measurement. As a result, Berkeley had no need to adopt Newton's mathematical reasons for positing absolute time, namely, to serve as an ideal rate-measurer. (See page 67). For Berkeley, the arbitrary structure of arithmetic provided by man was an ideal rate-measurer and absolute no­ tions of space and time, whether provided by nature or God, were unnecessary. ]·'Iathematics therefore served a useful role in the scientific interpretation of nature, which he saw as strictly a question of mathematics. This use of mathema­ tics in physical science will be dealt with further in Chap­ ter 8.

176Tdhitrow, "Berkeley's Critique of Newton," 82, 203. Chapter 8. Scientific Methodology.

Consideration of Berkeley's view of mathematics is an appropriate prelude to an examination of his account of scientific methodology. Our procedure will be to look first at his treatment of causality and explanation before we turn to his concept of nature, conr:uding by examining his scien­ tific methodology in the light of the essentialist and in­ strumentalist views of science. Generally speaking, he re­ stricted the term "cause" to refer to what he termed "truly active causes.,,177 In his extended treatment of motion in De Motu, he eliminated body, being passive and inert, as a possible cause of motion, which must therefore be produced by spirit or mind. Infinite spirit or God, as the cause of aIl things, produces motion in a manner analogous to the way in which we experience our own minds as producing motion, say, in a limb when we will a muscular effort. When cause is thus understood as the power of self-initiated activity, the only real causes are spirits, the subject of metaphysics and not of natural science. As part of his separation of science from metaphysics, Berkeley denounced physicists as meddlers when they trespassed into the field of metaphysics

177Works, IV, 52; De Motu, S. 72. by purporting to study real causes in this non-phenomenal sense. This meddling was responsible for introducing obscu­ rit y into both metaphysics and natural science. It was the popular custom in Berkeley's day to interpret causation rationally, that is, to claim that there is a logically necessary cause for each event, the character of the event revealing the nature of the cause.178 \~ether such causes were represented as phenomena or as an under- lying material substance, it is clear that Berkeley would reject such a notion of causality because neither inert ideas nor unintelligible abstract ideas can serve as the cause of anything. The fire is not strictly the cause of which my pain as l draw too close is the effectj rather, the fire is the sign which forewarns me of pain if l approach too closely. It matters little, Berkeley admitted, that in ordinary dis- course men refer to these signs as causes so long as they take cognizance in their conduct of these uniform signs pro­ vided by a benevolent God for man's well-betng. However, when physicists treat these signs as real causes, their error leads to the positing of mechanical causality by restricting aIl causes of corporeal things to the field of physics. Phy- sics should be limited to the observation of natural pheno- mena and to the discovery, by inference from such observation, of the laws of nature, which describe regularities among the phenomena. The value of physics lies in its predictive role,

178Kuypers, p. 44. which tells man how to act and what to expect.179 To pre­ serve this value, Berkeley wished to exclude from physics aIl talk of true cause or causal explanation and to reserve for metaphysics aIl explanation of the true nature of things. If cause means self-initiated activity, there are no causes in the world of objects and should be none in physics. Phy­ sics might be said to offer descriptive or mechanical expla­ nations, but not causal or essentialist explanation.180 To set this account of scientific explanation in perspective, let us identify the four levels whicb, according to Berkeley's philosophy, contribute to our knowledge of the world: (1) observations of particulars (2) laws of nature (3) mathematical hypotheses (4) causal explanations.181 Observations of particular phenomena can be known to be true by our ideas. The laws of nature are based on this observa- tion of particulars and can similarly be known to be true by experience. The physicist's task is to discover these laws by na diligent observation of the phenomena within our view,n the fundamental laws of physics being nthose primary laws of

179Works, II, 66-70, 87-8, V, 112; Principles, ss. 60-6, 105, 107 and Siris, S. 234. 180Ibid., IV, 40-1; De Motu, SS. 36-7. 181Popper, p. 170. 86

motions which have been proved by experiments.,,182 If this grounding of the truth of the laws of nature in observation reflects Berkeley's support for the empirical side of phy- sics, his approach to mathematical hypotheses reflects his distrust of its rational side. He recognized the value of mathematical hypotheses as useful tools in the scientific interpretation of nature, which he regarded as strictly a question of measurement. However, he maintained a clear distinction between mathematical hypotheses and scientific laws. Mathematical hypotheses depend on thought only and correspond to nothing in nature so that they have no reality value. Useful to science, they form no part of science and the question of their truth as opposed to their utility does not arise. If, like Newton's notions of absolute space, time and motion, they cannot be justified as useful abstrac­ tions, they must be eliminated in order to remove a possible source of obscurity and to preserve the experimental basis of physics. Causal explanations, as we have seen, belong to the realm of spirits and ultimately of God. Physical things are bundles of qualities which have their real cause in the realm of spirits and ultimately in God so that causal expla­ nations are the concern of the metaphysicians and not the physicists. Specifically, Berkeley's opposition was directed at those physicists who regarded motion not as a cause, but as an effect which could be explained by the introduction of

182Works, II, 88, IV, 40; Principles, S. 107 and De Motu, S. 36. the abstract ideas of force and inertia.la3 The "true effi- cient cause of motion" is to be found not in physics, but in the infinite mind of God. la4 It is now possible to outline Berkeley's concept of nature. Physical objects being combinations of Berkeleian ideas, we know the corporeal world through the ideas in our minds by which we perceive such qualities of objects as colour, hardness, shape and so on. Only spirits or minds and their ideas are real. The world as we perce ive it is the only real world. A benevolent God, the ultimate cause of all things, creates ideas in our minds in a uniform and consistent way as signs for our survival. The uniformity in the working of nature is a divine language to men. In analy- sing regularities in natural phenomena to discover the laws of nature, physicists act much as grammarians who arrive at rules of language.la5 Being based on observation of the per­ ceivable world, the laws of nature may be true, but the mathe­ matical hypotheses used in their formulation are mere tech­ nical devices which neither mirror reality nor form any part of it.186 Only metaphysicians and theologians study the real causes and essences in nature. In Berkeley's model of the universe, God provides l83Jessop, "Berkeley and Contemporary Physics," VII, 97-a. l84W·orks, IV, 50; De ~10tu, s. 69. l85Ardley, p. 3a-9. l86T. E• Jessop, George Berkeley (London, 1959), pp. 22-3. 88

an order in nature, but does not guarantee a world of logi­ 187 cal implication in the Lockean sense. Our knowledge of the natural world is contingent and depends on the will of God, who could introduce irregularities if he wished. That God does not in fact deviate from the rules is cited as a reason why men should abide by the "moral rule or law of na- ture." Berkeley distinguished clearly the role of the laws of nature in ethics from their role in science, but the com- mon ground of ethics and science in God reveals analogies which permitted him to discuss ethics in terms of the laws of nature. 188 In attempting to describe the world in clear terms, Berkeley developed a philosophie system in which everything is dependent on the will of God, leading one Ber- keleian supporter, the poet W.B. Yeats, to claim: "Descartes, Locke and Newton took away the world ••• Berkeley restored the world. n189 Professor Popper offers an illuminating interpreta­ tion of Berkeley's theory of science as a shift from one view of scientific knowledge to another: from essentialism to in­ strumentalism.190 Essentialism is the view that scientific theories "describe the 'essences' or the 'essential natures' lS7Kuypers, p. 62. lS8e.D. Broad, "Berkeley's Theory of Morals," Revue Interna­ tionale de Philosophie, VII (1953), 73, 81-2. lS9Luce , Berkeley's Immaterialism, p. viii. 190Popper, pp. 98-107. of things - the realities which lie behind the appearances." Such theories are treated as ultimate explanations, the fi­ nal truth of which can be established beyond aIl reasonable doubt by scientists. Galileo originated this view of the material universe as a closed system operating in accordance with mathematical laws and, despite sorne opposition from the Church, essentialism had won almost universal acceptance in scientific and philosophic circles by the time of Newton. Newton was an essentialist both in his theory of matter and in his kinetic theory with its basis in absolute space and time. Newton generally regarded his laws of motion as de­ scriptive of the essential nature of matter since, although they describe certain states of affairs in the world in mathe­ matical terms, these states of affairs are due to the inher­ ent properties of matter. This essentialism carried over into sorne, but not aIl, of Newton's $cientific notions. He consistently treated inertia and extension as essential prop­ erties of matter. His treatment of gravit y was less consis­ tent. Although he once dismissed as absurd the idea of grav­ ity as "innate, inherent and essential to matter," at other times he treated gravit y as being of the ultimate order of nature and not therefore reducible from qualities. ~fuile New­ ton imposed at least sorne qualification on his essentialism, Newtonians generally tended to adopt a more thoroughgoing essentialisme In the Preface to the second edition of New­ ton's Principles, Roger Cotes presents it as Newton's view 90

that every particle of matter is endowed with gravit y (the inherent power to attract other matter) and inertia (the in­ herent power to resist change in motion). Berkeley rejected aIl forms of essentialism includ­ ing both the migitated and slightly obscure essentialism of Newton and the thoroughgoing essentialism of the Newtonians. His arguments are based on his whole philosophie position and in particular on his rejection of abstraction. There are no lIessences'; or "essential qualities" of things and, even if essences could be introduced into his philosophy in the forro of archetypes existing only in the mind of God, these es­ sences or archetypes would be dealt with by metaphysics and not physics.

Fro~ his analysis of Newton's concepts, Berkeley concluded that !~ewtonian theory is based on a series of math­ ematical hypotheses. The value of Newton's laws of motion lies solely in their use by physicists as instruments for calculating and predicting phenomena in the corporeal world. Professor Popper suggests that, in ruling out the possibi­ lit Y that scientific theories can have other functions, Ber­ keley adopted an instrumentalist view of scientific know­ ledge, this being the view that scientific theories are no­ thing but instruments. Berkeley was clearly opposed to the essentialist claim that scientific theories describe the es­ sential qualities of things although his occasional use of similar expressions to the essentialist could create sorne 91

confusion here. However, when he claimed scientific theories to be descriptive, he meant that they describe the empirical world and not a world of essences. Similarly, his references to proof of a theory did not mean the demonstrative proof of a rational system, but rather the support derived from empir­ ical evidence. Berkeley's criticism of Newtonian science did not extend to its experimental method, which can be incorpo­ rated into instrumentalism as satisfactorily as into essen­ tialism. Although Professor Popper may make Berkeley too much the instrumentalist, this interpretation is valuable in setting the Berkeleian theory of science in its historical setting as an early reaction against the essentialism of New­ tonian theory. When his philosophy of science is interpreted inthis way, he becomes important to the instrumentalist move­ ment which began in the late nineteenth century in opposition to essentialism and subsequently lead to other views of scien­ tific theory. This relation cf Berkeley to later scientific theory will be taken up in Chapter 9. 92

Chapter 9. The Influence of His Analysis of Science.

Of the considerable volume of criticism of Berke­ ley's philosophy during his lifetime, comparatively little was directed against his philosophy of science. The article "Iv'f.atter" in Ephraim Chamber' s Cyclopaedia (published 1728), after giving Newton's view, made brief reference to Berke­ ley's rejection of rnaterial substance and quoted from Berke­ ley's Principles.191 However, it was not until late in the nineteenth century, when the foundations of Newtonian sci­ ence came under question, that Berkeley began to receive the attention of physicists and physical theorists. The attack on the mathematicians in the Analyst (1734) brought more immediate results in the form of numerous counter-attacks. In the following year, Berkeley responded to two: to Dr James Jurin in A Defence of Free-thinking in Mathematics and briefly to J. Walton in Reasons for not Replying to TvTr. Walton's Full Answer. Although neither the counter-attacks nor Berkeley's answers contributed signifi- cantly to the philosophic issues, the controversy continued so that, in commenting on the doctrine of fluxions in a note to Siris (1744), he remarked:

191Bracken, Early Reception, pp. 57, 120. 93

within these ten years, l have seen pub­ lished about twenty tracts and disserta­ tions, whose authors being utterly at variance and inconsistent with each other, instruct bystanders what to think of their pretentions to evidence.192

Later thinkers came very gradually to concede that his criti­ cism of the Newtonian and Leibnizian formulations of the calculus was justified. By 1862, a well-known mathematician, Sir \'lilliam Rowan Hamilton, could state privately but still not publicly, that Berkeley was right and that Newton's meth­ od was "sophistical.,,193 fVlore recently, F. Cajori, a distin­ guished historian of mathematics, has hailed the publication of the Analyst (1734) as "the most spectacular event of the century in the history of British mathematics.194 Perhaps because he, in the words of Professor Philippe Devaux, lacked "la t~te mathé'matique,,,195 Berkeley did not realize that the resolution of his problem rested, as we have seen in Chapter 7, in a revised theory of limits. Such a revised theory was offered by the French mathematician, Augustin Louis Cauchy, in 1821 with subsequent refinements being proposed to elimi­ nate entirely the intuitive dependence of the concept of

192Works, IV, 61, V, 127; Siris, S. 271. 193Wisdom, "Berkeley's Criticism of the Infinitesimal," IV, 23. 194Florian Cajori, ! History of the Conceptions of Limits and Fluxions in Great Britain from Newton to Woodbouse (Chicago, 1919 ), p. 57 • 195Devaux, VII, 102. 94

1imit on the concept of motion.196 Mathematical theorists are today in genera1 agreement that Berkeley's criticisrn has been satisfactorily answered by a reformu1ation of the calcu1us in terms of the current concept of limit. After being 1arge1y ignored for 175 years, Berke- 1ey's analysis of science began to attract the attention of physicists and phi1osophers of science 1ate in the last cen­ tury. Claims have subsequently been advanced concerning his role in two recent developments in physica1 theory: the growth of the instrumentalist view of science and the intro­ duction of re1ativity theory. We have already noted Profes­ sor Popper's interpretation of Berkeley as an instrurnenta1- ist in Chapter 8 and it is to the subsequent deve10pment of this view that we now turn. A number of thinkers, among them Mach, Duhem and Poincaré, adopted instrumentalist views of physica1 science in general accord with Berke1ey's denial of essences in sci­ ence. Instrumenta1ism, roughly the view that scientific theories are nothing but instruments, gradually replaced the earlier essentia1ist view of the Newtonians until it came to dorr.inate physical theory. Although the instrumenta1- ist movement exhibits sorr.e marked similarities to Berkeley's view of science, it is a matter of debate to what extent he anticipated instrumentalism and its derivatives. The rea­ sons which 1ed instrurnentalists to deny essences in science

196Wisdom, "Berkeley's Criticism of the Infinitesimal," IV, 23. 95

were not always his reasons. Whereas Berkeley believed that the only essences were spiritual and hence beyond the scope of science, Mach felt that there were no essences of any kind and Duhem felt that essences were in principle unknow­ able. In his criterion of mathematical hypotheses as use­ fuI, he has been compared to Mach, Quine and Nagel although

T~ch's application of the criterion of simplicity to mathe­ matical hypotheses, for example, goes weIl beyond Berkeley.197 Instrumentalism is associated with positivism and its reliance on a phenomenalist theory of meaning, by which an expression such as "force of attraction" would be dis- missed as meaningless since forces of attraction cannot be observed. Professor Popper identifies this phenomenalist theory of meaning with Berkeley's own view, represented as being that a term in science is meaningless if it has no association with Berkeleian ideas.198 This would appear to be an over-simplified interpretation. Berkeley certainly rejected sorne expressions as meaningless, including such ab- stractions as Locke's general idea of a triangle. But Locke's triangle was criticized for its contradictory qual­ ities as weIl as for its lack of empirical content, and the former criticism seems more reasonable grounds than the lat- ter to reject it as meaningless. In excluding such expres- sions as "force of attraction" from physics, Berkeley did not

197Popper, pp. 171-3. 198Ibid., pp. 109, 168. 96

criticize them for having contradictory qualities, but rather for being useless to science due to their lack of empirical content. As a result, he can hardly be said to have estab­ lished these expressions to be meaningless when he had only shown them to be useless to science.199 When elaborating his philosophy of language in the Principles, he subordinated the communicative role to the emotive role of language, a theory which requires a much broader theory of meaning than the phenomenalist theory.200 Although the occasional care­ less use of language may at tirnes imply that he rejected such terms as force and gravity as meaningless, it is by no means established that Berkeley was a phenor.:enalist in his theory of meaning or a positivist in his philosophy of science. In disagreement with Professor Popper, Professor Ardley suggests that Berkeley has little in common with J·'Iach's positivism while acknowledging the influence of the 3erkeleian critique of calculus on Machean phySics. 201

The popularity of the inst~entalist view of sci- entific knowledge has been attributed to its practical suc­ cesses, one of which was the resolution of sorne difficulties with quantum theory by the introduction in 1927 by Niels Bohr of the principle of complernentarity. In fact, as Professor Popper points out, successful application of this sort con-

1995uchting, 58, 191. 200Works, II, 36-8; Principles, Introduction, SS. 18-20. 201Ardley, pp. 28, 49. 97

firm the essentialist view, which admits that theories can at times function as instruments, as much as the instrument­ alist view. The main difficulty in instrumentalism is its inability to account for the falsifiability of a scientific theory. An instrument, including a scientific theory to the extent that it is an instrument, cannot be refutedj one can merely indicate the limits of its (safe or correct) applica­ tion. In contrast, the pure scientist treats the whole the­ ory as refuted and abandons it if experimental evidence fails to accord with any implication of the theory, however remote. Instrumentalism leads to complacency and stagnation by its failure to justify the highly critical attitude essential to the pure scientist in his search for the truth. The failures of essentialism and instrumentalism lead to a third view which combines aspects of the two ear­ lier views and of which Professor Popper's account of scient­ ific theories as "genuine conjectures" about the world is typical. Whether they are in fact true or whether we can know if they are true, scientific theories represent attempts to discover the truth. Theories can make predictions about two kinds of events: events of a kind already known to us and new kinds of events. Instrumentalism can accûunt only for the first kind of prediction. The second kind of prediction, which lead to the discovery of wireless waves, zero-point energy, artifical elements and so on, ~s of greater value and cannot be accounted for by instrumentalism. 202

202Popper, pp. 113-8. Although it is possible and at times may be help­ fuI to regard Berkeley as a forerunner of instrurnentalism, it would appear to be a mistake to identify his position too closely with the later movement, many of the conclusions of which would incur his opposition. Let it rather be said that his critical analysis of Newtonian science has contrib­ uted to a general intellectual climate which has encouraged recent developments in physical science. Compared to the often dogmatic claims of the Newtonians to have discovered the ultimate truth or reality, the instrumentalists have ad­ vanced fewer claims and the supporters of the third view have been even more tentative in attributing truth or reality to their views. If these later views can be considered as advances in the field of physical theory, part of the credit for this belongs to Berkeley, whose attack on the use of ab- stract terms in Newtonian physics represented an early reac­ tion against the essentialist view. Sorne scientific theo­ ries also share common ground with his analysis of science. For example, Planck's quantum theory reflects Berkeley's denial of infinite divisibility.203 But rather than treat him as a forerunner of Planck, ~~ch, the instrumentalists and so on by the drawing of connections which must inevitably be historically debatable, it seems preferable to regard Berke­ ley as a valuable contributor to the whole intellectual cli­ mate of contemporary physical science.

203 Ardley, p. 20.d 99

Berkeley's analysis of scientific concepts has also received credit for exerting a considerable influence on con- temporary relativity theory. Berkeley, it is said, antici­ pated Ernst ~~ach who in turn anticipated Einstein. Without diminishing the value of Berkeley's analysis of scientific concepts in general or of his critique of Newton's doctrine of absolute motion in particular, 1 would suggest that his direct impact on relativity theory has also been at times overemphasized. Professor "vVhitrow suggests that "Mach was antici- pated by Berkeley in aIl essentials, including the critical discussion of ~!ewton' s analysis of rotational motion. ,,204 Professor Popper makes the more cautious suggestion that Ber­ keley and Mach criticized Newtonian absolute space, time and mo t lono on very Slml° °1 ar 1°lnes. 205 Th a t Ma c h owe d muc h t 0 Berkeley is beyond question, but just how similar are their respective views is difficult to establish. For example, al­ though both repudiate Newton's claim of the bucket experiment as evidence of absolute motion, they differ in their ac­ counts. Berkeley appears to agree with Newton that there are no forces acting on the water in the bucket in stage (1) of the experiment whereas Iv'fach sa ys that there are forces, but that these would be present in measurable proportions

204 Whi trow ,"Berkeley' s Critique of Newton," 82, 110. 205Popper, pp. 171-2. 100

only if the bucket were several leagues thick. 206 There would appear also to be a difference in sorne degree in their conclusions. In commenting in a later edition of the recep­ tion of earlier editions of his 9cience of Mechanics, Mach presents his vie", to be that absolute motion is "meaningless, without any empirical content, and scientifically without use. ,,207 Berkeley would agree with the assertion of absolute motion to be devoid of empirical content and useless to sci­ ence, but whether he would want also to dismiss it as mean­ ingless is more debatable. (See pages 95 and 96). ~Vhile

Berkeley to sorne extent anticipated ~/Iach' s later views, i t seems inaccurate to present Yach as merely repeating Berke­ ley's critique of Newtonian absolute space, time and motion in a more careful and detailed formulation.

We may next enquire into the extent of ~~ch's in­ fluence on Einstein. Professor Suchting claims that the aspect of r,~ch' s thought relevant to Einstein' s rela ti vi ty the ory lies in the "conjecture regarding the causal influ­ ence of star masses and the conclusions drawn therefrom regarding the program for a relativization of aIl motion" and points out that this aspect does not appear in Berke­ ley.208 Berkeley recognized the need for a frame of refer­ ence based not on one star, but in principle on "the sky of

206Suchting, 58, 193-4. 207Popper, p. 172. 208S uchting, 58, 197. 101

the fixed stars. n209 However, he appeared to be unaware of the observational evidence of l'elative movement among the stars discovered by Halley in 1718, two years before the publication of De f\iotu. 210 Being unaware of this difficulty, Berkeley did not anticipate Mach's solution, which was rough­ ly that since we cannot distinguish experimentally between the collateral role played by the stars (as frame of refer­ ence) and their fundamental (causal) role, we should as a matter of convenience when using the fixed stars as our frame of reference regard aIl motions as determined by the fixed stars (causally and hence not the concern of physics).211 To pur sue further the link between Mach and Eins- tein, one item of evidence is Einstein's obituary notice for

~·iach: "It is not impossible that Mach would have found the Theory of Relativity if, at a time when his mind was still young, the problem of the constancy of velocity of light had agitated the physicists." In quoting this remark, Professor Popper acknowledges its extreme generousity since Mach strongly opposed the theory during the eleven years - eight of them active - by which he survived the 1905 publication of the Special Theory of Relativity.212 Recently published evidence has even discredited the influence on Einstein of

209Works, IV, 47; De Motu, S. 59. 210Whitrow, nBerkeley's Critique of Newton," 82, 109. 211r.lfach, p. 283. 212Popper, p. 172. 102

the 1887 Michelson-Morley experiment which first drew atten­ tion to the problem of the constancy of the velocity of light despite the motion of its source. After a study of Einstein's personal memorabilia, Professor Gerald Holton differs from early views in concluding that the experiment's effect on Einstein was negligible. In a letter written in 1954, one year before his death, Einstein remarked: "1 even do not remember if l knew of (the experiment) at aIl when l wrote my first papeJ.'" on the subject. "213 If the effect of the Hichelson-Morley experiment on Einstein can be so sud- denly diminished, any claim that Berkeley, through Mach, anticipated Einstein should ~a ~~bj8~t to very searching reappraisal. It remains to ask whether Berkeley contributed to other aspects of relativity theory. Certainly he in no sense anticipated Minkowski's concept of a four-dimensional space-time continuum in which a body is said to "lie" along a certain "world-li::1.e." Despite Berkeley's rejection of aIl three absolutes and Newton's acceptance of aIl three, they both regarded absolute space and absolute time as essential to absolute motion. In this both men were following the tradition ,.,rhich considers space and time in isolation as opposed to the comparatively recent tendency to treat them as a unity. Relativity theory is incompatible with any

213Gerald Holton, "Einstein and the 'Crucial' Experiment," American Journal of Physics, 37 (October, 1969), 968-982. 103

philosophical account which separates space from time2l4 and as a result is incompatible with both Berkeley's doctrine of relative space and time and Newton's doctrine of absolute space and time. Special relativity is consistent with any philosophical account of space-time which treats space-time rigorously as a unity. As a physical theory, special rela­ tivity is neutral between relational or absolute philoso­ phical theories. A relational theory might interpret space­ time interval conventionally in terms of geometrical defini­ tions (as does Professor \V.V.O. Quine 2l5 ) in contrast to an absolute theory which might interpret space-time interval ontologically in terms of inde pendent entities. (This may not be the case for the general theory of relativity in which the space-time interval de pends on distinctions of mat­ ter in the universe and which as a result may not be philo­ sophically neutral.) Berkeley's positive doctrine of space and time is therefore no more compatible than Newton's with contemporary relativity theory. The conception of alternative geometries to the Euclidian system is as remote frorn Berkeley's philosophy of rnathernatics as the concept of the four-dimensional space-time continuum is remote from his philosophy of science. Like

Ne~~on and all contemporary thinkers, Berkeley recognized the

2l4J.J.C. Smart, "Space," The :!.:ncyclopedia of Philosophy, 1967, VII, 510. 215W• V.o. Quine, ~'Jord and Object (Cambridge, 1960), pp. 252-7. 104

1 possibility of Euclidean geometry only and, in tieing geo­ metry so closely to the empirical, ruled out the possibil­ ity of such alternative systems as Lobachevskian and Rie­ mannian geometries. With this denial of the possibility of alternative geometries, Berkeley would have rejected the efforts of contemporary physicists and mathematicians to reformulate relativity theory in terms of various geometries and to provide translations from one geometric system to another. To identify Berkeley as the precursor of Mach and Sinstein without the very careful qualifications imposed by Professors Popper and Suchting is historically inaccurate and scientifically misleading. In reiterating the sugges­

tion that his direct influence on relativi~y theory as weIl as on instrumentalism has been at times overstated, l do not mean to diminish the significant contribution to the general intellectual climate of later years made by Berke­ ley's philosophy of science in general or by his critique of Newtonian physics in particular. Indeed, it would be difficult to exaggerate the value of Berkeley's analysis of science in the later development of scientific theory. A SELECTED BIBLIOGRAPHY

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