Frege, Lotze, and Boole
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On Dummett's Pragmatist Justification Procedure
On Dummett's Pragmatist Justification Procedure Herm´ogenesOliveira Abstract I show that propositional intuitionistic logic is complete with re- spect to an adaptation of Dummett's pragmatist justification proce- dure. In particular, given a pragmatist justification of an argument, I show how to obtain a natural deduction derivation of the conclusion of the argument from, at most, the same assumptions. 1 Introduction Proof-theoretic definitions of validity can be considered as loosely inspired by Wittgenstein's ideas relating meaning and use. They attempt to explain of the concept of logical validity in terms of the deductive use of the log- ical constants, as expressed by inference rules. In this context, Gentzen's investigations into deduction, particularly his calculus of natural deduction, are often used as a starting point for explaining the meaning of the logical constants on the basis of rules governing their use. In the standard natural deduction calculus [6, 10], the deductive use of a logical constant is governed by its introduction and elimination rules. Thus, from a semantic perspective where meaning is explained on the basis of use, arXiv:1701.03380v2 [math.LO] 30 Jul 2018 the introduction and elimination rules express the canonical manner in which a sentence with a logical constant as main operator is used in a deductive argument: the introduction rules express the canonical use of the sentence as a conclusion, the elimination rules express the canonical use of the sentence as an assumption. Along these lines, Dummett [2, 3] proposed that the analysis of the deductive meaning of a logical constant into introduction and elimination rules accounts for two distinct aspects of its use. -
Gottlob Frege Patricia A
Gottlob Frege Patricia A. Blanchette This is the penultimate version of the essay whose final version appears in the Oxford Handbook of Nineteenth-Century German Philosophy, M. Forster and K. Gjesdal (eds), Oxford University Press 2015, pp 207-227 Abstract Gottlob Frege (1848-1925) made significant contributions to both pure mathematics and philosophy. His most important technical contribution, of both mathematical and philosophical significance, is the introduction of a formal system of quantified logic. His work of a more purely- philosophical kind includes the articulation and persuasive defense of anti-psychologism in mathematics and logic, the rigorous pursuit of the thesis that arithmetic is reducible to logic, and the introduction of the distinction between sense and reference in the philosophy of language. Frege’s work has gone on to influence contemporary work across a broad spectrum, including the philosophy of mathematics and logic, the philosophy of language, and the philosophy of mind. This essay describes the historical development of Frege’s central views, and the connections between those views. Introduction Friedrich Ludwig Gottlob Frege was born on November 8, 1848 in the Hanseatic town of Wismar. He was educated in mathematics at the University of Jena and at the University of Göttingen, from which latter he received his doctorate in 1873. He defended his Habilitation the next year in Jena, and took up a position immediately at the University of Jena. Here he spent his entire academic career, lecturing in mathematics and logic, retiring in 1918. His death came on July 26, 1925 in the nearby town of Bad Kleinen.1 Frege is best known for three significant contributions to philosophy. -
Creativity in Nietzsche and Heidegger: the Relation of Art and Artist
Creativity in Nietzsche and Heidegger: The Relation of Art and Artist Justin Hauver Philosophy and German Mentor: Hans Sluga, Philosophy August 22, 2011 I began my research this summer with a simple goal in mind: I wanted to out- line the ways in which the thoughts of Friedrich Nietzsche and Martin Heidegger complement one another with respect to art. I had taken a few courses on each philosopher beforehand, so I had some inclination as to how their works might be brought into agreement. However, I almost immediately ran into difficulty. It turns out that Heidegger, who lived and thought two or three generations after Nietzsche, had actually lectured on the topic of Nietzsche's philosophy of art and had placed Nietzsche firmly in a long tradition characterized by its mis- understanding of art and of the work of art. This means that Heidegger himself did not agree with me|he did not see his thoughts on art as complementary with Nietzsche's. Rather, Heidegger saw his work as an improvement over the misguided aesthetic tradition. Fortunately for me, Heidegger was simply mistaken. At least, that's my thesis. Heidegger did not see his affinity with Nietzsche because he was misled by his own misinterpretation. Nevertheless, his thoughts on art balance nicely with those of Nietzsche. To support this claim, I will make three moves today. First, I will set up Heidegger's critique, which is really a challenge to the entire tradition that begins with Plato and runs its course up to Nietzsche. Next, I will turn to Heidegger's views on art to see how he overcomes the tradition and answers his own criticism of aesthetics. -
Gottlob Frege: on Sense and Reference Professor Jeeloo Liu [Introduction]
Phil/Ling 375: Meaning and Mind [Handout #13] Gottlob Frege: On Sense and Reference Professor JeeLoo Liu [Introduction] I. Language and the World ___ How does language depict reality? Does reality have the same structure as the structure of language? For instance, the basic linguistic structure is a subject and a predicate, and the basic structure of the world is a particular and a universal (e.g. “Socrates is wise”). The subject usually is something of the world and we describe some property it has or does not have. A is F is true is A is really F, is false when A is not F. II. Different Elements of Language Singular terms: Terms that designate particular things Proper names Indexicals: now, today, here, I… Demonstratives: that, this… Pronouns (singular): he, she,… Definite descriptions (the so-and-so): Indefinite (singular) descriptions (a so-and-so) General terms: Terms that designate a kind of things or a certain property Mass nouns ___ natural kind terms (‘water,’ ‘tiger,’ ‘lemon’) ___ non-natural kind terms (‘bachelor’, ‘contract,’ ‘chair’) Adjectives (predicates): colors, shapes, etc. III. Traditional Theories of Meaning Prior to Frege [A] The Ideational Theory ___ The meaning of a linguistic expression is the speaker’s idea that is associated with the expression. [B] Mill’s Theory [the Object Theory] ___ The meaning of a singular term is the thing designated by that term; ___ the meaning of a name is just what the name stands for; the name does not have any other meaning e.g. ‘Socrates’ means Socrates e.g. ‘Dartmouth’ e.g. -
Leibniz on Consciousness and Self-Consciousness Rocco J
Leibniz on Consciousness and Self-Consciousness Rocco J. Gennaro [Final version in NEW ESSAYS ON THE RATIONALISTS, Oxford U Press, 1999] In this paper I discuss the so-called "higher-order thought theory of consciousness" (the HOT theory) with special attention to how Leibnizian theses can help support it and how it can shed light on Leibniz's theory of perception, apperception, and consciousness. It will become clear how treating Leibniz as a HOT theorist can solve some of the problems he faced and some of the puzzles posed by commentators, e.g. animal mentality and the role of reason and memory in self-consciousness. I do not hold Leibniz's metaphysic of immaterial simple substances (i.e. monads), but even a contemporary materialist can learn a great deal from him. 1. What is the HOT Theory? In the absence of any plausible reductionist account of consciousness in nonmentalistic terms, the HOT theory says that the best explanation for what makes a mental state conscious is that it is accompanied by a thought (or awareness) that one is in that state.1 The sense of 'conscious state' I have in mind is the same as Nagel's sense, i.e. there is 'something it is like to be in that state' from a subjective or first-person point of view.2 Now, when the conscious mental state is a first-order world-directed state the HOT is not itself conscious; otherwise, circularity and an infinite regress would follow. Moreover, when the higher-order thought (HOT) is itself conscious, there is a yet higher-order (or third-order) thought directed at the second-order state. -
52 Philosophy in a Dark Time: Martin Heidegger and the Third Reich
52 Philosophy in a Dark Time: Martin Heidegger and the Third Reich TIMOTHY O’HAGAN Like Oscar Wilde I can resist everything except temptation. So when I re- ceived Anne Meylan’s tempting invitation to contribute to this Festschrift for Pascal Engel I accepted without hesitation, before I had time to think whether I had anything for the occasion. Finally I suggested to Anne the text of a pub- lic lecture which I delivered in 2008 and which I had shown to Pascal, who responded to it with his customary enthusiasm and barrage of papers of his own on similar topics. But when I re-read it, I realized that it had been written for the general public rather than the professional philosophers who would be likely to read this collection of essays. So what was I to do with it? I’ve decided to present it in two parts. In Part One I reproduce the original lecture, unchanged except for a few minor corrections. In Part Two I engage with a tiny fraction of the vast secondary literature which has built up over the years and which shows no sign of abating. 1. Part One: The 2008 Lecture Curtain-Raiser Let us start with two dates, 1927 and 1933. In 1927 Adolf Hitler’s Mein Kampf (volume II) was published. So too was Martin Heidegger’s magnum opus Being and Time. In 1933 two appointments were made: Hitler as Chancellor of the German Reich and Heidegger as Rector of Freiburg University. In 1927 it was a case of sheer coincidence; in 1933 the two events were closely linked. -
Ethics, Information, and Our “It-From-Bit” Universe Terrell Ward Bynum Southern Connecticut State University
1 Terrell Ward Bynum February 25, 2018 Ethics, Information, and Our “It-from-Bit” Universe Terrell Ward Bynum Southern Connecticut State University The essence of the Computer Revolution is found in the It from bit . every particle, every field of force, even the spacetime nature of a computer itself. What is revolutionary about continuum itself . derives its function, its meaning, its very existence computers is logical malleability. James H. Moor 1985 from [bits]. John Archibald Wheeler 1990 Abstract: Using information technology, humans have brought about the “Information Revolution,” which is changing the world faster and more profoundly than ever before, and generating an enormous number of ethical “policy vacuums”. How is this possible? An answer is suggested by ideas from James Moor regarding “logical malleability,” in his classic paper “What is Computer Ethics?” (1985) The present essay combines Moor’s ideas with the hypothesis that all physical entities — including spacetime and the universe as a whole — are dynamic data structures. To show the usefulness of taking such an approach, in both physics and in computer ethics, a suggested “it-from-bit” model of the universe is briefly sketched, and relevant predictions are offered about the future of computer and information ethics. 1. Introduction One of the most fruitful and insightful claims about the nature of the universe was made by philosopher/scientist Norbert Wiener in an address to the New York Academy of Sciences in autumn of 1946. Apparently, Wiener was the first to recognize the physical nature of “environmental information,” as it is often called today. It suddenly became clear to him — while advising Claude Shannon on how to determine the amount of information being carried in a telephone wire (Conway and Siegelman, 2005, 164, 186) — that environmental information is physical and is fundamentally related to the second law of thermodynamics. -
Lotze and the Early Cambridge Analytic Philosophy
LOTZE AND THE EARLY CAMBRIDGE ANALYTIC PHILOSOPHY ―This summer I‘ve read about a half of Lotze‘s Metaphysik. He is the most delectable, certainly, of all German writers—a pure genius.‖ William James, September 8, 1879.1 Summary Many historians of analytic philosophy consider the early philosophy of Moore, Russell and Wittgenstein as much more neo-Hegelian as once believed. At the same time, the authors who closely investigate Green, Bradley and Bosanquet find out that these have little in common with Hegel. The thesis advanced in this chapter is that what the British (ill-named) neo-Hegelians brought to the early analytic philosophers were, above all, some ideas of Lotze, not of Hegel. This is true regarding: (i) Lotze’s logical approach to practically all philosoph- ical problems; (ii) his treating of the concepts relation, structure (constructions) and order; (iii) the discussion of the concepts of states of affairs, multiple theory of judgment, general logical form; (iv) some common themes like panpsychism and contemplating the world sub specie aeternitatis. 1. LOTZE, NOT HEGEL, LIES AT THE BOTTOM OF CAMBRIDGE ANALYTIC PHILOSOPHY Conventional wisdom has it that the early philosophy of Moore and Russell was under the strong sway of the British ―neo-Hegelians‖. In the same time, however, those historians who investigate the British ―neo-Hegelians‖ of 1880–1920 in detail, turn attention to the fact that the latter are not necessarily connected with Hegel: William Sweet made this point in regard to 1 Perry (1935), ii, p. 16. Bosanquet,2 Geoffrey Thomas in regard to Green,3 and Peter Nicholson in regard to Bradley.4 Finally, Nicholas Griffin has shown that Russell from 1895–8, then an alleged neo-Hegelian, ―was very strongly influenced by Kant and hardly at all by Hegel‖.5 These facts are hardly surprising, if we keep in mind that the representatives of the school of T. -
Michael Dummett the Nature and Future of Philosophy. New York: Columbia University Press 2010
Philosophy in Review XXXI (2011), no. 1 Michael Dummett The Nature and Future of Philosophy. New York: Columbia University Press 2010. 158 pages US$69.50 (cloth ISBN 978-0-231-15052-1); US$19.95 (paper ISBN 978-0-231-15053-8) This essay, first published in 2001 in Italian, is more a personal statement than an essay on the nature and future of philosophy. Dummett says how he thinks philosophy should be done and how he would like to see it develop. In particular, he summarizes his views regarding language, thought and the world with sidelong glances at other philosophers’ ideas and wrong turns. In Chapter 1 common apologies for philosophy are discounted in favor of defending the discipline on the grounds that ‘thought, without any specialized input from experience, can advance knowledge in unexpected directions’ (5). Next, in Chapter 2 (‘What is a Philosophical Question?’) and Chapter 3 (‘Philosophy as the Grammar of Thought’), Dummett nails his flag to the mast. We learn that philosophy ‘concerns our view of reality by seeking to clarify the concepts in terms of which we conceive of it, and hence the linguistic expressions by means of which we formulate our conception’ (11). So philosophy is not, as Quine would have it, continuous with ‘the most abstract part of science’, nor, as Wittgenstein insists, devoted to ‘cast[ing] light on what we already know from other sources, enabling us to see it with eyes unclouded by intellectual confusion’ (7). Indeed, when we consider how philosophers debate a philosophical question—Dummett discusses ‘Does time really pass?’ (8-10)—we see that philosophy is from beginning to end a conceptual endeavor. -
NEW Spirit and Secularity
NAHME - CHAPTER 3 DRAFT- NOT FOR CITATION Chapter 3 Race, Religion, and Identity: the (Theo-)Politics of Kantianism and the Predicament of German Jewish Liberalism In the century since their first, limited experience of emancipation in 1812, many German Jews gained an increasing awareness of the strengths and weaknesses of appealing to civic rights and individual freedoms to seek recognition in German public institutions. On the one hand, these liberal ideals of freedom and equality, duty and obligation to the rational legal state (Rechtstaat) gave German Jews a sense of belonging to the German Fatherland and held up the image of the rights-bearing citizen as an ideal to strive toward. But on the other hand, as we saw in the previous chapter, the Jewish Question was also increasingly framed as a problem implicit in the developing discourse of liberalism and gave rise to an anxiety over the secularization of political and moral public discourse about values, norms, and social ideals in Wilhelmine Germany. The Jewish Question, as I argued, was both an epistemological and a political predicament. Whether all “Germans” acknowledged Jews as belonging to a community and fraternity of national identity is less important, however, than the diversity in normative goals represented by the introduction of a liberal philosophical worldview in Imperial Germany as the means for articulating a still inchoate national identity. And because the Jews, like many of their compatriots, participated in a collective imagining of what a “civic” identity could be, their engagement with both the liberalism and idealism of the late nineteenth century gives voice to the significant influence of 197 NAHME - CHAPTER 3 DRAFT- NOT FOR CITATION this intellectual worldview on the broader social and cultural moment. -
Laws of Thought and Laws of Logic After Kant”1
“Laws of Thought and Laws of Logic after Kant”1 Published in Logic from Kant to Russell, ed. S. Lapointe (Routledge) This is the author’s version. Published version: https://www.routledge.com/Logic-from-Kant-to- Russell-Laying-the-Foundations-for-Analytic-Philosophy/Lapointe/p/book/9781351182249 Lydia Patton Virginia Tech [email protected] Abstract George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire normative force when constrained to mathematical reasoning. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s thorough and flexible work in these areas influenced the development of model theory (see Hodges, forthcoming), and has much in common with contemporary inferentialist approaches to logic (found in, e.g., Peregrin and Resnik). 1 I would like to thank Sandra Lapointe for providing the intellectual framework and leadership for this project, for organizing excellent workshops that were the site for substantive collaboration with others working on this project, and for comments on a draft. -
Computer Ethics: Basic Concepts and Historical Overview
Computer Ethics: Basic Concepts and Historical Overview http://plato.stanford.edu/archives/win2001/entries/ethics-computer/ This is a file in the archives of the Stanford Encyclopedia of Philosophy . Stanford Encyclopedia of Philosophy A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z Computer Ethics: Basic Concepts and Historical Overview Computer ethics is a new branch of ethics that is growing and changing rapidly as computer technology also grows and develops. The term "computer ethics" is open to interpretations both broad and narrow. On the one hand, for example, computer ethics might be understood very narrowly as the efforts of professional philosophers to apply traditional ethical theories like utilitarianism, Kantianism, or virtue ethics to issues regarding the use of computer technology. On the other hand, it is possible to construe computer ethics in a very broad way to include, as well, standards of professional practice, codes of conduct, aspects of computer law, public policy, corporate ethics--even certain topics in the sociology and psychology of computing. In the industrialized nations of the world, the "information revolution" already has significantly altered many aspects of life -- in banking and commerce, work and employment, medical care, national defense, transportation and entertainment. Consequently, information technology has begun to affect (in both good and bad ways) community life, family life, human relationships, education, freedom, democracy, and so on (to name a few examples). Computer ethics in the broadest sense can be understood as that branch of applied ethics which studies and analyzes such social and ethical impacts of information technology.