Quine and the Problem of Truth Volume 4, Number 10 Joshua Schwartz Editor in Chief Kevin C
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Kripke's Theory of Truth
Kripke’s Theory of Truth (for the strong Kleene scheme) Presented by Christopher Gauker Version: July 26, 2006 Contemporary discussions of truth often make reference to Kripke’s theory of truth (presented by Kripke only his 1975 Journal of Philosophy paper). What Kripke did was show how to interpret a language in such a way that it contains its own truth predicate. The fact that the language he describes contains its own truth predicate is proved by means of something called a fixed-point theorem. I have written this document and posted it on the web because it is hard to find a presentation of Kripke’s theory that will be understandable even to readers who have had only a first course in logic. It is my intention that this presentation will be understandable to all readers who have been exposed to at least the following: The languages of ordinary predicate logic. Recursive definitions of truth in a structure for such languages. (Structures are also called models or interpretations.) The basic concepts and notation of set theory, such as curly brackets, membership (“∈”), inclusion (“⊆”), ordered n-tuples, relations and functions. Kripke’s theory of truth builds on a three-valued interpretation of a language. (So sentences may be neither true nor false (N) as well as (T) or false (F).) Various three- valued valuation schemes may be used. Here we will consider only the strong Kleene scheme, which is the only one most people care about. I can take no credit for this presentation. It is nothing more than a distillation from the more general presentation in Anil Gupta and Nuel Belnap’s book, The Revision Theory of Truth (MIT Press, 1993) (who in turn acknowledge debts to Fitting and Visser). -
Story of Logic – Class Notes Fall 2010 Revised August 2012 CS 4860 Fall 2012 By: Robert L
Applied Logic The Story of Logic – Class Notes Fall 2010 Revised August 2012 CS 4860 Fall 2012 By: Robert L. Constable 1 Classical Period These brief notes on the history of logic are meant to be an easily understood basis for stating very informally some of the great ideas in logic.1 Appreciating how the basic concepts were discovered and why they were needed is an accessible basis for a technical understanding of these concepts. For many students, this historical approach has been a route by which they have come to deeply understand and appreciate logic. Logic is one of the oldest continuously studied academic subjects, and while investigating its central questions, Alan M. Turing gave birth to computer science in 1936 as you will see toward the end of these notes. He and his thesis advisor at Princeton University, Alonzo Church, laid theoretical foundations for computer science that continue to frame some of the deepest questions and provide the conceptual tools for important applications. Indeed, their ideas underlie one of the most enduring contributions of computer science to intellectual history, the discovery that we can program computers to assist us in solving mathematical and scientific problems that we could not solve without them. It is no longer in doubt that computers can be programmed to perform high level mental operations that were once regarded as the pinnacle of human mental activity. Let us start as far back as is historically sensible as far as we know. 1.1 Epimenides of Crete circa 500 BCE Epimenides is reputed to have posed a version of the Liar’s Paradox, “All Cretans are liars” said a known Cretan. -
Philosophy of Science and Philosophy of Chemistry
Philosophy of Science and Philosophy of Chemistry Jaap van Brakel Abstract: In this paper I assess the relation between philosophy of chemistry and (general) philosophy of science, focusing on those themes in the philoso- phy of chemistry that may bring about major revisions or extensions of cur- rent philosophy of science. Three themes can claim to make a unique contri- bution to philosophy of science: first, the variety of materials in the (natural and artificial) world; second, extending the world by making new stuff; and, third, specific features of the relations between chemistry and physics. Keywords : philosophy of science, philosophy of chemistry, interdiscourse relations, making stuff, variety of substances . 1. Introduction Chemistry is unique and distinguishes itself from all other sciences, with respect to three broad issues: • A (variety of) stuff perspective, requiring conceptual analysis of the notion of stuff or material (Sections 4 and 5). • A making stuff perspective: the transformation of stuff by chemical reaction or phase transition (Section 6). • The pivotal role of the relations between chemistry and physics in connection with the question how everything fits together (Section 7). All themes in the philosophy of chemistry can be classified in one of these three clusters or make contributions to general philosophy of science that, as yet , are not particularly different from similar contributions from other sci- ences (Section 3). I do not exclude the possibility of there being more than three clusters of philosophical issues unique to philosophy of chemistry, but I am not aware of any as yet. Moreover, highlighting the issues discussed in Sections 5-7 does not mean that issues reviewed in Section 3 are less im- portant in revising the philosophy of science. -
Raymond Smullyan, the Amazing Mathematician and Logician, Died
Remembering Raymond 1 S. Parthasarathy [email protected] His looks would remind you of the wizard from Harry Potter movies. His nimble fingers can play effortlessly, Mozart and Chopin, on the piano. He can wave his empty hands and pull out a pigeon from nowhere. All this would have happened till 6 February 2017. That was when Raymond Smullyan, the amazing mathematician and logician, died. Raymond Merrill Smullyan (aka Raymond Smullyan), was born on May 25, 1919, in Far Rockaway, N.Y., the son of Isidore Smullyan and Rosina Freeman Smullyan. He was educated at the University of Chicago and Princeton University. He was a mathematician and logician, professor emeritus of philosophy at Lehman College and the Graduate Center, City University of New York, and Oscar Ewing professor of philosophy at Indiana University Bloomington. He was one of many logi- cians to have studied under Alonzo Church. As an academic, he was known for his work in math and logic. He was also an author of a series of popular books on recreational logic, including, "What is the name of this book?" and \The lady and the tiger". A review of his book \Satan, Cantor and Infinity: Mind-Boggling Puzzles" appeared sometime ago in Gonitsora. Smullyan's life itself was closely influenced by logic. Here are two instances: The following story (published earlier in Gonitsora) was narrated by Smullyan himself in a video presentation: When Smullyan, the master of puzzles, met his date, he challenged her to a logical puzzle. The contract: Smullyan was to make a statement. • If the statement were true, the date had to give Smullyan an autograph. -
Life with Augustine
Life with Augustine ...a course in his spirit and guidance for daily living By Edmond A. Maher ii Life with Augustine © 2002 Augustinian Press Australia Sydney, Australia. Acknowledgements: The author wishes to acknowledge and thank the following people: ► the Augustinian Province of Our Mother of Good Counsel, Australia, for support- ing this project, with special mention of Pat Fahey osa, Kevin Burman osa, Pat Codd osa and Peter Jones osa ► Laurence Mooney osa for assistance in editing ► Michael Morahan osa for formatting this 2nd Edition ► John Coles, Peter Gagan, Dr. Frank McGrath fms (Brisbane CEO), Benet Fonck ofm, Peter Keogh sfo for sharing their vast experience in adult education ► John Rotelle osa, for granting us permission to use his English translation of Tarcisius van Bavel’s work Augustine (full bibliography within) and for his scholarly advice Megan Atkins for her formatting suggestions in the 1st Edition, that have carried over into this the 2nd ► those generous people who have completed the 1st Edition and suggested valuable improvements, especially Kath Neehouse and friends at Villanova College, Brisbane Foreword 1 Dear Participant Saint Augustine of Hippo is a figure in our history who has appealed to the curiosity and imagination of many generations. He is well known for being both sinner and saint, for being a bishop yet also a fellow pilgrim on the journey to God. One of the most popular and attractive persons across many centuries, his influence on the church has continued to our current day. He is also renowned for his influ- ence in philosophy and psychology and even (in an indirect way) art, music and architecture. -
A Note on Extension, Intension, and Truth Author(S): Anil Gupta and Nuel Belnap Source: the Journal of Philosophy, Vol
Journal of Philosophy, Inc. A Note on Extension, Intension, and Truth Author(s): Anil Gupta and Nuel Belnap Source: The Journal of Philosophy, Vol. 84, No. 3 (Mar., 1987), pp. 168-174 Published by: Journal of Philosophy, Inc. Stable URL: http://www.jstor.org/stable/2026597 Accessed: 28/05/2009 11:06 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=jphil. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. Journal of Philosophy, Inc. is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Philosophy. http://www.jstor.org 168 THE JOURNAL OF PHILOSOPHY A NOTE ON EXTENSION, INTENSION, AND TRUTH* I T is common knowledge that two predicates may coincide in extension but differ in intension and that, for any predicate, one can construct an infinity of coextensional predicates that differ in intension. -
Philosophy of Chemistry: an Emerging Field with Implications for Chemistry Education
DOCUMENT RESUME ED 434 811 SE 062 822 AUTHOR Erduran, Sibel TITLE Philosophy of Chemistry: An Emerging Field with Implications for Chemistry Education. PUB DATE 1999-09-00 NOTE 10p.; Paper presented at the History, Philosophy and Science Teaching Conference (5th, Pavia, Italy, September, 1999). PUB TYPE Opinion Papers (120) Speeches/Meeting Papers (150) EDRS PRICE MF01/PC01 Plus Postage. DESCRIPTORS *Chemistry; Educational Change; Foreign Countries; Higher Education; *Philosophy; Science Curriculum; *Science Education; *Science Education History; *Science History; Scientific Principles; Secondary Education; Teaching Methods ABSTRACT Traditional applications of history and philosophy of science in chemistry education have concentrated on the teaching and learning of "history of chemistry". This paper considers the recent emergence of "philosophy of chemistry" as a distinct field and explores the implications of philosophy of chemistry for chemistry education in the context of teaching and learning chemical models. This paper calls for preventing the mutually exclusive development of chemistry education and philosophy of chemistry, and argues that research in chemistry education should strive to learn from the mistakes that resulted when early developments in science education were made separate from advances in philosophy of science. Contains 54 references. (Author/WRM) ******************************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. ******************************************************************************** 1 PHILOSOPHY OF CHEMISTRY: AN EMERGING FIELD WITH IMPLICATIONS FOR CHEMISTRY EDUCATION PERMISSION TO REPRODUCE AND U.S. DEPARTMENT OF EDUCATION DISSEMINATE THIS MATERIAL HAS Office of Educational Research and improvement BEEN GRANTED BY RESOURCES INFORMATION SIBEL ERDURAN CENTER (ERIC) This document has been reproducedas ceived from the person or organization KING'S COLLEGE, UNIVERSITYOF LONDON originating it. -
Is Truth an Epistemic Value?∗
Is Truth an Epistemic Value?∗ Mar´ıa J. Fr´apolli Departamento de Filosof´ıa Universidad de Granada (Espana)˜ [email protected] Introduction That truth is an epistemic value is a thesis that at least has the following two interpretations: Truth can be defined through, or identified with, some epistemic notion or other. This is the epistemic side Truth is something that science, or research, should pursue. Truth is some- thing valuable. This is the value side. Whereas interpretation (i) makes a false statement, interpretation (ii) ex- presses something that is true, although empty. But both interpretations have a grain of truth, and both are, in their own way, somewhat misleading. Their confusing offsprings have been epistemic and metaphysical theories of truth, respectively. The grain of truth in (i) is that the truth predicate is omnipresent when we deal with epistemic notions, and so that not even the most basic theses in epis- temology can be stated without using the truth predicate essentially. Besides, the endorsement role that the truth predicate performs in natural languages is applied in many cases to the items that have passed the kind of justificatory filters sanctioned by epistemology. The grain of truth in (ii) is that the best, and shortest, way of codifying the infinity of contents to whose knowledge science is aimed to is by the help of sentences that involve the truth predicate. The misleading aspect of (i) is that it suggests that truth should be identified with some item out of a set of epistemic situations: ideal justification, results of reliable processes, what the best scientific theories say, etc., and all this in order to seal the gap through which the sceptical menaces to slip in. -
Coherence, Truth, and the Development of Scientific Knowledge*
Coherence, Truth, and the Development of Scientific Knowledge* Paul Thagard†‡ What is the relation between coherence and truth? This paper rejects numerous answers to this question, including the following: truth is coherence; coherence is irrelevant to truth; coherence always leads to truth; coherence leads to probability, which leads to truth. I will argue that coherence of the right kind leads to at least approximate truth. The right kind is explanatory coherence, where explanation consists in describing mech- anisms. We can judge that a scientific theory is progressively approximating the truth if it is increasing its explanatory coherence in two key respects: broadening by explaining more phenomena and deepening by investigating layers of mechanisms. I sketch an explanation of why deepening is a good epistemic strategy and discuss the prospect of deepening knowledge in the social sciences and everyday life. 1. Introduction. The problem of the relation between coherence and truth is important for philosophy of science and for epistemology in general. Many epistemologists maintain that epistemic claims are justified, not by a priori or empirical foundations, but by assessing whether they are part of the most coherent account (see, e.g., Bonjour 1985; Harman 1986; Lehrer 1990). A major issue for coherentist epistemology concerns whether we are ever warranted in concluding that the most coherent account is true. In the philosophy of science, the problem of coherence and truth is part of the ongoing controversy about scientific realism, the view that science aims at and to some extent succeeds in achieving true theories. The history of science is replete with highly coherent theories that have turned out to be false, which may suggest that coherence with empirical evidence is a poor guide to truth. -
Pragmatism, Phenomenalism, and Truth Talk ROBERT BRANDOM
MIDWEST STUDIES IN PHILOSOPHY, XI1 Pragmatism, Phenomenalism, and Truth Talk ROBERT BRANDOM his essay offers a rational reconstruction of the career of a certain heroic ap- Tproach to truth-the approach whose leading idea is that the special linguistic roles of truth ascriptions are to be explained in terms of features of the ascribinns of truth, rather than of what is ascrided. The explanatory emphasis placed on the act of calling something true, as opposed to its descriptive content, qualifies theories displaying this sort of strategic commitment as ‘pragmatic’theories of truth, by con- trast to ‘semantic’ ones. The starting point is an articulation of a central insight of the classical pragmatist theories of truth espoused in different versions by James and Dewey. Developing this insight in response to various objections yields a sequence of positions ending in contemporary anaphoric semantics: prosentential theories of ‘true’ and pronominal theories of ‘refers’. These theories articulate an antirealist posi- tion about truth and reference, of the sort here called ‘phenomenalist’.Insofar as the- ories of this sort offer adequate accounts of the phenomena they address, they assert relatively narrow and clearly defined limits to the explanatory ambitions of theories couched in traditional semantic vocabularies. I The popular conception of the theory of truth of classical pragmatism is summed up in the slogan ‘The truth is what works.’ According to this view, the pragmatists were trying to give a theory of truth in the sense of offering necessary and sufficient condi- tions for possession of that property. Their innovation is then seen to consist in tak- ing the possession of this property by a belief to consist in a relation not simply to what is believed, but also to what is desired. -
An Obituary of Raymond Smullyan - 02-20-2017 by S
Remembering Raymond: An Obituary of Raymond Smullyan - 02-20-2017 by S. Parthasarathy - Gonit Sora - http://gonitsora.com Remembering Raymond: An Obituary of Raymond Smullyan by S. Parthasarathy - Monday, February 20, 2017 http://gonitsora.com/obituary-raymond-smullyan/ His looks would remind you of the wizard from Harry Potter movies. His nimble fingers can play effortlessly, Mozart and Chopin, on the piano. He can wave his empty hands and pull out a pigeon from nowhere. All this would have happened till 6 February 2017. That was when Raymond Smullyan, the amazing mathematician and logician, died. Raymond Merrill Smullyan (aka Raymond Smullyan), was born on May 25, 1919, in Far Rockaway, N.Y., the son of Isidore Smullyan and Rosina Freeman Smullyan. He was educated at the University of Chicago and Princeton University. He was a mathematician and logician, professor emeritus of philosophy at Lehman College and the Graduate Center, City University of New York, and Oscar Ewing professor of philosophy at Indiana University Bloomington. He was one of many logicians to have studied under Alonzo Church. As an academic, he was known for his work in math and logic. He was also an author of a series of popular books on recreational logic, including, "What is the name of this book?" and ``The lady and the tiger''. A review of his book ``Satan, Cantor and Infinity: Mind-Boggling Puzzles'' appeared sometime ago in this website. Smullyan's life itself was closely influenced by logic. Here are two instances: The following story (published earlier in this website) was narrated by Smullyan himself in a video presentation: When Smullyan, the master of puzzles, met his date, he challenged her to a logical puzzle. -
Gupta Comment
Discussion of Anil Gupta's “Outline of an Account of Experience” The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Byrne, Alex et al. "Discussion of Anil Gupta's “Outline of an Account of Experience”." Analytic Philosophy 59, 1 (March 2018): 75-88 © 1999-2020 John Wiley & Sons, Inc. As Published http://dx.doi.org/10.1111/phib.12121 Publisher Wiley Version Author's final manuscript Citable link https://hdl.handle.net/1721.1/123434 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ Comments on Gupta Alex Byrne 1. Transitions Fundamental to Gupta’s picture is the idea of a “rational transition”. The role of experience, he thinks, “is not to provide the subject knowledge of anything or to bestow a rational or justificatory status on…beliefs or judgments”, but to “render rational certain transitions, including transitions from views to judgments”. His central non-perceptual example of a rational transition involves modus-ponens reasoning from the two premises, B and if B then C, to the conclusion C. And that does indeed seem to be rational or reasonable, in some sense of these elastic terms. Something is going right if someone reasons in this way—at least it’s better than affirming the consequent. Since valid reasoning, as Gupta emphasizes, implies nothing about whether the premises are true, or justifiably believed, or known, this example might seem to suggest that the rationality of transitions and the rationality of beliefs are quite different matters.