Gail Stine, "Skepticism, Relevant Alternatives, and Deductive Closure"
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Logic, Reasoning, and Revision
Logic, Reasoning, and Revision Abstract The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this paper I first place Harman’s challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms for belief can be captured. introduction The canons of classical deductive logic provide, at least according to a widespread but presumably naive view, general as well as infallible norms for reasoning. Obviously, few instances of actual reasoning have such prop- erties, and it is therefore not surprising that the naive view has been chal- lenged in many ways. Four kinds of challenges are relevant to the question of where the naive view goes wrong, but each of these challenges is also in- teresting because it allows us to focus on a particular aspect of the relation between deductive logic, reasoning, and logical revision. Challenges to the naive view that classical deductive logic directly yields norms for reason- ing come in two sorts. Two of them are straightforwardly revisionist; they claim that the consequence relation of classical logic is the culprit. The remaining two directly question the naive view about the normative role of logic for reasoning; they do not think that the philosophical notion of en- tailment (however conceived) is as relevant to reasoning as has traditionally been assumed. -
Mathematical Logic
Proof Theory. Mathematical Logic. From the XIXth century to the 1960s, logic was essentially mathematical. Development of first-order logic (1879-1928): Frege, Hilbert, Bernays, Ackermann. Development of the fundamental axiom systems for mathematics (1880s-1920s): Cantor, Peano, Zermelo, Fraenkel, Skolem, von Neumann. Giuseppe Peano (1858-1932) Core Logic – 2005/06-1ab – p. 2/43 Mathematical Logic. From the XIXth century to the 1960s, logic was essentially mathematical. Development of first-order logic (1879-1928): Frege, Hilbert, Bernays, Ackermann. Development of the fundamental axiom systems for mathematics (1880s-1920s): Cantor, Peano, Zermelo, Fraenkel, Skolem, von Neumann. Traditional four areas of mathematical logic: Proof Theory. Recursion Theory. Model Theory. Set Theory. Core Logic – 2005/06-1ab – p. 2/43 Gödel (1). Kurt Gödel (1906-1978) Studied at the University of Vienna; PhD supervisor Hans Hahn (1879-1934). Thesis (1929): Gödel Completeness Theorem. 1931: “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”. Gödel’s First Incompleteness Theorem and a proof sketch of the Second Incompleteness Theorem. Core Logic – 2005/06-1ab – p. 3/43 Gödel (2). 1935-1940: Gödel proves the consistency of the Axiom of Choice and the Generalized Continuum Hypothesis with the axioms of set theory (solving one half of Hilbert’s 1st Problem). 1940: Emigration to the USA: Princeton. Close friendship to Einstein, Morgenstern and von Neumann. Suffered from severe hypochondria and paranoia. Strong views on the philosophy of mathematics. Core Logic – 2005/06-1ab – p. 4/43 Gödel’s Incompleteness Theorem (1). 1928: At the ICM in Bologna, Hilbert claims that the work of Ackermann and von Neumann constitutes a proof of the consistency of arithmetic. -
In Defence of Constructive Empiricism: Metaphysics Versus Science
To appear in Journal for General Philosophy of Science (2004) In Defence of Constructive Empiricism: Metaphysics versus Science F.A. Muller Institute for the History and Philosophy of Science and Mathematics Utrecht University, P.O. Box 80.000 3508 TA Utrecht, The Netherlands E-mail: [email protected] August 2003 Summary Over the past years, in books and journals (this journal included), N. Maxwell launched a ferocious attack on B.C. van Fraassen's view of science called Con- structive Empiricism (CE). This attack has been totally ignored. Must we con- clude from this silence that no defence is possible against the attack and that a fortiori Maxwell has buried CE once and for all, or is the attack too obviously flawed as not to merit exposure? We believe that neither is the case and hope that a careful dissection of Maxwell's reasoning will make this clear. This dis- section includes an analysis of Maxwell's `aberrance-argument' (omnipresent in his many writings) for the contentious claim that science implicitly and per- manently accepts a substantial, metaphysical thesis about the universe. This claim generally has been ignored too, for more than a quarter of a century. Our con- clusions will be that, first, Maxwell's attacks on CE can be beaten off; secondly, his `aberrance-arguments' do not establish what Maxwell believes they estab- lish; but, thirdly, we can draw a number of valuable lessons from these attacks about the nature of science and of the libertarian nature of CE. Table of Contents on other side −! Contents 1 Exordium: What is Maxwell's Argument? 1 2 Does Science Implicitly Accept Metaphysics? 3 2.1 Aberrant Theories . -
1 Hilary Putnam, Reason, Truth and History, (Cambridge: Harvard University Press, 1979). Henceforth 'RTH'. the Position Th
[The Journal of Philosophical Research XVII (1992): 313-345] Brains in a Vat, Subjectivity, and the Causal Theory of Reference Kirk Ludwig Department of Philosophy University of Florida Gainesville, FL 32611-8545 1. Introduction In the first chapter of Reason, Truth and History,1 Putnam argued that it is not epistemically possible that we are brains in a vat (of a certain sort). If his argument is correct, and can be extended in certain ways, then it seems that we can lay to rest the traditional skeptical worry that most or all of our beliefs about the external world are false. Putnam’s argument has two parts. The first is an argument for a theory of reference2 according to which we cannot refer to an object or a type of object unless we have had a certain sort of causal interaction with it. The second part argues from this theory to the conclusion that we can know that we are not brains in a vat. In this paper I will argue that Putnam’s argument to show that we cannot be brains in a vat is unsuccessful. However, the flaw is not in the argument from the theory of reference to the conclusion 1 Hilary Putnam, Reason, Truth and History, (Cambridge: Harvard University Press, 1979). Henceforth ‘RTH’. The position that Putnam advances in this first chapter is one that in later chapters of RTH he abandons in favor of the position that he calls ‘internal realism’. He represents the arguments he gives in chapter 1 as a problem posed for the ‘external realist’, who assumes the possibility of a God’s eye point of view. -
Qt11c0x4n5.Pdf
UC Berkeley Working Papers Title Figure and Ground in Logical Space Permalink https://escholarship.org/uc/item/11c0x4n5 Author Yalcin, Seth Publication Date 2015-12-02 eScholarship.org Powered by the California Digital Library University of California Figure and Ground in Logical Space⇤ Seth Yalcin [email protected] April 22, 2011 1Introduction The idea that states of belief are, in a certain sense, sensitive to questions, or to subject matters, or more generally to ways of resolving logical space,helpsin some simple ways with aspects of the classical problem of logical omniscience. So I argue here. Focusing on belief, I begin by reviewing a version of a familiar story about belief and belief content, what I will call the map picture of belief. I will suggest that the picture is incomplete in ways that lead to the problems of logical omniscience, and that the addition of the aforementioned kind of sensitivity helps to fill in the picture in ways that start to address the problems. My larger aim is to explore the extent to which the idea of belief as question- sensitive state can be motivated by considerations in the philosophy of content, considered largely in abstraction from issues in descriptive semantics per se (e.g., in abstraction from the detailed compositional semantics of belief ascription). By the end, we will not have fully resolved the problems of logical omniscience, but we will have made some headway. 2Themappicture The motto of the map picture is: belief is the map by which we steer.1 You will have heard some version this story before, but we need a single version of it for operating on. -
Interactive Models of Closure and Introspection
Interactive Models of Closure and Introspection 1 introduction Logical models of knowledge can, even when confined to the single-agent perspective, differ in many ways. One way to look at this diversity suggests that there doesn’t have to be a single epistemic logic. We can simply choose a logic relative to its intended context of application (see e.g. Halpern [1996: 485]). From a philosophical perspective, however, there are at least two features of the logic of “knows” that are a genuine topic of disagreement, rather than a source of mere diversity or pluralism: closure and introspec- tion. By closure, I mean here the fact that knowledge is closed under known implication, knowing that p puts one in a position to come to know what one knows to be implied by p. By introspection, I shall (primarily) refer to the principle of positive introspection which stipulates that knowing puts one in a position to know that one knows.1 The seemingly innocuous princi- ple of closure was most famously challenged by Dretske [1970] and Nozick [1981], who believed that giving up closure—and therefore the intuitively plausible suggestion that knowledge can safely be extended by deduction— was the best way to defeat the sceptic. Positive introspection, by contrast, was initially defended in Hintikka’s Knowledge and Belief [1962], widely scrutinized in the years following its publication (Danto [1967], Hilpinen [1970], and Lemmon [1967]), and systematically challenged (if not conclu- sively rejected) by Williamson [2000: IV–V]. A feature of these two principles that is not always sufficiently acknowl- edged, is that that there isn’t a unique cognitive capability that corresponds to each of these principles. -
REVIEW ARTICLE on the Philosophical
REVIEW ARTICLE On the philosophical applications of Cognitive Science Alvin Goldman (ed), Readings in Philosophy and Cognitive Science. Cambridge, MA: The MIT Press, 1993. Goldman collected thirty-eight papers in Philosophy and in Cognitive Science that are of interest to people from both disciplines. In the following I describe the motivation behind Readings in Philosophy and Cognitive Science (henceforth RPCS), and review its structure. I also point to recent selections, probably less familiar to the potential reader, but certainly worth noticing. I then discuss the bounds of the philosophical applications of Cognitive Science. 1. General overview The very first reaction to RPCS is to wonder why we need another anthology for the philosophy of cognitive science. RPCS, however, is different from Block (1980), Lycan (1990) and many other anthologies. Unlike the others, whose focus is the so-called philosophical foundations of cognitive science, RPCS focuses on the applications of cognitive science to philosophy. As such, most of the papers in RPCS make explicit the connection between empirical findings and significant philosophical theses. Another distinctive feature of RPCS is that half of the papers in it were written by cognitive scientists. These essays describe important empirical work in social psychology, developmental psychology, computational linguistics, artificial intelligence, decision-making theory, vision and neuroscience. Some of the papers, such as Chomsky’s "On the Nature, Use, and Acquisition of Language", and Tversky and Kahneman's "Probabilistic Reasoning" are already very familiar to philosophers and have had their impact on the philosophical literature. Many other papers report or summarize more recent empirical findings. An explicit goal of Goldman in RPCS is to show “how cognitive science bears on most of the major branches in philosophy” (p. -
The Ascent from Nominalism Philosophical Studies Series
THE ASCENT FROM NOMINALISM PHILOSOPHICAL STUDIES SERIES Editors: WILFRID SELLARS, University of Pittsburgh KEITH LEHRER, University of Arizona Board of Consulting Editors: J ON A THAN BENNETT, Syracuse University ALLAN GIBBARD, University of Michigan ROBERT STALNAKER, Cornell University ROBERT G. TURNBULL, Ohio State University VOLUME 37 TERR Y PENNER Department of Philosophy, The University of Wisconsin at Madison, U.S.A. THE ASCENT FROM NOMINALISM Some Existence Arguments in Plato's Middle Dialogues D. REIDEL PUBLISHING COMPANY ~~ A MEMBER OF THE KLUWER . ACADEMIC PUBLISHERS GROUP DORDRECHTj BOSTONj LANCASTERjTOKYO Library of Congress Cataloging in Publication Data Penner, Terry, 1936- The ascent from nominalism. (Philosophical studies series; v. 37) Bibliography: p. Includes indexes. 1. Plato. 2. Aristotle. 3. Metaphysics-History. 4. Nominalism-History. I. Title. II. Series. B395.P347 1987 111'.2'0924 86·31641 ISBN-13: 978-94-010-8186-3 e-ISBN-13: 978-94-009-3791-8 DOl: 10.1007/978-94-009-3791-8 Published by D. Reidel Publishing Company, P.O. Box 17, 3300 AA Dordrecht, Holland. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, Holland. All Rights Reserved © 1987 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover I 5t edition 1987 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical induding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner ACKNOWLEDGEMENTS Much of this work was conceived and executed between 1971 and 1975, though some of it was done much earlier, and a few bits are quite recent. -
Laws and Natures
Philosophy of Science: Laws Nancy Cartwright (LSE and UCSD) Anna Alexandrova (UCSD) with Sophia Efstathiou (UCSD) Andrew Hamilton (UCSD) Ioan Muntean (UCSD) Part I: Introduction1 For a long time the analytic tradition in philosophy of science focused on two main questions about laws: ‘Can one reasonably take a realist stand about the laws of science?’ and ‘What distinguishes a law from other kinds of truths, especially from universal and statistical truths that are not laws?’ For a discussion of the first question, look to the entry on ‘realism’. The second was taken to be important because laws were thought to be ontologically fundamental – the basis responsible for all other natural facts – and to be the source of scientific prediction, explanation and technology. Nowadays these assumptions are under attack from a variety of vantage points and the second question is overshadowed by a prior one: 'Of what use are laws to begin with?' In Part III we shall discuss five overlapping positions that downplay the role of laws in science and nature. The slogan of all of these could be Ronald Giere's “Science without laws!” Before that in Part II we describe more traditional views that take laws as central, either as the repository of scientific knowledge (laws of science) or as the basic sources or governors for what happens (laws of nature). Part II: Traditional views What we call the traditional view takes laws to be a fundamental aim and a crowning achievement of modern science. The problem is only to find an adequate definition of them. What does it mean to be a law of nature? This question dominated metaphysics and philosophy of science in the second half of 20th century. -
Inconsistency and Uncertainty Handling in Lightweight Description Logics
Inconsistency and uncertainty handling in lightweight description logics THÈSE présentée et soutenue publiquement le 5 juin 2015 en vue de l’obtention du Doctorat de l’Université d’Artois (Spécialité Informatique) par : Zied Bouraoui devant le jury composé de Anthony HUNTER Professor - University College London, United Kingdom (Rapporteur) Henri PRADE Directeur de recherche CNRS - IRIT Toulouse (Rapporteur) Salem BENFERHAT Professeur des universités - Université d’Artois (Directeur de Thèse) Sylvain LAGRUE Maître de conférences (HDR) - Université d’Artois (Examinateur) Marie-Laure MUGNIER Professeur des universités- Université de Montpellier II (Examinatrice) Odile PAPINI Professeur des universités - Université d’Aix Marseille (Examinatrice) Ramón PINO PÉREZ Professor - University of the Andes, Venezuela (Examinateur) Karim TABIA Maître de conférences - Université d’Artois (Examinateur) CENTRE DE RECHERCHE EN INFORMATIQUE DE LENS – CNRS UMR-8188 UNIVERSITÉ D’ARTOIS, RUE JEAN SOUVRAZ, S.P. 18 F-62307, LENS CEDEX FRANCE SECRÉTARIAT :TÉL.: +33(0)321791723–FAX : +33(0)321791770 http://www.cril.univ-artois.fr ABSTRACT Abstract This thesis investigates the dynamics of beliefs and uncertainty management in DL-Lite, one of the most important lightweight description logics. The first part of the thesis concerns the problem of han- dling uncertainty in DL-Lite. First, we propose an extension of the main fragments of DL-Lite to deal with the uncertainty associated with axioms using a possibility theory framework without additional ex- tra computational costs. We then study the revision of possibilistic DL-Lite bases when a new piece of information is available. Lastly, we propose a min-based assertional merging operator when assertions of ABox are provided by several sources of information having different levels of priority. -
Minds, Machines, and Money: What Really Explains Behavior
FRED DRETSKE MINDS, MACHINES, AND MONEY: WHAT REALLY EXPLAINS BEHAVIOR According to a certain philosophical picture of the way mind and body are related, the mind is to intentional action what money is to the behavior of a vending machine. Just as coins are in (or get deposited in) vending machines, beliefs, desires, and intentions are in us. Just as the right coins deposited in the machine cause the machine to behave in a certain way - to yield its contents: cokes, cigarettes, or candy, as the case may be - so the right mental entities occurring in us cause us to perform various actions. Furthermore, just as what makes money money is not its intrinsic character - shape, size and density of the coins, for example - but certain extrinsic or relational facts about these coins (the fact that they possess monetary value) so too what makes a belief a belief is not its intrinsic neurobiological character, but, rather, certain extrinsic facts about it - the fact that it has a certain meaning or content, the fact that it has certain intentional properties. But if we take this analogy seriously, it suggests that beliefs, qua beliefs, are as irrelevant to animal behavior as is money, qua money, to the behavior of vending machines. Since it is facts about the shape and size of coins, not facts about their monetary value, that explain why coins cause a machine to yield its contents, the analogy, if we take it seriously - and a good many philosophers do - compels us to con clude that it is the intrinsic features of beliefs, their neurobiological pro perties, not their extrinsic properties, their meaning or content, that explains why we do what we do. -
Epistemic Logic, Relevant Alternatives, and the Dynamics of Context?
Epistemic Logic, Relevant Alternatives, and the Dynamics of Context? Wesley H. Holliday Abstract. According to the Relevant Alternatives (RA) Theory of knowl- edge, knowing that something is the case involves ruling out (only) the relevant alternatives.Theconceptionofknowledgeinepistemiclogicalso involves the elimination of possibilities, but without an explicit distinc- tion, among the possibilities consistent with an agent’s information, be- tween those relevant possibilities that an agent must rule out in order to know and those remote, far-fetched or otherwise irrelevant possibilities. In this article, I propose formalizations of two versions of the RA theory. Doing so clarifies a famous debate in epistemology, pitting Fred Dretske against David Lewis, about whether the RA theorist should accept the principle that knowledge is closed under known implication, familiar as the K axiom in epistemic logic. Dretske’s case against closure under known implication leads to a study of other closure principles, while Lewis’s defense of closure by appeal to the claimed context sensitivity of knowledge attributions leads to a study of the dynamics of context. Having followed the first lead at length in other work, here I focus more on the second, especially on logical issues associated with developing a dynamic epistemic logic of context change over models for the RA theory. 1Introduction Example 1 (Medical Diagnosis). Suppose that two medical students, A and B, are subjected to a test. Their professor introduces them to the same patient, who presents various symptoms, and the students are to make a diagnosis of the patient’s condition. After some independent investigation, both students conclude that the patient has a common condition c.