QUANTIFIERS, QUESTIONS and QUANTUM PHYSICS Quantifiers, Questions and Quantum Physics Essays on the Philosophy of Jaakko Hintikka
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Transworld Heir Lines 89
Transworld Heir Lines 89 It is desirable that symposia be limited to nine; 4 and, It is believable that nine is prime illustrate such contexts. These occurrences ofthe word "nine" are neither Transworld Heir Lines . so vulgar as that in Nine is larger than five DA VID KAPLAN nor so accidental as that in University of California, Los Angeles Canines are larger than felines. Presumably there are no logical or semantical problems concerned with vulgar or accidental occurrences. Vulgar occurrences of "nine" denote a certain number, are open to substitution and generalization, and contribute to the meaning of the containing sentence. Accidental occurrences are A certain kind of linguistic context has come in for increasing attention ! irrelevant to all such concerns. But analysis of the intermediate contexts over the past several years. The occurrences of the word "nine" in produced by "provable," "possible," "permissible," "probable," "be lievable, " and "desirable" is neither trivial nor pointless. It is provable in arithmetic that nine is the square of three; Gottlob Frege, who tried to assimilate such intermediate occurrences to It is possible that the number of planets is nine; the vulgar ones by means of a doctrine about ambiguity and indirect deno It is permissible that the number of occupants exceed nine; .tation, called such contexts "oblique" or "indirect." W. V. O. Quine, It is probable that the number of enrolled students will be less than who often seems to want to assimilate the intermediate occurrences to nine; accidental ones by means of a doctrine of indissolubility, calls such con texts opaque. Copyright © 1978 by David Kaplan. -
Automating Free Logic in HOL, with an Experimental Application in Category Theory
Noname manuscript No. (will be inserted by the editor) Automating Free Logic in HOL, with an Experimental Application in Category Theory Christoph Benzm¨uller and Dana S. Scott Received: date / Accepted: date Abstract A shallow semantical embedding of free logic in classical higher- order logic is presented, which enables the off-the-shelf application of higher- order interactive and automated theorem provers for the formalisation and verification of free logic theories. Subsequently, this approach is applied to a selected domain of mathematics: starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. As a side-effect of this work some (minor) issues in a prominent category theory textbook have been revealed. The purpose of this article is not to claim any novel results in category the- ory, but to demonstrate an elegant way to “implement” and utilize interactive and automated reasoning in free logic, and to present illustrative experiments. Keywords Free Logic · Classical Higher-Order Logic · Category Theory · Interactive and Automated Theorem Proving 1 Introduction Partiality and undefinedness are prominent challenges in various areas of math- ematics and computer science. Unfortunately, however, modern proof assistant systems and automated theorem provers based on traditional classical or intu- itionistic logics provide rather inadequate support for these challenge concepts. Free logic [24,25,30,32] offers a theoretically appealing solution, but it has been considered as rather unsuited towards practical utilization. Christoph Benzm¨uller Freie Universit¨at Berlin, Berlin, Germany & University of Luxembourg, Luxembourg E-mail: [email protected] Dana S. -
EPISTEMOLOGY and PHILOSOPHY of MIND HISTORICAL Historical Dictionaries of Religions, Philosophies, and Movements, No
PHILOSOPHY • EPISTEMOLOGY AND PHILOSOPHY OF MIND HISTORICAL Historical Dictionaries of Religions, Philosophies, and Movements, No. 70 DICTIONARY OF BAERGEN Epistemology Epistemology is the branch of philosophy that investigates our beliefs, evidence, and claims of knowledge. It is one of the core areas of philosophy and is relevant to an DICTIONARY astonishingly broad range of issues and situations. Epistemological issues arise when HISTORICAL we recognize that there is a fact of the matter but we do not know what it is; when we wonder about the future, the past, or distant places; and when we seek answers in the sciences and even in our entertainment (for example, murder mysteries and comedies of misunderstanding). OF Epistemology Historical Dictionary of Epistemology provides an overview of this field of study and its theories, concepts, and personalities. It begins with a chronology of important events (from 385 BC to AD 2005) and is followed by an introduction, which gives a historical overview. The book contains more than 500 entries covering notable concepts, theo- ries, arguments, publications, issues, and philosophers and concludes with an exten- sive bibliography of historical and contemporary epistemological works. Students and those who want to acquaint themselves with epistemology will be greatly aided by this book. RALPH BAERGEN is a professor of philosophy at Idaho State University. For orders and information please contact the publisher SCARECROW PRESS, INC. A wholly owned subsidiary of ISBN-13: 978-0-8108-5518-2 The Rowman & Littlefield Publishing Group, Inc. ISBN-10: 0-8108-5518-6 4501 Forbes Boulevard, Suite 200 Lanham, Maryland 20706 1-800-462-6420 • fax 717-794-3803 www.scarecrowpress.com RALPH BAERGEN HDEpistempologyLITH.indd 1 6/12/06 1:07:32 PM 06-236_01_Front.qxd 6/12/06 12:54 PM Page i HISTORICAL DICTIONARIES OF RELIGIONS, PHILOSOPHIES, AND MOVEMENTS Jon Woronoff, Series Editor 1. -
Mathematical Logic. Introduction. by Vilnis Detlovs And
1 Version released: May 24, 2017 Introduction to Mathematical Logic Hyper-textbook for students by Vilnis Detlovs, Dr. math., and Karlis Podnieks, Dr. math. University of Latvia This work is licensed under a Creative Commons License and is copyrighted © 2000-2017 by us, Vilnis Detlovs and Karlis Podnieks. Sections 1, 2, 3 of this book represent an extended translation of the corresponding chapters of the book: V. Detlovs, Elements of Mathematical Logic, Riga, University of Latvia, 1964, 252 pp. (in Latvian). With kind permission of Dr. Detlovs. Vilnis Detlovs. Memorial Page In preparation – forever (however, since 2000, used successfully in a real logic course for computer science students). This hyper-textbook contains links to: Wikipedia, the free encyclopedia; MacTutor History of Mathematics archive of the University of St Andrews; MathWorld of Wolfram Research. 2 Table of Contents References..........................................................................................................3 1. Introduction. What Is Logic, Really?.............................................................4 1.1. Total Formalization is Possible!..............................................................5 1.2. Predicate Languages.............................................................................10 1.3. Axioms of Logic: Minimal System, Constructive System and Classical System..........................................................................................................27 1.4. The Flavor of Proving Directly.............................................................40 -
The Modal Logic of Potential Infinity, with an Application to Free Choice
The Modal Logic of Potential Infinity, With an Application to Free Choice Sequences Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ethan Brauer, B.A. ∼6 6 Graduate Program in Philosophy The Ohio State University 2020 Dissertation Committee: Professor Stewart Shapiro, Co-adviser Professor Neil Tennant, Co-adviser Professor Chris Miller Professor Chris Pincock c Ethan Brauer, 2020 Abstract This dissertation is a study of potential infinity in mathematics and its contrast with actual infinity. Roughly, an actual infinity is a completed infinite totality. By contrast, a collection is potentially infinite when it is possible to expand it beyond any finite limit, despite not being a completed, actual infinite totality. The concept of potential infinity thus involves a notion of possibility. On this basis, recent progress has been made in giving an account of potential infinity using the resources of modal logic. Part I of this dissertation studies what the right modal logic is for reasoning about potential infinity. I begin Part I by rehearsing an argument|which is due to Linnebo and which I partially endorse|that the right modal logic is S4.2. Under this assumption, Linnebo has shown that a natural translation of non-modal first-order logic into modal first- order logic is sound and faithful. I argue that for the philosophical purposes at stake, the modal logic in question should be free and extend Linnebo's result to this setting. I then identify a limitation to the argument for S4.2 being the right modal logic for potential infinity. -
Existence As a Real Property
Francesco Berto Existence as a Real Property The Ontology of Meinongianism For Graham Priest, Long-distance teacher Prologue: Much Ado About Nothing Some philosophers think that something’s having intuitive content is very inconclusive evidence in favor of it. I think it is very heavy evidence in favor of anything, myself. I really don’t know, in a way, what more conclusive evidence one can have about anything, ultimately speaking. –Saul Kripke, Naming and Necessity 1 In an episode of The Today Show of some years ago, Gene Shalit – NBC’s film and book critic, famous for his wits – reviews several books sharing the feature of bearing entertaining titles. The highpoint of the monologue comes with Nonexistent Objects, by the UCLA philosopher Terence Parsons. Shalit wonders how one could write a whole book on things that do not exist!1 This whole book, too, is about things that do not exist. But if one stops to think, one may find that, in a sense, there is nothing special about this. There are, in fact, thousands of books speaking about unreal things. You have probably read quite a few of them: Sir Arthur Conan Doyle’s stories portrait the adventures of the detective Sherlock Holmes; The Lord of the Rings speaks at length of Gandalf the wizard. Doyle represents Sherlock Holmes as a detective living in London, Baker Street (precisely, at number 221b), describes his remarkable observational and deductive abilities, makes of him the arch-enemy of the criminal mastermind Moriarty. J.R.R. Tolkien characterizes Gandalf as a wizard with a pointy hat and a grey robe (a white one, from a certain point of the story onwards), a heavy pipe-herb 1 The anecdote is reported by Roy Sorensen [2003], p. -
Forming the Mind Studies in the History of Philosophy of Mind
FORMING THE MIND STUDIES IN THE HISTORY OF PHILOSOPHY OF MIND Volume 5 Editors Henrik Lagerlund, The University of Western Ontario, Canada Mikko Yrjönsuuri, Academy of Finland and University of Jyväskylä, Finland Board of Consulting Editors Lilli Alanen, Uppsala University, Sweden Joël Biard, University of Tours, France Michael Della Rocca, Yale University, U.S.A. Eyjólfur Emilsson, University of Oslo, Norway André Gombay, University of Toronto, Canada Patricia Kitcher, Columbia University, U.S.A. Simo Knuuttila, University of Helsinki, Finland Béatrice M. Longuenesse, New York University, U.S.A. Calvin Normore, University of California, Los Angeles, U.S.A. Aims and Scope The aim of the series is to foster historical research into the nature of thinking and the workings of the mind. The volumes address topics of intellectual history that would nowadays fall into different disciplines like philosophy of mind, philo- sophical psychology, artificial intelligence, cognitive science, etc. The monographs and collections of articles in the series are historically reliable as well as congenial to the contemporary reader. They provide original insights into central contem- porary problems by looking at them in historical contexts, addressing issues like consciousness, representation and intentionality, mind and body, the self and the emotions. In this way, the books open up new perspectives for research on these topics. FORMING THE MIND Essays on the Internal Senses and the Mind/Body Problem from Avicenna to the Medical Enlightenment Edited by HENRIK LAGERLUND The University of Western Ontario, Canada A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-6083-0 (HB) ISBN 978-1-4020-6084-7 (e-book) Published by Springer, P.O. -
Principles of Knowledge, Belief and Conditional Belief Guillaume Aucher
Principles of Knowledge, Belief and Conditional Belief Guillaume Aucher To cite this version: Guillaume Aucher. Principles of Knowledge, Belief and Conditional Belief. Interdisciplinary Works in Logic, Epistemology, Psychology and Linguistics, pp.97 - 134, 2014, 10.1007/978-3-319-03044-9_5. hal-01098789 HAL Id: hal-01098789 https://hal.inria.fr/hal-01098789 Submitted on 29 Dec 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Principles of knowledge, belief and conditional belief Guillaume Aucher 1 Introduction Elucidating the nature of the relationship between knowledge and belief is an old issue in epistemology dating back at least to Plato. Two approaches to addressing this problem stand out from the rest. The first consists in providing a definition of knowledge, in terms of belief, that would somehow pin down the essential ingredient binding knowledge to belief. The second consists in providing a complete characterization of this relationship in terms of logical principles relating these two notions. The accomplishement of either of these two objectives would certainly contribute to solving this problem. The success of the first approach is hindered by the so-called ‘Gettier problem’. Until recently, the view that knowledge could be defined in terms of belief as ‘justified true belief’ was endorsed by most philosophers. -
Existence and Reference in Medieval Logic
GYULA KLIMA EXISTENCE AND REFERENCE IN MEDIEVAL LOGIC 1. Introduction: Existential Assumptions in Modern vs. Medieval Logic “The expression ‘free logic’ is an abbreviation for the phrase ‘free of existence assumptions with respect to its terms, general and singular’.”1 Classical quantification theory is not a free logic in this sense, as its standard formulations commonly assume that every singular term in every model is assigned a referent, an element of the universe of discourse. Indeed, since singular terms include not only singular constants, but also variables2, standard quantification theory may be regarded as involving even the assumption of the existence of the values of its variables, in accordance with Quine’s famous dictum: “to be is to be the value of a variable”.3 But according to some modern interpretations of Aristotelian syllogistic, Aristotle’s theory would involve an even stronger existential assumption, not shared by quantification theory, namely, the assumption of the non-emptiness of common terms.4 Indeed, the need for such an assumption seems to be supported not only by a number of syllogistic forms, which without this assumption appear to be invalid, but also by the doctrine of Aristotle’s De Interpretatione concerning the logical relationships among categorical propositions, commonly summarized in the Square of Opposition. For example, Aristotle’s theory states that universal affirmative propositions imply particular affirmative propositions. But if we formalize such propositions in quantification theory, we get formulae between which the corresponding implication does not hold. So, evidently, there is some discrepancy between the ways Aristotle and quantification theory interpret these categoricals. -
Transparency and the KK Principle
Transparency and the KK Principle Nilanjan Das (MIT) and Bernhard Salow (Trinity College Cambridge) Penultimate Draft – Please Cite Published Version Abstract An important question in epistemology is whether the KK principle is true, i.e., whether an agent who knows that p is also thereby in a position to know that she knows that p. We explain how a “transparency” account of self-knowledge, which maintains that we learn about our attitudes towards a proposition by reflecting not on ourselves but rather on that very proposition, supports an affirmative answer. In particular, we show that such an account allows us to reconcile a version of the KK principle with an “externalist” or “reliabilist” conception of knowledge commonly thought to make that principle particularly problematic. The KK principle states that someone who knows that p is in a position to know that she knows that p. In addition to an enviable pedigree of historical supporters,1 this thesis has considerable intuitive appeal. For, to put it roughly, if the KK principle is false, rational agents can be alienated from their own attitudes and actions in a counterintuitive manner. One way to bring this out is by noting that there seems something self-undermining or incoherent about someone who says (in thought or out loud) something of the form “while it is raining, I’m not willing to take a stance on whether I know that it is.” But if nothing in the vicinity of the KK principle is correct, this is hard to explain. For if there are counterexamples to KK, there are fully coherent agents who know p without being in a position to know that they know this. -
A Priori Skepticism and the KK Thesis
A Priori Skepticism and the KK Thesis James R. Beebe (University at Buffalo) International Journal for the Study of Skepticism (forthcoming) In Beebe (2011), I argued against the widespread reluctance of philosophers to treat skeptical challenges to our a priori knowledge of necessary truths with the same seriousness as skeptical challenges to our a posteriori knowledge of contingent truths. Vahid (2013) offers several reasons for thinking the unequal treatment of these two kinds of skepticism is justified, one of which is a priori skepticism’s seeming dependence upon the widely scorned KK thesis. In the present article, I defend a priori skepticism against Vahid’s criticisms. Keywords: Skepticism; a priori skepticism; second-order knowledge; KK thesis In a previous issue of this journal, Hamid Vahid (2013) offers a thorough examination of some recent non-standard approaches to philosophical skepticism (e.g., Beebe 2010; 2011; Kraft MS; Kung MS; Schaffer 2010). One non-standard form of skepticism, dubbed ‘a priori skepticism,’ challenges our ability to have a priori knowledge of necessary truths (cf. Beebe 2011). Against proponents of these approaches, Vahid argues that many non-standard skeptical challenges fail to raise any significant doubts concerning first-order knowledge claims—i.e., claims of the form ‘S knows that p,’ for some domain of propositions. Rather, Vahid maintains that these challenges at best contest our ability to have second-order knowledge—i.e., to know that we know the propositions in question. Because skepticism about second-order knowledge claims is seen as significantly less threatening to our overall view of ourselves as knowledgeable creatures, Vahid suggests that non-standard skepticism should be considered philosophically less interesting than its supporters maintain. -
Quine and Whitehead: Ontology and Methodology 3
McHENRY I QUINE AND WHITEHEAD: ONTOLOGY AND METHODOLOGY 3 philosophical scene as of late (e.g., deconstructionism, postmodem relativism), the and Whitehead: Ontology and gulf that separates Whitehead and analytical philosophy is not as great as it used to Quine 'be.3 Before I begin to explore the affinities, as well as some contrasts, between Methodology . Quine and Whitehead, a word of caution is in order. It is well known that Quine wrote his doctoral dissertation, "The Logic of Sequences: A Generalization of LeemonMcHenry Principia Mathematica," under Whitehead's direction.4 Quine also took two of Whitehead's seminars at Harvard,"Science and the Modem World" and "Cosmol I LEEMON McHENRY reaches philosophy at Loyola Marymount University, Los ogies Ancient and Modem," but he says that he "responded little to these courses" Angeles, CA 90045, E-mail: [email protected] and "took refuge in his relatively mathematical material on 'extensive abstrac tion. "'s Despite Quine's statement that he "retained a vivid sense of being in the presence of the great," he does not acknowledge any philosophical influence from · Introduction . the ph!losoph!es o!'W.V . Qu�e an d Whitehead. Rather, Camap and Russell are cited as the inspirations of Quine's The very idea· of a basis for comparing . , mcluding Qume himself. early development. A.N. Whitehead may be surprising to most philosophe� . philosophy two completely Both produced systems of thought that have taken m When Quine overlapped with Whitehead at Harvard, Whitehead was deeply at the forefron: of c�ntemp� involved in working out the details of his metaphysics of process--a philosophic different directions.