The History of Formal Semantics, Going Beyond What I Know First-Hand
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Abstract 1. Russell As a Mereologist
THE 1900 TURN IN BERTRAND RUSSELL’S LOGIC, THE EMERGENCE OF HIS PARADOX, AND THE WAY OUT Prof. Dr. Nikolay Milkov, Universität Paderborn, [email protected] Abstract Russell‘s initial project in philosophy (1898) was to make mathematics rigorous reducing it to logic. Before August 1900, however, Russell‘s logic was nothing but mereology. First, his acquaintance with Peano‘s ideas in August 1900 led him to discard the part-whole logic and accept a kind of intensional predicate logic instead. Among other things, the predicate logic helped Russell embrace a technique of treating the paradox of infinite numbers with the help of a singular concept, which he called ‗denoting phrase‘. Unfortunately, a new paradox emerged soon: that of classes. The main contention of this paper is that Russell‘s new con- ception only transferred the paradox of infinity from the realm of infinite numbers to that of class-inclusion. Russell‘s long-elaborated solution to his paradox developed between 1905 and 1908 was nothing but to set aside of some of the ideas he adopted with his turn of August 1900: (i) With the Theory of Descriptions, he reintroduced the complexes we are acquainted with in logic. In this way, he partly restored the pre-August 1900 mereology of complexes and sim- ples. (ii) The elimination of classes, with the help of the ‗substitutional theory‘,1 and of prop- ositions, by means of the Multiple Relation Theory of Judgment,2 completed this process. 1. Russell as a Mereologist In 1898, Russell abandoned his short period of adherence to the Neo-Hegelian position in the philosophy of mathematics and replaced it with what can be called the ‗analytic philoso- phy of mathematics‘, substantiated by the logic of relations. -
Invitation to Semantics
Varieties of meaning http://www-rohan.sdsu.edu/~gawron/semantics Jean Mark Gawron San Diego State University, Department of Linguistics 2012-01-25 Ling 525 Jean Mark Gawron ( SDSU ) Gawron: Semantics intro 2012-01-25 Ling 525 1 / 59 Outline 1 Semantics and pragmatics 2 Lexical vs. structural meaning 3 Sense and denotation 4 Determining denotations 5 Sentence denotations 6 Intensions and possible worlds 7 Conclusion Jean Mark Gawron ( SDSU ) Gawron: Semantics intro 2012-01-25 Ling 525 2 / 59 Outline 1 Semantics and pragmatics 2 Lexical vs. structural meaning 3 Sense and denotation 4 Determining denotations 5 Sentence denotations 6 Intensions and possible worlds 7 Conclusion Jean Mark Gawron ( SDSU ) Gawron: Semantics intro 2012-01-25 Ling 525 3 / 59 What is semantics? Definition Semantics Semantics is the study of the meaning of linguistic forms, what the words and the syntax contribute to what is communicated. Jean Mark Gawron ( SDSU ) Gawron: Semantics intro 2012-01-25 Ling 525 4 / 59 Literal meaning We call the meaning of a linguistic form its literal meaning. Sentence Literal meaning I forgot the paper Past forget(I, the paper) At some time in the past, someone forgets something [forget( , )] The speaker is the someone. The paper is the something. Each part of the sentence contributes something to this literal meaning. I the speaker of the utterance the paper an object appropriately describable as a paper forget the relation that holds between an indi- vidual and something they forget Past Tense (ed) the relation holds in the past Jean Mark Gawron ( SDSU ) Gawron: Semantics intro 2012-01-25 Ling 525 5 / 59 Semantics and pragmatics Literal meaning excludes a lot of what might actually be communicated on a particular occasion of utterance. -
Paul Rastall, a Linguistic Philosophy of Language, Lewiston, Queenston
Linguistica ONLINE. Published: July 10, 2009 http://www.phil.muni.cz/linguistica/art/mulder/mul-001.pdf ISSN 1801-5336 PAUL RASTALL: A LINGUISTIC PHILOSOPHY OF LANGUAGE, LAMPETER – LEWISTON, 2000[*] review article by Jan W. F. Mulder (University of St. Andrews, UK) Introductory note by Aleš Bičan In 2006 I happened to have a short e-mail conversation with Jan Mulder. I asked him for off-prints of his articles, as some of them were rather hard to find. He was so generous to send me, by regular post, a huge packet of them. It took me some time to realize that some of the included writings had never been published. One of them was a manuscript (type- script) of a discussion of a book by Paul Rastall, a former student of his, which was pub- lished in 2000 by The Edwin Press. I naturally contacted Paul Rastall and asked him about the article. He was not aware of it but supported my idea of having it published in Linguis- tica ONLINE. He consequently spoke to Mulder who welcomed the idea and granted the permission. The article below is thus published for the first time. It should be noted, how- ever, that Jan Mulder has not seen its final form. The text is reproduced here as it appears in the manuscript. I have only corrected a few typographical errors here and there. The only significant change is the inclusion of a list of references. Mulder refers to a number of works, but bibliographical information is not pro- vided. I have tried to list all that are mentioned in the article. -
Intensional Models for the Theory of Types∗
Intensional Models for the Theory of Types∗ Reinhard Muskens Abstract In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theo- rem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. 1 Introduction The axiom scheme of Extensionality states that whenever two predicates or relations are coextensive they must have the same properties: 8XY (8~x(X~x $ Y ~x) ! 8Z(ZX ! ZY )) (1) Historically Extensionality has always been problematic, the main problem be- ing that in many areas of application, though not perhaps in the foundations of mathematics, the statement is simply false. This was recognized by White- head and Russell in Principia Mathematica [32], where intensional functions such as `A believes that p' or `it is a strange coincidence that p' are discussed at length. -
Frege and the Logic of Sense and Reference
FREGE AND THE LOGIC OF SENSE AND REFERENCE Kevin C. Klement Routledge New York & London Published in 2002 by Routledge 29 West 35th Street New York, NY 10001 Published in Great Britain by Routledge 11 New Fetter Lane London EC4P 4EE Routledge is an imprint of the Taylor & Francis Group Printed in the United States of America on acid-free paper. Copyright © 2002 by Kevin C. Klement All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any infomration storage or retrieval system, without permission in writing from the publisher. 10 9 8 7 6 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data Klement, Kevin C., 1974– Frege and the logic of sense and reference / by Kevin Klement. p. cm — (Studies in philosophy) Includes bibliographical references and index ISBN 0-415-93790-6 1. Frege, Gottlob, 1848–1925. 2. Sense (Philosophy) 3. Reference (Philosophy) I. Title II. Studies in philosophy (New York, N. Y.) B3245.F24 K54 2001 12'.68'092—dc21 2001048169 Contents Page Preface ix Abbreviations xiii 1. The Need for a Logical Calculus for the Theory of Sinn and Bedeutung 3 Introduction 3 Frege’s Project: Logicism and the Notion of Begriffsschrift 4 The Theory of Sinn and Bedeutung 8 The Limitations of the Begriffsschrift 14 Filling the Gap 21 2. The Logic of the Grundgesetze 25 Logical Language and the Content of Logic 25 Functionality and Predication 28 Quantifiers and Gothic Letters 32 Roman Letters: An Alternative Notation for Generality 38 Value-Ranges and Extensions of Concepts 42 The Syntactic Rules of the Begriffsschrift 44 The Axiomatization of Frege’s System 49 Responses to the Paradox 56 v vi Contents 3. -
Analyticity, Necessity and Belief Aspects of Two-Dimensional Semantics
!"# #$%"" &'( ( )#"% * +, %- ( * %. ( %/* %0 * ( +, %. % +, % %0 ( 1 2 % ( %/ %+ ( ( %/ ( %/ ( ( 1 ( ( ( % "# 344%%4 253333 #6#787 /0.' 9'# 86' 8" /0.' 9'# 86' (#"8'# Analyticity, Necessity and Belief Aspects of two-dimensional semantics Eric Johannesson c Eric Johannesson, Stockholm 2017 ISBN print 978-91-7649-776-0 ISBN PDF 978-91-7649-777-7 Printed by Universitetsservice US-AB, Stockholm 2017 Distributor: Department of Philosophy, Stockholm University Cover photo: the water at Petite Terre, Guadeloupe 2016 Contents Acknowledgments v 1 Introduction 1 2 Modal logic 7 2.1Introduction.......................... 7 2.2Basicmodallogic....................... 13 2.3Non-denotingterms..................... 21 2.4Chaptersummary...................... 23 3 Two-dimensionalism 25 3.1Introduction.......................... 25 3.2Basictemporallogic..................... 27 3.3 Adding the now operator.................. 29 3.4Addingtheactualityoperator................ 32 3.5 Descriptivism ......................... 34 3.6Theanalytic/syntheticdistinction............. 40 3.7 Descriptivist 2D-semantics .................. 42 3.8 Causal descriptivism ..................... 49 3.9Meta-semantictwo-dimensionalism............. 50 3.10Epistemictwo-dimensionalism................ 54 -
Philosophy of Language in the Twentieth Century Jason Stanley Rutgers University
Philosophy of Language in the Twentieth Century Jason Stanley Rutgers University In the Twentieth Century, Logic and Philosophy of Language are two of the few areas of philosophy in which philosophers made indisputable progress. For example, even now many of the foremost living ethicists present their theories as somewhat more explicit versions of the ideas of Kant, Mill, or Aristotle. In contrast, it would be patently absurd for a contemporary philosopher of language or logician to think of herself as working in the shadow of any figure who died before the Twentieth Century began. Advances in these disciplines make even the most unaccomplished of its practitioners vastly more sophisticated than Kant. There were previous periods in which the problems of language and logic were studied extensively (e.g. the medieval period). But from the perspective of the progress made in the last 120 years, previous work is at most a source of interesting data or occasional insight. All systematic theorizing about content that meets contemporary standards of rigor has been done subsequently. The advances Philosophy of Language has made in the Twentieth Century are of course the result of the remarkable progress made in logic. Few other philosophical disciplines gained as much from the developments in logic as the Philosophy of Language. In the course of presenting the first formal system in the Begriffsscrift , Gottlob Frege developed a formal language. Subsequently, logicians provided rigorous semantics for formal languages, in order to define truth in a model, and thereby characterize logical consequence. Such rigor was required in order to enable logicians to carry out semantic proofs about formal systems in a formal system, thereby providing semantics with the same benefits as increased formalization had provided for other branches of mathematics. -
A Bibliography on Event Semantics and Related Matters
A Bibliography on Event Semantics and Related Matters Events: Modification, Aspect and Lexical Meaning Cleo Condoravdi and Hana Filip LSA Institute Stanford July, 2007 References [1] Abusch, Dorit. 1985. On Verbs and Time. Doctoral dissertation, University of Massachusetts at Amherst. [2] Abusch, Dorit. 1986. Verbs of Change, Causation, and Time. Technical Report CSLI-86-50, Center for the Study of Language and Information, Stanford University. [3] Abusch, Dorit. 2005. Causatives and Mixed Aspectual Type. In Gregory N. Carlson and Francis J. Pelletier, eds., 29–61. [4] Abusch, Dorit and Mats Rooth. 1990. Temporal Adverbs and the English Perfect. NELS 20, 1–15. [5] Alexiadou Artemis, Monika Rathert and Arnim von Stechow (eds.). 2003. Perfect Explorations. Berlin: Mouton de Gruyter. [6] Allen, James. 1983. Maintaining Knowledge about Temporal Intervals. CACM 26, 832–843. [7] Allen, James. 1984. Towards a General Theory of Action and Time. Arti- ficial Intelligence 23, 123–154. [8] Arregui, Ana. To appear. When aspect matters: the case of would- conditionals. Natural Language Semantics. [9] Artstein, Ron. 2006. Quantificational Arguments in Temporal Adjunct Clauses. Linguistics and Philosophy 28, 541–597. 1 [10] Asher, Nicholas. 1992. A Default, Truth Conditional Semantics for the Progressive. Linguistics and Philosophy 15, 463–508. [11] Asher, Nicholas. 1993. Reference to Abstract Objects in Discourse. Dor- drecht: Kluwer Academic Publishers. [12] Asher, Nicholas and Pierre Sablayrolles. 1995. A Typology and Discourse Semantics for Motion verbs and Spatial PPs in French. Journal of Seman- tics 12, 163–209. [13] Bach, Emmon. 1981. On Time, Tense, and Aspect: An Essay in English Metaphysics. In Peter Cole, ed., Radical Pragmatics, 63–81. -
Wittgenstein and Embodied Cognition: a Critique of the Language of Thought Amber Sheldon University of San Diego, [email protected]
University of San Diego Digital USD Keck Undergraduate Humanities Research Fellows Humanities Center Spring 2019 Wittgenstein and Embodied Cognition: A Critique of the Language of Thought Amber Sheldon University of San Diego, [email protected] Follow this and additional works at: https://digital.sandiego.edu/hc-keck Part of the Other Philosophy Commons, Philosophy of Language Commons, and the Philosophy of Mind Commons Digital USD Citation Sheldon, Amber, "Wittgenstein and Embodied Cognition: A Critique of the Language of Thought" (2019). Keck Undergraduate Humanities Research Fellows. 2. https://digital.sandiego.edu/hc-keck/2 This Working Paper is brought to you for free and open access by the Humanities Center at Digital USD. It has been accepted for inclusion in Keck Undergraduate Humanities Research Fellows by an authorized administrator of Digital USD. For more information, please contact [email protected]. Sheldon Fall 2018 Wittgenstein and Embodied Cognition: A Critique of the Language of Thought Amber Sheldon University of San Diego, 2018 1 Sheldon Fall 2018 Wittgenstein and Embodied Cognition: A Critique of the Language of Thought Amber Sheldon University of San Diego, 2018 Introduction The “computer metaphor” views the content of the mind as being akin to software. Our brains are coded using abstract symbols to represent concepts and semantic rules.1 Such models for understanding the relation between mind and body have been popular among cognitive scientists and philosophers.2 Computational Functionalism views the mind/brain like a computer that works according to a system of symbolic inputs and corresponding outputs. The framework of these computational mental representations is the “language of thought.”3 This symbolic mental language is often analogized with the symbolic “language” of a computer. -
The Logic of Sense and Reference
The Logic of Sense and Reference Reinhard Muskens Tilburg Center for Logic and Philosophy of Science (TiLPS) Days 4 and 5 Reinhard Muskens (TiLPS) The Logic of Sense and Reference Days 4 and 5 1 / 56 Overview 1 Introduction 2 Types and Terms 3 Models 4 Proofs 5 Model Theory 6 Applications 7 Worlds 8 Conclusion Reinhard Muskens (TiLPS) The Logic of Sense and Reference Days 4 and 5 2 / 56 Introduction Intensional Models for the Theory of Types When we looked at Thomason's work, we saw that it is possible to work with propositions as primitive entities within the framework of classical type theory. Today and tomorrow we'll develop an alternative. We will generalize standard type theory so that a sense-reference distinction becomes available. We shall give up the Axiom of Extensionality. And we shall generalize the `general models' of Henkin (1950) in order to make our models match the weaker logic. Many desired notions will become available in the generalized logic and logical omniscience problems will disappear. See Muskens (2007) for references and technical details. Reinhard Muskens (TiLPS) The Logic of Sense and Reference Days 4 and 5 3 / 56 Introduction Intensionality and Extensionality Whitehead and Russell (1913) call a propositional function of propositional functions F extensional if, in modern notation: 8XY (8~x(X~x $ Y ~x) ! (FX ! FY )). (This is slightly generalized to the case where X and Y take an arbitrary finite number of arguments, not just one.) In a relational version of type theory (Orey 1959; Sch¨utte1960) the formula above defines the extensionality of relations of relations. -
Seth Cable Formal Semantics Spring 2018 Ling 620 1 the Basics Of
Seth Cable Formal Semantics Spring 2018 Ling 620 The Basics of Intensional Semantics, Part 1: The Motivation for Intensions and How to Formalize Them 1 1. The Inadequacies of a Purely Extensional Semantics (1) Extensional Semantics a. The interpretation function “[[ ]]” is (always) a function from natural language expressions to their extensions in the (actual) world. b. The extension of a complex phrase is (always) derived by computing the extensions (and only the extensions) of its component parts. In LING 610, you saw that – amazingly – an extensional semantics is sufficient for a semantic theory of many natural language structures… …However, it won’t be enough for all natural language… (2) Negative Consequence: No ‘Counterfactual’ Language a. The Consequence: In an extensional semantics, all predicates are of type <et>, <eet>, etc.. Thus, all sentences will be T or F depending only upon properties and relations that hold in the actual world. • [[ golfs ]] = [λx : x golfs] = yields T iff x golfs (in the actual world) • [[ Seth golfs ]] = T iff Seth golfs (in the actual world) b. The Empirical Problem: There are sentences of natural language whose truth or falsity depends on properties or relations holding in (purely) hypothetical worlds. (i) Vincent might golf. (ii) Rajesh believes that Seth golfs. (iii) If Rajesh golfed, then Seth wouldn’t be alone. Nothing in our purely extensional ‘semantic toolkit’ seems like it will provide a decent analysis of these kinds of structures. 1 These notes are based upon Heim & Kratzer (1998; Chapter 12) and von Fintel & Heim (2011; Chapter 1). 1 Seth Cable Formal Semantics Spring 2018 Ling 620 (3) Negative Consequence: Arguments are Always Extensions a. -
The Logica Yearbook
- -- - - -- - the logica yearbook 2006 - -- - - - --- the logica yearbook -- - 2006 Are concepts a priori? 1 2 Materna Are concepts a priori? 3 the logica yearbook 2006 4 Materna Are concepts a priori? 5 THE LOGICA YEARBOOK 2006 Edited by Ondřej Tomala and Radek Honzík FILOSOFIA Prague 2019 6 Materna Publication of the Logica Yearbook 2006 as well as the organisation of the Logica 2006 conference was supported by grant no. 401/04/0117 of the Grant Agency of the Czech Republic. Published by , 2007 Institute of Philosophy Academy of Sciences of the Czech Republic, Prague Edited by Ondřej Tomala and Radek Honzík Design and typesetting by Martin Pokorný Cover © Marta Bílková Copyright of the papers held by the individual authors, unless otherwise noted Printed by PB tisk Příbram, Czech Republic ISBN 978-80-7007-254-7 (print book) ISBN 978-80-7007-582-1 (e-book) DOI 10.47376/filosofia.2007.1 Are concepts a priori? 7 TABLE OF CONTENTS A PREFACE .................................................... 9 Francesco Belardinelli COUNTERPART SEMANTICS FOR QUANTIFIED MODAL LOGIC ............... 11 Alexandre Costa-Leite COMBINING MODAL CONCEPTS: PHILOSOPHICAL APPLICATIONS ............. 23 Marie Duží THE USE-MENTION DISTINCTION .................................... 33 Antonín Dvořák and Vilém Novák FUZZY TYPE THEORY AS A TOOL FOR LINGUISTIC ANALYSIS ................ 51 María J. Frápolli WHAT IS A LOGICAL CONSTANT? THE INFERENCE-MARKER VIEW ............ 63 Brian Hill “REALISTIC” BELIEF DYNAMICS ..................................... 77 Bjørn Jespersen SIX WAYS OF KNOWING WHETHER .................................. 93 John T. Kearns RECAPTURING THE EPISTEMIC DIMENSION OF LOGIC ..................... 105 Katarzyna Kijania-Placek ON CIRCULAR ACCEPTANCE ....................................... 117 Vojtěch Kolman LOGICISM AND THE RECURSION THEOREM ............................. 127 Arnold Koslow A TALE OF twO SCHEMATA: TARSKIAN (FINITARY) TRUTH AND RAMSEYAN MENTAL STATES ...................................