DOCSLIB.ORG

Abelard and Frege: the Semantics of Words and Propositions

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Abelard and Frege: the Semantics of Words and Propositions Sonderdrucke aus der Albert-Ludwigs-Universität Freiburg KLAUS JACOBI Abelard and Frege: The semantics of words and propositions Originalbeitrag erschienen in: Vito M. Abrusci (Hrsg.): Atti del Convegno Internazionale di Storia della Logica : San Gimignano, 4 - 8 dic. 1982. Bologna: Ed. CLUEB, 1983, S. [81] - 96 A 7TI dd Convr~noInlrrnazionulr di Boria drllo Lo~ic-U. Saii Giiriigiinno. 4-8 diicrnbrc 1982. (-'IIJFIt. tIoIog11a (llaly) C) 1983. ABELARD AND FREGE: THE SEMANTlCS OF WORDS AND PROPOSITIONS Klaus Jacobi Universiiic lluisburg, Ciesaniihochschulc. FB I - Fach Philosophic. Lotharstr. 65. 4100 Duibburg Petcr iibrlard was born in the year 1079 and djcd in 1142. Gottlob Frcge lived from 1848 to 1925. Frcgc's Begriffsschrift was published in 1879, eight hundred years after Abelard's birth. Historians of uhilosophy say that cach man marks the beginning of an epoch in the history of logic, and beyond that, that each left a deep imprint on thc coursc of further developments. It is wcll-known that Preqe felt himself isolated and deprived of due recognjtion. Fcw of his colleaques, whether from thc-mathe- matics or the philosophy dcpartmcnt, bothered to study his works. Surcly none of his contemporaries adjudqed Frege's works to be epoch-makina. Nor did F'regc havc students who continucd his in- vestigations. His impact began with Russeii, Wittgenstein, and Carnap. Although the threc diffcr widely in the style of thcir thinking and in the questions they pose, all claim Freqe as their true intellectual fathcr. Abelard, on the other hand, found cnthusiastic listeners wherever he lcctured. He was a famous man, such that the mention of his namc cvokcd either sreat admiration or bitter enmity. Nonetheless, thc substance of his success as a teacher is not casy to grasp. Abelard was not dcstined to found a ncw nhilo- sophical tradition, as Peter Lombard and latcr Thomas Aquinas and John Duns Scotus were. Abelard was never an "authority" in thc scnsc in which thc scholdstics used the word. His influence is less to be attributed to a sct of theses which he developed than to his distinctive manner of approaching questions. The historical transmission of his thcological and loqical works was weak, but his philosophically probinq, discussinq, and analyzinq attitude toward knowledgc camc to be reaarded as exemplary. Frege was not familiar with Abelard or any of the other scholastics. Thcre is no hjstorical connection between the two philosophers, be it direct or indirect. When I speak on Rbelard and Fregc hcre, the theme is selected with different intentions from thosc for a papcr on say Freqe and Leibniz. I intend to conduct a comparison in systematic perspective. This comparison cannot bc bascd on thc dcmonstration of an influence of Abelard on Preqe undiscovered until now or upon somc aqreeing or dis- senting reference to Abelard in Freqe's works. Thus I vould likc to provide you witha brief explanation of what motivated me to the comparison. First, I wish to makc clcar that in selectinu this theme I do not intend to Open a debate nn Progress or reqrcssion in phi.10- sophy or the field of logic. I am not goinq to have the two philosophcrs compete with each other. I am not going t-o measure the one against the other. Thus no attempt will be madc here to demonstrate that Abelard "anticipated" later insights of Frege or that Freqe "rediscovered" carlier insiqhts which Abelard had reached. In my lectures and writings on scholastic loqic, I am con- fronted with thc problem of translatinq the medieval technical terms into a modern vocabulary. One has no choicc herc but to cmploy words whi.ch have become technical terms in modcrn loqic theory thanks to Freqe and his successors. Now we are often warned of the dangcrs inherent in a translation of scholastic d.iscussions into modern synibolic lanquagc. But whercas onc can forego such translations or devclop a more appropriate syrnbolisni in the field of loqical Syntax, in scmantics and philosophy of logic onc cannot avoid the dangcr of misinterpretation by simply renouncing all translation. One docsn'l: nct very far without such terms as 'sense', 'refcrcncc', 'designation', and 'dcnomination'. In ordinary languagc, these terms have hroad semantic fields. Thcy are used in various senses which oftcn ovcrlap. In scholarly usage the mcaninqs of such terms arc defined more precisely, at the very minimum by coordinatin~them wiLh or scttinq thcm in opposition to other terms within thc theory nt hnnd. When one makcs use of them to translate scholastic terms, it is necessary to state plainly which scnse is considered appropriatc ror thc new context. A rcturn to the everyday usagc can hardly be satis- factory, for the philnsophical or scientific theorics within which these words havc become technical tcrnis must also be taken into consideration. I am myself better versed in thc scholastic scientia sermo- --cinalis khan in modern theorics of loqic. Occasionally, in reading Fregc or one of his succcssors, I try out translations into the tcrminoloqy of thc scholastic controversics in ordcr to sharpen my conception of thc problem under discussinn. In- evitably, I ask myselF if any similaritics between the modern trains OE thought and ccrtain positions in the scholastic con- troversies can be found, This is of Course just as much a matter of clarifying thc differences as of holdinq on to TO- inciding elemcnts. Abclard stands at the outset of the scholastic development in loqic, Frege at the outset of modern developments. Neither finds a finished terminology for his philosoylhical investiqa- tions laid at his disposal. He must develop such a terminology himsclf. In questions of semantics, Abelard could find more Support in the preparatory work of his predccessors than Freqe. Abelard worked on questions which had been dealt with hy Boethius, Priscian, grammarians of the time, and Abelard's own logic teachers. Yet his lanquage often impresses us as being awkward and forccd in comparison with the crystalline clarity and elcqant brevity of tiiqh sctiolnst i.c aiithors. On thc othcr hand, Ahclard is free of ttie Set scheniata of qucstioninq and thinking wiiich bccamc charactc:ristic of later sctiolastics. He discussed lincjuistic [ihenomena such as impersonal. construct i.ons whi ch arc lat.cr ncgl.cctcd bc:causc they arc sim~lynot accessible to ttie analytic iristrunients of the thcory of the sup~iosj.tio.Ire furthcrmorc considcred alternative approaches to sucti problems as the theory of predication, whereas later other authors dis- cusscd a conspiciously narrowcr spcctrum oF lihcorics. - The samc can gcncrally be said of Frcqc in comparison with say Carnap, to takc onc cxamplc. Frcgc Corcihly wrcsLcd his tcrmino- loqical distinctions, such as that between 'Sinn' and 'Weutung' , froin ttie languacyc, whcreas Carriap simply laid down such distinc- tions by definition. Freqe strained to dcvelo? adequate formu- 1.ations 01 new questions and to discover new intergretational t.cchniqucs. IIis successors rnerely took ttiern over. - Thus it sccms Lhat a comparison 01 Abelard and Freqe recommends itself as a starting point whcn onc wishes to undcrt-akc a comparison 01 scholastic and rriodern loc~ic. Howevcr, a comparison will be mcaningful only if thcrc is a manifest Consensus on relevant points. This also tiolds wtien Lhc objcct of the comy?arison is to point out the differences in the rcspccLivc positions. Or coursc, d i.sti nctions arc of valiic only when it is possible to mark out preciselv to wtiat extent the basis upon which the disLincLions havc bccn drawn is a common one. Thus the question presents itself whcther this fundamental prcrcquisitc For a comyiarison is fulfilled in our case. Well, in the Course of rny studies of Abelard with an cyc to parallels to Preqc and of Frcgc wiLh an eye to Abclard, I have swayed back and rort-h on how to answer ttiis r:uestion. Sornetimes I find a surprising dcgrce OE similarity in the way each approaches semantic questions, despite their quitc diffcrcnL sLartinq points - for Abclard thc scicniia scrmoncinal is as a Loqical analysis of the language of argumcnLaiion and scholarly in- vcstj.ga(iion, Tor Freqe the demonstration ttiat ttie axiorns of arithmetic acc of a purely lociical nature. At ottier times, I sccm to have deceived niyself: the aqreemcnt secms to be no more ttiari verbal - cach man uscs cxnressions which sound prac- tically alike to discuss cornpletcly diFFcrcnti mattcrs. To work my wav out of this con"usion, I have carefully noted what it is T pay attention to in eacti case. 1 would li.kc t-o take you alonq for a part of my scarch. In the cxccl,lcnt prcscnLati.on of Ircqc's work givcn by Willia~nKneale, onc finds thc following: "In thc ordinary use 01 languaqe for maklncj statements, asking yuestions, qiving orders, &C., ii is to bc assumed that every dist-inquishable complctc sign has both sense and reference. The reference is an object of some kind, but not nccessarily a perceptible object. ... Thc sense, on the ottier hand, is sorncthing by which the object may bc singlcd out for attention. It is not an idca, if by that we mean an imaqe or sorncthing private to an individual thinkcr. For all comniunication dcpends on thc exnression of sense by one man to another, and in spccial circumstances siys may have a public sense cvcn though they lack all reference." 84 KIA IJS JA CORI (The Development of Loqic, p. 496; cf. p. 578). The Passage could be taken word for word to characterize Abe- lard's semantics. Comparc: "Nomina ... et verba duplicem siqni- ficationem habent, unam cpidrm dc rcbus, altcram dc intcllccti- ,~us.Res enim significant constituendo intellectus ad eas per- tinentes, hoc est naturam aliquam earum vel proprietatem at- tendentes." (Super Peri crm., 307, 26-30; cf.
Load more

Recommended publications
  • Tractatus Logico-Philosophicus</Em>
    University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 8-6-2008 Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus Thomas J. Brommage Jr. University of South Florida Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the American Studies Commons Scholar Commons Citation Brommage, Thomas J. Jr., "Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus" (2008). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/149 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus by Thomas J. Brommage, Jr. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Philosophy College of Arts and Sciences University of South Florida Co-Major Professor: Kwasi Wiredu, B.Phil. Co-Major Professor: Stephen P. Turner, Ph.D. Charles B. Guignon, Ph.D. Richard N. Manning, J. D., Ph.D. Joanne B. Waugh, Ph.D. Date of Approval: August 6, 2008 Keywords: Wittgenstein, Tractatus Logico-Philosophicus, logical empiricism, resolute reading, metaphysics © Copyright 2008 , Thomas J. Brommage, Jr. Acknowledgments There are many people whom have helped me along the way. My most prominent debts include Ray Langely, Billy Joe Lucas, and Mary T. Clark, who trained me in philosophy at Manhattanville College; and also to Joanne Waugh, Stephen Turner, Kwasi Wiredu and Cahrles Guignon, all of whom have nurtured my love for the philosophy of language.
    [Show full text]
  • First Order Logic
    Artificial Intelligence CS 165A Mar 10, 2020 Instructor: Prof. Yu-Xiang Wang ® First Order Logic 1 Recap: KB Agents True sentences TELL Knowledge Base Domain specific content; facts ASK Inference engine Domain independent algorithms; can deduce new facts from the KB • Need a formal logic system to work • Need a data structure to represent known facts • Need an algorithm to answer ASK questions 2 Recap: syntax and semantics • Two components of a logic system • Syntax --- How to construct sentences – The symbols – The operators that connect symbols together – A precedence ordering • Semantics --- Rules the assignment of sentences to truth – For every possible worlds (or “models” in logic jargon) – The truth table is a semantics 3 Recap: Entailment Sentences Sentence ENTAILS Representation Semantics Semantics World Facts Fact FOLLOWS A is entailed by B, if A is true in all possiBle worlds consistent with B under the semantics. 4 Recap: Inference procedure • Inference procedure – Rules (algorithms) that we apply (often recursively) to derive truth from other truth. – Could be specific to a particular set of semantics, a particular realization of the world. • Soundness and completeness of an inference procedure – Soundness: All truth discovered are valid. – Completeness: All truth that are entailed can be discovered. 5 Recap: Propositional Logic • Syntax:Syntax – True, false, propositional symbols – ( ) , ¬ (not), Ù (and), Ú (or), Þ (implies), Û (equivalent) • Semantics: – Assigning values to the variables. Each row is a “model”. • Inference rules: – Modus Pronens etc. Most important: Resolution 6 Recap: Propositional logic agent • Representation: Conjunctive Normal Forms – Represent them in a data structure: a list, a heap, a tree? – Efficient TELL operation • Inference: Solve ASK question – Use “Resolution” only on CNFs is Sound and Complete.
    [Show full text]
  • 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.
    [Show full text]
  • Toward a Logic of Everyday Reasoning
    Toward a Logic of Everyday Reasoning Pei Wang Abstract: Logic should return its focus to valid reasoning in real-world situations. Since classical logic only covers valid reasoning in a highly idealized situation, there is a demand for a new logic for everyday reasoning that is based on more realistic assumptions, while still keeps the general, formal, and normative nature of logic. NAL (Non-Axiomatic Logic) is built for this purpose, which is based on the assumption that the reasoner has insufficient knowledge and resources with respect to the reasoning tasks to be carried out. In this situation, the notion of validity has to be re-established, and the grammar rules and inference rules of the logic need to be designed accordingly. Consequently, NAL has features very different from classical logic and other non-classical logics, and it provides a coherent solution to many problems in logic, artificial intelligence, and cognitive science. Keyword: non-classical logic, uncertainty, openness, relevance, validity 1 Logic and Everyday Reasoning 1.1 The historical changes of logic In a broad sense, the study of logic is concerned with the principles and forms of valid reasoning, inference, and argument in various situations. The first dominating paradigm in logic is Aristotle’s Syllogistic [Aristotle, 1882], now usually referred to as traditional logic. This study was carried by philosophers and logicians including Descartes, Locke, Leibniz, Kant, Boole, Peirce, Mill, and many others [Bochenski,´ 1970, Haack, 1978, Kneale and Kneale, 1962]. In this tra- dition, the focus of the study is to identify and to specify the forms of valid reasoning Pei Wang Department of Computer and Information Sciences, Temple University, Philadelphia, USA e-mail: [email protected] 1 2 Pei Wang in general, that is, the rules of logic should be applicable to all domains and situa- tions where reasoning happens, as “laws of thought”.
    [Show full text]
  • Real and Imaginary Parts of Decidability-Making Gilbert Giacomoni
    On the Origin of Abstraction : Real and Imaginary Parts of Decidability-Making Gilbert Giacomoni To cite this version: Gilbert Giacomoni. On the Origin of Abstraction : Real and Imaginary Parts of Decidability-Making. 11th World Congress of the International Federation of Scholarly Associations of Management (IF- SAM), Jun 2012, Limerick, Ireland. pp.145. hal-00750628 HAL Id: hal-00750628 https://hal-mines-paristech.archives-ouvertes.fr/hal-00750628 Submitted on 11 Nov 2012 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. On the Origin of Abstraction: Real and Imaginary Parts of Decidability-Making Gilbert Giacomoni Institut de Recherche en Gestion - Université Paris 12 (UPEC) 61 Avenue de Général de Gaulle 94010 Créteil [email protected] Centre de Gestion Scientifique – Chaire TMCI (FIMMM) - Mines ParisTech 60 Boulevard Saint-Michel 75006 Paris [email protected] Abstract: Firms seeking an original standpoint, in strategy or design, need to break with imitation and uniformity. They specifically attempt to understand the cognitive processes by which decision-makers manage to work, individually or collectively, through undecidable situations generated by equivalent possible choices and design innovatively. The behavioral tradition has largely anchored on Simon's early conception of bounded rationality, it is important to engage more explicitly cognitive approaches particularly ones that might link to the issue of identifying novel competitive positions.
    [Show full text]
  • Formalizing Common Sense Reasoning for Scalable Inconsistency-Robust Information Integration Using Direct Logictm Reasoning and the Actor Model
    Formalizing common sense reasoning for scalable inconsistency-robust information integration using Direct LogicTM Reasoning and the Actor Model Carl Hewitt. http://carlhewitt.info This paper is dedicated to Alonzo Church, Stanisław Jaśkowski, John McCarthy and Ludwig Wittgenstein. ABSTRACT People use common sense in their interactions with large software systems. This common sense needs to be formalized so that it can be used by computer systems. Unfortunately, previous formalizations have been inadequate. For example, because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic. Our goal is to develop a standard foundation for reasoning in large-scale Internet applications (including sense making for natural language) by addressing the following issues: inconsistency robustness, classical contrapositive inference bug, and direct argumentation. Inconsistency Robust Direct Logic is a minimal fix to Classical Logic without the rule of Classical Proof by Contradiction [i.e., (Ψ├ (¬))├¬Ψ], the addition of which transforms Inconsistency Robust Direct Logic into Classical Logic. Inconsistency Robust Direct Logic makes the following contributions over previous work: Direct Inference Direct Argumentation (argumentation directly expressed) Inconsistency-robust Natural Deduction that doesn’t require artifices such as indices (labels) on propositions or restrictions on reiteration Intuitive inferences hold including the following: . Propositional equivalences (except absorption) including Double Negation and De Morgan . -Elimination (Disjunctive Syllogism), i.e., ¬Φ, (ΦΨ)├T Ψ . Reasoning by disjunctive cases, i.e., (), (├T ), (├T Ω)├T Ω . Contrapositive for implication i.e., Ψ⇒ if and only if ¬⇒¬Ψ . Soundness, i.e., ├T ((├T) ⇒ ) . Inconsistency Robust Proof by Contradiction, i.e., ├T (Ψ⇒ (¬))⇒¬Ψ 1 A fundamental goal of Inconsistency Robust Direct Logic is to effectively reason about large amounts of pervasively inconsistent information using computer information systems.
    [Show full text]
  • How Peircean Was the “'Fregean' Revolution” in Logic?
    HOW PEIRCEAN WAS THE “‘FREGEAN’ REVOLUTION” IN LOGIC? Irving H. Anellis Peirce Edition, Institute for American Thought Indiana University – Purdue University at Indianapolis Indianapolis, IN, USA [email protected] Abstract. The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this conception are Jean van Heijenoort (1912–1986) and Don- ald Angus Gillies. The innovations and characteristics that comprise mathematical logic and distinguish it from Aristotelian logic, according to this conception, created ex nihlo by Gottlob Frege (1848–1925) in his Begriffsschrift of 1879, and with Bertrand Rus- sell (1872–1970) as its chief This position likewise understands the algebraic logic of Augustus De Morgan (1806–1871), George Boole (1815–1864), Charles Sanders Peirce (1838–1914), and Ernst Schröder (1841–1902) as belonging to the Aristotelian tradi- tion. The “Booleans” are understood, from this vantage point, to merely have rewritten Aristotelian syllogistic in algebraic guise. The most detailed listing and elaboration of Frege’s innovations, and the characteristics that distinguish mathematical logic from Aristotelian logic, were set forth by van Heijenoort. I consider each of the elements of van Heijenoort’s list and note the extent to which Peirce had also developed each of these aspects of logic. I also consider the extent to which Peirce and Frege were aware of, and may have influenced, one another’s logical writings. AMS (MOS) 2010 subject classifications: Primary: 03-03, 03A05, 03C05, 03C10, 03G27, 01A55; secondary: 03B05, 03B10, 03E30, 08A20; Key words and phrases: Peirce, abstract algebraic logic; propositional logic; first-order logic; quantifier elimina- tion, equational classes, relational systems §0.
    [Show full text]
  • Augmenting Mathematical Formulae for More Effective Querying & Efficient Presentation
    Augmenting Mathematical Formulae for More Effective Querying & Efficient Presentation vorgelegt von Diplom-Physiker Moritz Schubotz geb. in Offenbach am Main von der Fakult¨atIV { Elektrotechnik und Informatik der Technischen Universit¨atBerlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften { Dr. rer. nat. { genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr. Odej Kao Gutachter: Prof. Dr. Volker Markl Gutachter: Prof. Abdou Youssef, PhD Gutachter: Prof. James Pitman, PhD Tag der wissenschaftlichen Aussprache: 31. M¨arz2017 Berlin 2017 ii Abstract Mathematical Information Retrieval (MIR) is a research area that focuses on the Information Need (IN) of the Science, Technology, Engineering and Mathematics (STEM) domain. Unlike traditional Information Retrieval (IR) research, that extracts information from textual data sources, MIR takes mathematical formulae into account as well. This thesis makes three main contributions: 1. It analyses the strengths and weaknesses of current MIR systems and establishes a new MIR task for future evaluations; 2. Based on the analysis, it augments mathematical notation as a foundation for future MIR systems to better fit the IN from the STEM domain; and 3. It presents a solution on how large web publishers can efficiently present math- ematics to satisfy the INs of each individual visitor. With regard to evaluation of MIR systems, it analyses the first international MIR task and proposes the Math Wikipedia Task (WMC). In contrast to other tasks, which evaluate the overall performance of MIR systems based on an IN, that is described by a combination of textual keywords and formulae, WMC was designed to gain insights about the math-specific aspects of MIR systems. In addition to that, this thesis investigates how different factors of similarity measures for mathematical expressions influence the effectiveness of MIR results.
    [Show full text]
  • An Introduction to Prolog
    Appendix A An Introduction to Prolog A.1 A Short Background Prolog was designed in the 1970s by Alain Colmerauer and a team of researchers with the idea – new at that time – that it was possible to use logic to represent knowledge and to write programs. More precisely, Prolog uses a subset of predicate logic and draws its structure from theoretical works of earlier logicians such as Herbrand (1930) and Robinson (1965) on the automation of theorem proving. Prolog was originally intended for the writing of natural language processing applications. Because of its conciseness and simplicity, it became popular well beyond this domain and now has adepts in areas such as: • Formal logic and associated forms of programming • Reasoning modeling • Database programming • Planning, and so on. This chapter is a short review of Prolog. In-depth tutorials include: in English, Bratko (2012), Clocksin and Mellish (2003), Covington et al. (1997), and Sterling and Shapiro (1994); in French, Giannesini et al. (1985); and in German, Baumann (1991). Boizumault (1988, 1993) contain a didactical implementation of Prolog in Lisp. Prolog foundations rest on first-order logic. Apt (1997), Burke and Foxley (1996), Delahaye (1986), and Lloyd (1987) examine theoretical links between this part of logic and Prolog. Colmerauer started his work at the University of Montréal, and a first version of the language was implemented at the University of Marseilles in 1972. Colmerauer and Roussel (1996) tell the story of the birth of Prolog, including their try-and-fail experimentation to select tractable algorithms from the mass of results provided by research in logic.
    [Show full text]
  • Sense and Analysis − Studies in Frege
    Sense and Analysis − Studies in Frege Gilead Bar-Elli 1 Sense and Analysis − Studies in Frege Gilead Bar-Elli Contents: Introduction - i-v Synopsis - vi-ix Chapter 1: The Essentials of Frege's Logic - 1 The Formal Achievement of Begriffsschrift - 5; The Logical Notation of Begriffsschrift - 13; Some Later Developments - 16; Logic and Philosophy - 18 Chapter 2: Frege's Early Conception of Logic - 21 Reference and Inference - 22; Frege on the Deficiencies of Earlier Logical Systems - 25;Lingua Characterica and Calculus Ratiocinator - 30 Chapter 3: Sense and Objectivity in Frege's Logic - 34 Two Characterizations of Sense - 36; Sense and Justification - 40; Logical Objects - 42; Frege's Principle and Equivalence-Relations - 47; Digging into the Self-Evident - 50 Chapter 4: Identity in the Begriffsschrift - 55 The Main Point of the Identity Section (8) in Begriffsschrift and Its Relation to Ueber Sinn und Bedeutung - 56; The Identity Relation, and What Identity Statements Are About - 62; The Change in Ueber Sinn und Bedeutung - 67; The "Identity Puzzle", Cognitive Value and Conceptual Content - 68 Chapter 5: Logical Structure and Intentionality - Frege and Russell on Descriptions - 71 Descriptions and Terms Lacking Reference - 73; Meaning - 79; Logical Structure in Frege - 81; Definite Descriptions In Frege's Logic - 87; Logical Structure and Intentionality in Russell's Theory of Descriptions - 90; The Status of the About- relation - 91; The Object-directedness of Descriptive Propositions - 93; "Remote Intentionality" - 96; Intentionality
    [Show full text]
  • Expression and Symbol in Wittgenstein's Tractatus Logico
    Metalogicon (1990) III, 2 Expression and Symbol in Wittgenstein’s Tractatus Logico-philosophicus Francesco Ferrante The last proposition of Wittgenstein's Tractatus logico- philosophicus states, < Wherof one cannot speak, thereof one must be silent >1. The simplicity of the phrase hides a complex philosophical position: this is to be found in the tradiction of Frege's Thought 2 . It is possible to overlook the ontology of TLPh 3 , and to concentrate one's attention on the uses of terms expression and symbol in this work. Expressiveness is the kernel of tractarian philosophy, just as intentionality plays a basic role in the second period of Wittgenstein's Thought. The phenomenological problems that aroused the interest of the austrian philosopher ( in the period of 1 LUDWIG WITTGENSTEIN, Tractatus logico-philosophicus, Routledge & Keagan Paul, London 1922, prop.7. 2 See G. BAKER, Wittgenstein, Frege & the Vienna Circle, Basil Blackwell, 1988, chapters 1, 2, 3. 3 In TLPh 1 Wittgenstein says, < the world is everything that is the case >, and states in TLPh 5.621, < the world and life are one >. If one replaces "world" with "life" in TLPh 6.373 and 6.374, then one understands that < solipsism strictly carried out coincides with pure realism.. > ( TLPh 5.64 ). Regarding tractarian ontology see HINTIKKA-HINTIKKA, [ Investigating Wittgenstein ], Basil Blackwell, Oxford-New York 1986, chapters 2, 3. About solipsism see P.CARRUTHERS, The Methaphysics of Tractatus, Cambridge University Press, Cambridge 1990, chapter 8. 110 Metalogicon (1990) III, 2 transition, as Hintikka's analysis has showed ) 4 could only have been generated in a philosophical investigation, which presents some common attributs between expression and intentionality.
    [Show full text]
  • Ontologies on the Semantic Web1 Dr
    1 Annual Review of Information Science and Technology 41 (2007), pp. 407-452. Ontologies on the Semantic Web1 Dr. Catherine Legg, University of Waikato [email protected] 1. Introduction As an informational technology the World Wide Web has enjoyed spectacular success, in just ten years transforming the way information is produced, stored and shared in arenas as diverse as shopping, family photo albums and high-level academic research. The “Semantic Web” is touted by its developers as equally revolutionary, though it has not yet achieved anything like the Web’s exponential uptake. It seeks to transcend a current limitation of the Web – that it is of necessity largely indexed merely on specific character strings. Thus a person searching for information about ‘turkey’ (the bird), receives from current search engines many irrelevant pages about ‘Turkey’ (the country), and nothing about the Spanish ‘pavo’ even if they are a Spanish-speaker able to understand such pages. The Semantic Web vision is to develop technology by means of which one might index information via meanings not just spellings. For this to be possible, it is widely accepted that semantic web applications will have to draw on some kind of shared, structured, machine-readable, conceptual scheme. Thus there has been a convergence between the Semantic Web research community and an older tradition with roots in classical Artificial Intelligence research (sometimes referred to as ‘knowledge representation’) whose goal is to develop a formal ontology. A formal ontology is a machine-readable theory of the most fundamental concepts or ‘categories’ required in order to understand the meaning of any information, whatever the knowledge domain or what is being said about it.
    [Show full text]