1、The Logic of Language Language From Within In this ambitious two-volume work, Pieter Seuren seeks a theoretical unity that can bridge the chasms of modern linguistics as he sees them, bringing togetherthelogical,thepsychological,andthepragmatic;theempiricaland the theoretical; the formalist and the
2、empiricist; and situating it all in the context of two and a half millennia of language study. Volume I: Language in Cognition Volume II: The Logic of LanguageThis page intentionally left blank The Logic of Language PIETERA.M.SEUREN 13 Great Clarendon Street, Oxford OX26 DP Oxford University Press i
3、s a department of the University of Oxford. It furthers the Universitys objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai T
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5、s Published in the United States by Oxford University Press Inc., New York # Pieter A. M. Seuren 2010 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2010 All rights reserved. No part of this publication may be reproduced, stored in a
6、retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of th
7、e above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cata
8、loging in Publication Data Data available Typeset by SPI Publisher Services, Pondicherry, India Printed in Great Britain on acid-free paper by CPI Antony Rowe, Chippenham, Wiltshire ISBN 9780199559480 135791 08642to Pim Levelt for his unfailing support, advice and friendshipThis page intentionally l
9、eft blank Contents Preface xii Abbreviations and symbols xiv 1 Logic and entailment 1 1.1 What is a logic and why do we need one in the study of language? 1 1.2 The denition of entailment 7 1.2.1 The general concept of entailment 7 1.2.2 The specic concept of logical entailment 10 1.3 The referentia
10、l independence of logic: no truth-value gaps 13 1.4 Logical form and L-propositions 16 1.5 The Bivalence Principle, sentence types, and utterance tokens 17 1.6 Some problems with the assignment of truth values 22 2 Logic: a new beginning 27 2.1 Entailment, contrariety and contradiction: the natural
11、triangle 27 2.2 Internal negation and duality: the natural square and the Boethian square 31 2.3 Logical operators as predicates 37 2.3.1 Meaning postulates 40 2.3.2 Boolean algebra and the operators of propositional calculus 43 2.3.3 Valuation space modelling: a formal denition 46 2.3.4 Satisfactio
12、n conditions of the propositional operators 50 2.3.5 Satisfaction conditions of the quantiers 52 2.3.5.1 Russellian quantiers 52 2.3.5.2 Generalized quantiers 54 2.4 Internal negation, the Conversions and De Morgans laws 59 2.4.1 The internal negation again 59 2.4.2 The Conversions and De Morgans la
13、ws 63 3 Natural set theory and natural logic 67 3.1 Introductory observations 67 3.2 Some set-theoretic principles of natural cognition 713.2.1 Are sume of standard set theory 71 3.2.2 The restrictions imposed by NST 74 3.3 Consequences for set-theoretic and (meta)logical relations and functions 79
14、3.3.1 Consequences for set-theoretic relations and functions 79 3.3.2 Consequences for (meta)logical relations and functions 84 3.4 The basic-natural systems of logic 88 3.4.1 Basic-natural predicate logic: the necessity of a cognitive base 89 3.4.2 Hamiltons predicate logic 103 3.4.3 Basic-natural
15、propositional logic 108 3.5 Neither *nand nor *nall: NST predicts their absence 114 3.5.1 The problem and the solution proposed by pragmaticists 114 3.5.2 Preliminary objections 116 3.5.3 The main objection and a stronger solution 117 3.5.4 Parallel lexical gaps in epistemic-modal and causal logic?
16、119 4 Logical power, Abelard, and empirical success rates 122 4.1 Aristotelian predicate calculus rescued from undue existential import 122 4.2 The notion of logical power 127 4.2.1 The logical power of propositional calculus 129 4.2.2 The logical power of Aristotelian-Boethian predicate calculus 13
17、2 4.2.3 The logical power of standard modern predicate calculus 133 4.2.4 The logical power of Aristotelian-Abelardian predicate calculus 136 4.3 Distributive quantiers 138 4.4 Predicate logics and intuitions: a scale of empirical success 144 5 Aristotle, the commentators, and Abelard 147 5.1 A reca
18、pitulation of ABPC 147 5.2 The not quite Aristotelian roots of ABPC 149 5.2.1 Aristotles own predicate logic 149 5.2.2 The ancient commentators 155 5.2.3 The Square representation 156 viii Contents5.2.4 An aside on Horns and Parsons proposal as regards theO-corner 158 5.2.5 Logic and mysticism: what
19、 made logic popular? 170 5.3 Abelards remedy 172 6 The functionality of the Square and of BNPC 181 6.1 How to isolate the cases with a null F-class: the purpose of space 4 181 6.2 Extreme values are uninformative in standard modern predicate calculus 183 6.3 The functionality of excluding extreme va
20、lues 184 6.4 The functionality of BNPC 190 6.5 Conclusion 193 7 The context-sensitivity of speech and language 194 7.1 What is context-sensitivity? 194 7.2 Discourse domains 196 7.2.1 The commitment domain and further subdomains 199 7.2.1.1 The notion of subdomain 199 7.2.1.2 Extensional and intensi
21、onal subdomains 201 7.2.1.3 The epistemic modal subdomains 203 7.2.2 The Principle of Maximal Unity 207 7.2.2.1 Transdominial denotational transparency 207 7.2.2.2 Upward presupposition projection 209 7.2.2.3 Subdomain unication: transdominial consistency 212 7.2.2.4 Minimal D-change 214 7.3 Conditi
22、ons for text coherence 215 7.3.1 Consistency 215 7.3.2 Informativity 217 7.3.3 Subdomain hierarchies: subsidiary subdomains 219 7.4 Open parameters in lexical meaning 222 8 Discourse incrementation 229 8.1 The incrementation procedure 229 8.1.1 Singular entity addresses and address closure 230 8.1.2
23、 Plurality and quantication 240 8.1.2.1 Plurality and existential quantication 240 8.1.2.2 Discourse-sensitive universal quantication 249 8.1.3 Subordinate subdomains 252 Contents ix8.2 Instructions 254 8.2.1 Conjunction 254 8.2.2 Negation 259 8.2.3 Disjunction 264 8.2.4 Conditionals 270 9 Primary a
24、nd donkey anaphora 284 9.1 Introduction 284 9.2 Reference by anaphora 288 9.3 Primary anaphora: bound variable or external anaphor? 293 9.4 Donkey sentences 294 9.4.1 The problem 294 9.4.2 The history of the problem 300 9.5 The reference-xing algorithm 304 9.6 The solution 307 9.6.1 Donkey anaphora
25、under disjunction 307 9.6.2 Donkey anaphora in conditionals 308 9.6.3 Donkey anaphora under universal quantication 309 10 Presupposition and presuppositional logic 311 10.1 Presupposition as an anchoring device 311 10.1.1 Some early history 312 10.1.2 The Russell tradition 317 10.1.3 The Frege-Straw
26、son tradition 321 10.2 The origin and classication of presuppositions 327 10.3 Operational criteria for the detection of presuppositions 331 10.4 Some data that were overlooked 334 10.5 Presupposition projection 342 10.5.1 What is presupposition projection? 342 10.5.2 Projection from lexical subdoma
27、ins 343 10.5.3 Projection from instructional subdomains 348 10.5.4 Summary of the projection mechanism 351 10.6 The presuppositional logic of the propositional operators 354 10.7 The presuppositional logic of quantication 363 10.7.1 The presuppositional version of the Square and of SMPC 363 x Conten
28、ts10.7.2 The presuppositional version of BNPC 368 10.7.3 The victorious Square 370 10.8 The attempt at equating anaphora with presupposition 372 11 Topiccomment modulation 378 11.1 What is topiccomment modulation? 378 11.1.1 The Aristotelian origin of topiccomment modulation 378 11.1.2 The discovery
29、 of the problem in the nineteenth century 380 11.1.3 The dynamics of discourse: the questionanswer game 386 11.2 Phonological, grammatical, and semantic evidence for TCM 391 11.3 The comment-predicate Be v 395 11.4 Only, even, and Neg-Raising 398 11.5 Why TCM is a semantic phenomenon: the SSV test 4
30、06 Bibliography 409 Index 421 Contents xiPreface Thisisthesecondandlastvolumeof LanguagefromWithin.Therstvolume dealt with general methodology in the studyof language (which is seen as an element in and product of human cognition), with the intrinsically inten- sional ontology that humans operate wi
31、thwhen thinking and speaking, with the socially committing nature of linguistic utterances, with the mechanisms involvedin theproductionandinterpretationofutterances,withthenotions of utterance meaning, sentence meaning, and lexical meaning, and, nally, withthedifcultiesencounteredwhenonetriestocapt
32、urelexicalmeaningsin denitional terms. The present volume looks more closely at the logic inher- ent in natural language and at the ways inwhich utterance interpretation has to fall back on the context of discourse and on general knowledge. It deals extensively with the natural semantics of the oper
33、ators that dene human logic, both in its presumed innate form and in the forms it has taken as a result of culturaldevelopment. And it does so in the context of the historyof logic, as it is assumed that this history mirrors the path followed in Western culture from primitive logical (and mathematic
34、al) thinking to the raried heights of perfection achieved in these areas of study over the past few centuries. The overall and ultimate purpose of the whole work is to lay the founda- tions for a general theory of language, which integrates language into its ecological setting of cognition and socie
35、ty, given the physical conditions of human brain structure and general physiology and the physics of sound productionandperception.Thisgeneraltheoryshouldeventually providean overall, maximally motivated, and maximally precise, even formal, interpre- tative framework for linguistic diversity, thus s
36、upporting typological studies with a more solid theoretical basis. The present work restricts itself tosemanticsand, toalesserextent, alsotogrammar,whicharemore directly dependent on cognition and society, leaving aside phonology, which appears to nd its motivational roots primarily in the physics a
37、nd the psychology of sound production and perception, as well as in the input phonological systems receive from grammar. The two volumes are not presented as a complete theory but rather as aprolegomenaand,atthesametime,asanactualstart,intheoverallandall- pervasive perspective of the cognitive and s
38、ocial embedding of languageaperspective that has been hesitantly present in modern language studies but has not so far been granted the central position it deserves. In this context, it has proved necessary, rst of all, to break open the far too rigid and too narrow restrictions and dogmas that have
39、 dominated the study of language over the past half-century, which has either put formal completeness above theconstraintsimposedbycognitionor,bywayofcontrast,rejectedanykind of formal treatment and has tried to reduce the whole of language to intui- tion-based folk psychology. The present, second,
40、volume is, regrettably but unavoidably, much more technicalthantherst,owingtotheintrinsicformalnatureofthetopicsdealt with. Avoiding technicalities would have reduced the book either to utter trivialityor toincomprehensibility,butIhavedonemybesttobegentlewith my readers, requiring no more than a bas
41、ic ability (and willingness) to read formulaic text and presupposing an elementary knowledge of logic and set theory. Again, as in the rst volume, I wish to express my gratitude to those who have helped me along with their encouragement and criticisms. And again, I must start by mentioning my friend
42、 of forty years standing Pim Levelt, to whom I have dedicated bothvolumes. He made it possible for me to work at the Max Planck Institute for Psycholinguistics at Nijmegen after my retire- mentfromNijmegenUniversityandwas aconstantsourceofinspiration not only on account of the thoughts he shared wit
43、h me but also because of his moral example. Then I must mention my friend and colleague Dany Jaspers of the University of Brussels, whose wide knowledge, well-formulated com- ments, and infectious enthusiasm were a constant source of inspiration. Ferdinando Cavaliere made many useful suggestions reg
44、arding predicate logic and its history. Finally, I want to thank Kyle Jasmin, whose combined kindnessandcomputersavvinesswereindispensabletogetthetextright.The manyothers whohavehelped mecarryonbygivingtheir intellectual,moral, andpersonalsupportaretoonumeroustobementionedindividually.Yetmy gratitud
45、e to them is none the less for that. Some, who will not be named, inspired me by their erce opposition, which forced me to be as keen as they were at nding holes in my armour. I hope I have found and repaired them all. P. A. M. S. Nijmegen, December 2008. Preface xiiiAbbreviations and symbols AAPC A
46、ristotelian-Abelardian predicate calculus ABPC Aristotelian-Boethian predicate calculus (=the Square of Opposition) BNPC basic-natural predicate calculus BNST basic-natural set theory fprop at proposition without TCM IP incrementation procedure modprop proposition with TCM M-partial mutually partial
47、 NPI negative polarity item NST natural set theory OSTA Optimization of sense, truth and actuality PEM Principle of the Excluded Middle PET Principle of the Excluded Third PNST principle of natural set theory PPI positive polarity item SA semantic analysis SMPC standard modern predicate calculus SNPC strict-natural predicate calculus (=ABPC) SNST strict-natural set theory SST standard (constructed) set theory SSV Substitution salva veritate TCM topiccomment modulation UEI undue existential import
