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Linguistics and Natural Logic

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Part of the book series: Synthese Library ((SYLI,volume 40))

Abstract

Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a ‘natural logic’, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed.

This work was partially supported by grant GS-2939 from the National Science Foundation to The University of Michigan. This work is the result of lengthy and informative conversations with the following persons: Lee Bowie, Wallace Chafe, Charles Fillmore, Georgia Green, Gilbert Harman, Lawrence Horn, Robin Lakoff, James D. McCawley, Jerry Morgan, Paul Neubauer, Paul Postal, Peter Railton, John R. Ross, John Tinnon and Bas Van Fraassen. In addition, I have relied heavily on observations of C. Leroy Baker and Lauri Karttunen. They are in no way responsible for any mistakes I may have made.

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Bibliography

  • Lennart Åqvist, A New Approach to the Logical Theory of Interrogatives, Part I: Analysis, Uppsala 1965.

    Google Scholar 

  • Emmon Bach and Robert T. Harms (eds.), Universals in Linguistic Theory, Holt, Rinehart and Winston, New York 1968.

    Google Scholar 

  • C. Leroy Baker, ‘Definiteness and Indefiniteness in English’, University of Illinois master’s thesis, 1966.

    Google Scholar 

  • C. Leroy Baker, Indirect Questions in English, University of Illinois doctoral dissertation, 1968.

    Google Scholar 

  • C. Leroy Baker, ‘Double Negatives’, Linguistic Inquiry (1970).

    Google Scholar 

  • C. Leroy Baker, ‘Notes on the Description of English Questions: The Role of an Abstract Question Morpheme’, 1970b, in Foundations of Language.

    Google Scholar 

  • Nuel Belnap, ‘An Analysis of Questions’, TM-1287/000/000, Systems Development Corporation, 1957.

    Google Scholar 

  • Robert Binnick, Studies in the Derivation of Predicative Structures, University of Chicago Dissertation, 1969.

    Google Scholar 

  • Guy Carden, ‘English Quantifiers’, Harvard master’s thesis, 1968.

    Google Scholar 

  • Guy Carden, Idiolect Variation and Logical Predicates in English, Harvard doctoral dissertation, 1970a.

    Google Scholar 

  • Guy Carden, ‘A Note on Conflicting Idiolects’, Linguistic Inquiry (1970b).

    Google Scholar 

  • Brian Chellas, The Logical Form of Imperatives, Stanford doctoral dissertation, Perry Lane Press, 1969.

    Google Scholar 

  • Noam Chomsky, Syntactic Structures, Mouton, The Hague, 1957.

    Google Scholar 

  • Noam Chomsky, ‘Current Issues in Linguistic Theory’, in The Structure of Language (ed. by Jerry A. Fodor and Jerrold J. Katz), Prentice-Hall, Englewood Cliffs, N.J., 1964.

    Google Scholar 

  • Östen Dahl, ‘Some Notes on Indefinites’, Language, 1970.

    Google Scholar 

  • Donald Davidson, The Logical Form of Action Sentences’ in The Logic of Decision and Action (ed. by Nicholas Rescher), University of Pittsburgh Press, Pittsburgh, Pennsylvania, 1966.

    Google Scholar 

  • Charles Fillmore, ‘Verbs of Judging: An Exercise in Semantic Description’, Papers in Linguistics (1969).

    Google Scholar 

  • Charles Fillmore, ‘Types of Lexical Information’ to appear in Semantics: An Interdisciplinary Reader in Philosophy, Linguistics, Anthropology and Psychology (ed. by Leon Jakobovits and Danny Steinberg), Cambridge University Press, Cambridge.

    Google Scholar 

  • Jerry A. Fodor and Jerrold J. Katz (eds.), The Structure of Language, Prentice-Hall, Englewood Cliffs, N.J., 1964.

    Google Scholar 

  • H. P. Grice, The Logic of Conversation, Berkeley mimeo, 1968.

    Google Scholar 

  • Morris Halle, The Sound Pattern of Russian, Mouton, The Hague 1959.

    Google Scholar 

  • Jaakko Hintikka, Knowledge and Belief, Cornell University Press, Ithaca, N.Y., 1962.

    Google Scholar 

  • Laurence Horn, ‘A Presuppositional Analysis of “Only” and “Even”’in Papers from the Fifth Regional Meeting of the Chicago Linguistic Society, University of Chicago Press, Chicago, Ill., 1969.

    Google Scholar 

  • Laurence Horn, ‘Ain’t It Hard Anymore?’ in Papers from the Sixth Regional Meeting of the Chicago Linguistic Society, University of Chicago Press, Chicago, Ill., 1970.

    Google Scholar 

  • Laurence Horn, Studies in the Semantics of Negation, U.C.L.A. doctoral dissertation, in preparation.

    Google Scholar 

  • G. E. Hughes and M. J. Cresswell, An Introduction to Modal Logic, Methuen, 1968.

    Google Scholar 

  • Richard Jeffrey, Formal Logic, McGraw-Hill, New York 1967.

    Google Scholar 

  • David Kaplan, ‘Quantifying In’, Synthese 19 (1968–69).

    Google Scholar 

  • Lauri Karttunen, ‘Problems of Reference in Syntax’, University of Texas mimeograph, 1969.

    Google Scholar 

  • Edward Keenan, A Logical Base for English, University of Pennsylvania doctoral dissertation, 1969.

    Google Scholar 

  • Edward L. Keenan, ‘Names, Quantifiers, and a Solution to the Sloppy Identity Problem’, University of Pennsylvania, Unpublished, 1970.

    Google Scholar 

  • Edward L. Keenan, ‘Quantifier Structures in English’, to appear in Foundations of Language.

    Google Scholar 

  • Saul Kripke, ‘Semantical Considerations on Modal Logic’, Acta Philosophica Fennica 16 (1963).

    Google Scholar 

  • George Lakoff, On the Nature of Syntactic Irregularity, Report NSF-16, Harvard University Computation Laboratory, 1965; reprinted as Irregularity in Syntax, Holt, Rinehart and Winston, New York 1970.

    Google Scholar 

  • George Lakoff, ‘Some Verbs of Causation and Change’ in Report NSF-20, 1968.

    Google Scholar 

  • George Lakoff, ‘Presuppositions and Relative Grammatically’ in Philosophical Linguistics, Series I (ed. by William Todd), Great Expectations, Evanston, Ill., 1969.

    Google Scholar 

  • George Lakoff, ‘Repartee’, Foundations of Language (1970).

    Google Scholar 

  • George Lakoff, ‘On Generative Semantics’ in Semantics: An Interdisciplinary Reader in Philosophy, Linguistics, Anthropology and Psychology (ed. by Leon Jakobovits and Danny Steinberg), Cambridge University Press, Cambridge, in press.

    Google Scholar 

  • George Lakoff, Generative Semantics, Holt, Rinehart and Winston, New York, in preparation.

    Google Scholar 

  • George Lakoff, ‘Some Thoughts on Transderivational Constraints’, to appear.

    Google Scholar 

  • George Lakoff and Peter Railton, ‘Some Types of Presupposition and Entailment in Natural Language’, University of Michigan mimeo, 1970.

    Google Scholar 

  • Robin Lakoff, Abstract Syntax and Latin Complementation, M.I.T. Press, Cambridge, Mass., 1968.

    Google Scholar 

  • Robin Lakoff, ‘A Syntactic Argument for Not-Transportation’ in Papers from the Fifth Regional Meeting of the Chicago Linguistic Society, University of Chicago Press, Chicago, Ill., 1969.

    Google Scholar 

  • Karel Lambert, ‘Notes on E!III: A Theory of Descriptions’, Philosophical Studies (1962).

    Google Scholar 

  • Karel Lambert, The Logical Way of Doing Things, Yale University Press, New Haven, Conn., 1969.

    Google Scholar 

  • Ronald Langacker, ‘An Analysis of Questions’, U.C.S.D. mimeograph, 1969.

    Google Scholar 

  • E. J. Lemmon, ‘Deontic Logic and the Logic of Imperatives’, Logique et analyse 29 (1965).

    Google Scholar 

  • E. J. Lemmon and Dana Scott, Intensional Logic (preliminary draft of initial chapters by E. J. Lemmon), Stanford mimeograph, 1966.

    Google Scholar 

  • David Lewis, ‘General Semantics’, this volume, p. 169.

    Google Scholar 

  • David Lewis, ‘Counterpart Theory and Quantified Modal Logic’, Journal of Philosophy (1968).

    Google Scholar 

  • Gerald J. Massey, Understanding Symbolic Logic, Harper and Row, 1969.

    Google Scholar 

  • James D. McCawley, ‘The Role of Semantics in a Grammar’ in Universals in Linguistic Theory (ed. by Emmon Bach and Robert T. Harms), Holt, Rinehart and Winston, New York 1968.

    Google Scholar 

  • James D. McCawley, ‘Lexical Insertion in a Transformational Grammar without Deep Structure’ in Papers from the Fourth Regional Meeting of the Chicago Linguistic Society, University of Chicago Press, Chicago, Ill., 1968a.

    Google Scholar 

  • James D. McCawley, ‘Meaning and the Description of Languages’, Kotoba no Uchii 1968b.

    Google Scholar 

  • James D. McCawley, ‘Semantic Representations’, to appear in Cognition: A Multiple View (ed. by Paul Garvin), Spartan Books, New York.

    Google Scholar 

  • James D. McCawley, 1972 ‘A Program for Logic’, this volume, p. 498.

    Google Scholar 

  • Richard Montague, ‘Pragmatics and Intensional Logic’, U.C.L.A. mimeograph, 1967.

    Google Scholar 

  • Richard Montague, ‘English as a Formal Language I’, U.C.L.A. mimeograph, 1968.

    Google Scholar 

  • Jerry Morgan, ‘On the Treatment of Presupposition in Transformational Grammar’ in Papers from the Fifth Regional Meeting of the Chicago Linguistic Society, University of Chicago Press, Chicago, Ill., 1969.

    Google Scholar 

  • Jerry Morgan, ‘On the Derivation of If-Clauses’, University of Michigan mimeograph, 1970.

    Google Scholar 

  • Jerry Morgan, Presuppositional Structure, University of Chicago doctoral dissertation, in preparation.

    Google Scholar 

  • Terence D. Parsons, A Semantics for English, University of Illinois at Chicago Circle mimeograph, 1968.

    Google Scholar 

  • Paul Postal, ‘The Surface Verb “Remind”’, Linguistic Inquiry (1970).

    Google Scholar 

  • A. N. Prior, Time and Modality, Oxford University Press, Oxford 1957.

    Google Scholar 

  • A. N. Prior, Past, Present, and Future, Oxford 1967.

    Google Scholar 

  • A. N. Prior, Time and Tense, Oxford 1968.

    Google Scholar 

  • W. V. Quine, Word and Object, M.I.T. Press, Cambridge, Mass., 1960.

    Google Scholar 

  • W. V. Quine, Ontological Relativity, Columbia University Press, New York 1969.

    Google Scholar 

  • Hans Reichenbach, Elements of Symbolic Logic, Macmillan, New York 1947.

    Google Scholar 

  • Nicholas Rescher, The Logic of Commands, Dover, 1966.

    Google Scholar 

  • John R. Ross, Constraints on Variables in Syntax, M.I.T. doctoral dissertation, 1967.

    Google Scholar 

  • John R. Ross, ‘On Declarative Sentences’ in Readings in English Transformational Grammar (ed. by Roderick Jacobs and Peter S. Rosenbaum), Blaisdell, Boston, 1970.

    Google Scholar 

  • Dana Scott, ‘The Logic of Tenses’, Stanford mimeograph, December 1965.

    Google Scholar 

  • Dana Scott, ‘An Outline for Quantified Intensional Logic’, Stanford mimeograph, June 1967.

    Google Scholar 

  • Dana Scott, ‘Advice on Modal Logic’, Stanford dittograph, in Philosophical Problems in Logic: Some Recent Developments (ed. by Karel Lambert), Reidel, Dordrecht, 1970.

    Google Scholar 

  • Dana Scott, ‘Formalizing Intensional Notions’, Stanford mimeograph, 1968.

    Google Scholar 

  • Robert Stalnaker, ‘Pragmatics’, this volume, p. 380.

    Google Scholar 

  • P. F. Strawson, Introduction to Logical Theory, Methuen, 1952.

    Google Scholar 

  • John Tinnon, ‘A Minimal System of Modal Logic’, in preparation.

    Google Scholar 

  • William Todd (ed.), Philosophical Linguistics, Series I, Great Expectations, Evanston, Ill., 1969.

    Google Scholar 

  • G. H. von Wright, Logical Studies, Routledge and Ketan Paul, London 1957.

    Google Scholar 

  • G. H. von Wright, Norm and Action, Routledge and Kegan Paul, London 1963.

    Google Scholar 

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© 1972 D. Reidel Publishing Company, Dordrecht-Holland

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Lakoff, G. (1972). Linguistics and Natural Logic. In: Davidson, D., Harman, G. (eds) Semantics of Natural Language. Synthese Library, vol 40. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2557-7_19

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  • DOI: https://doi.org/10.1007/978-94-010-2557-7_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-0310-1

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