Notre Dame Journal of Formal Logic

The Cognitive Ontogenesis of Predicate Logic

Pieter A. M. Seuren

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Since Aristotle and the Stoa, there has been a clash, worsened by modern predicate logic, between logically defined operator meanings and natural intuitions. Pragmatics has tried to neutralize the clash by an appeal to the Gricean conversational maxims. The present study argues that the pragmatic attempt has been unsuccessful. The “softness” of the Gricean explanation fails to do justice to the robustness of the intuitions concerned, leaving the relation between the principles evoked and the observed facts opaque. Moreover, there are cases where the Gricean maxims fail to apply. A more adequate solution consists in the devising of a sound natural logic, part of the innate cognitive equipment of mankind. This account has proved successful in conjunction with a postulated cognitive mechanism in virtue of which the universe of discourse (Un) is stepwise and recursively restricted, so that the negation selects different complements according to the degree of restrictedness of Un. This mechanism explains not only the discrepancies between natural logical intuitions and known logical systems; it also accounts for certain systematic lexicalization gaps in the languages of the world. Finally, it is shown how stepwise restriction of Un produces the ontogenesis of natural predicate logic, while at the same time resolving the intuitive clashes with established logical systems that the Gricean maxims sought to explain.

Article information

Notre Dame J. Formal Logic, Volume 55, Number 4 (2014), 499-532.

First available in Project Euclid: 7 November 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 00-22
Secondary: 03A99: None of the above, but in this section

Abelard Aristotle Boethius Hamilton natural logic ontogenesis of logic Russell undue existential import


Seuren, Pieter A. M. The Cognitive Ontogenesis of Predicate Logic. Notre Dame J. Formal Logic 55 (2014), no. 4, 499--532. doi:10.1215/00294527-2798718.

Export citation


  • [1] Blanché, R., “Sur l’opposition des concepts,” Theoria, vol. 19 (1953), pp. 89–130.
  • [2] Blanché, R., Structures intellectuelles: Essai sur l’organisation systématique des concepts, edited by J. Vrin, Librarie Philosophique, Paris, 1966.
  • [3] Grice, H. P., “Logic and conversation,” pp. 41–58 in Speech Acts, edited by P. Cole and J. L. Morgan, Academic Press, New York, 1975.
  • [4] Hamilton, W., “Lectures on metaphysics and logic, IV” in Lectures on Logic. Vol. II, edited by H. L. Mansel and J. Veitch, reprint of the 1886 edition, Michigan Historical Reprint Series, Scholarly Publishing Office, University of Michigan Library, Ann Arbor, 2005.
  • [5] Horn, L. R., A Natural History of Negation, University of Chicago Press, Chicago, 1989.
  • [6] Horn, L. R., “On the semantic properties of logical operators in English,” Ph.D. dissertation, University of California, Los Angeles, Los Angeles, Calif., 1972.
  • [7] Jacoby, P., “A triangle of opposites for types of propositions in Aristotelian logic,” The New Scholasticism, vol. 24 (1950), pp. 32–56.
  • [8] Jacoby, P., “Contrariety and the triangle of opposites in valid inferences,” The New Scholasticism, vol. 34 (1960), pp. 141–69.
  • [9] Jaspers, D., “Operators in the lexicon: On the negative logic of natural language,” Ph.D. thesis, Leiden University, LOT, Utrecht, Netherlands, 2005.
  • [10] Jespersen, O., Negation in English and Other Languages, vol. 1.5 of Det Kgl. Danske Videnskabernes Selskab, Historisk-filologiske Meddelelser, Høst, Copenhagen, 1917.
  • [11] Levinson, S. C., Presumptive Meanings: The Theory of Generalized Conversational Implicature, MIT Press, Cambridge, Mass., 2000.
  • [12] Löbner, S., Wahr neben Falsch: Duale Operatoren als die Quantoren natürlicher Sprache, Niemeyer, Tübingen, 1990.
  • [13] Sesmat, A., Logique, II: Les raisonnements, la logistique, Hermann, Paris, 1951.
  • [14] Seuren, P. A. M., “Taaluniversalia in de transformationele grammatika,” Leuvense Bijdragen, vol. 61 (1972), pp. 311–70.
  • [15] Seuren, P. A. M., Discourse Semantics, Blackwell, Oxford, 1985.
  • [16] Seuren, P. A. M., A View of Language, Oxford Univ. Press, Oxford, 2001.
  • [17] Seuren, P. A. M., “The importance of being modular,” Journal of Linguistics, vol. 40 (2004), pp. 593–635.
  • [18] Seuren, P. A. M., The Logic of Language: Language from Within, Vol. II, Oxford Univ. Press, Oxford, 2010.
  • [19] Seuren, P. A. M., “A reaction to Jackendoff’s discussion note,” Language, vol. 88 (2012), pp. 174–76.
  • [20] Seuren, P. A. M., From Whorf to Montague: Explorations in the Theory of Language, Oxford Univ. Press, Oxford, 2013.
  • [21] Seuren, P. A. M., and D. Jaspers, “Logico-cognitive structure in the lexicon,” to appear in Language, (2014).
  • [22] Van Fraassen, B. C., Formal Semantics and Logic, Macmillan, New York, 1971.
  • [23] Zadeh, L. A., “Fuzzy logic and approximate reasoning,” Synthese, vol. 30 (1975), pp. 407–28.