Notre Dame Journal of Formal Logic

The Cognitive Ontogenesis of Predicate Logic

Pieter A. M. Seuren

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Abstract

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

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

Dates
First available in Project Euclid: 7 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1415382953

Digital Object Identifier
doi:10.1215/00294527-2798718

Mathematical Reviews number (MathSciNet)
MR3276409

Zentralblatt MATH identifier
1335.03007

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

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

Citation

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. https://projecteuclid.org/euclid.ndjfl/1415382953


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