The natural logic of language and cognition

Pieter A.M. Seuren

Abstract

This paper aims at an explanation of the discrepancies between natural intuitions and standard logic in terms of a distinction between NATURAL and CONSTRUCTED levels of cognition, applied to the way human cognition deals with sets. NATURAL SET THEORY (NST) restricts standard set theory cutting it down to naturalness. The restrictions are then translated into a theory of natural logic. The predicate logic resulting from these restrictions turns out to be that proposed in Hamilton (1860) and Jespersen (1917). Since, in this logic, NO is a quantifier in its own right, different from NOT-SOME, and given the assumption that natural lexicalization processes occur at the level of basic naturalness, single-morpheme lexicalizations for NOT-ALL should not occur, just as there is no single-morpheme lexicalization for NOT-SOME at that level. An analogous argument is developed for the systematic absence of lexicalizations for NOT-AND in propositional logic.

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Barwise, Jon, and Robin Cooper
(1981) Generalized quantifiers and natural language. Linguistics and Philosophy 4.2: 159–219. DOI logoGoogle Scholar
Butterworth, Brian
(1999) The Mathematical Brain. London: Macmillan.Google Scholar
De Morgan, Augustus
(1847) Formal logic: or, the calculus of inference, necessary and probable. London: Taylor & Walton.Google Scholar
Dehaene, Stanislas
(1997) The number sense. New York: Oxford University Press.Google Scholar
(2005) Evolution of human cortical circuits for reading and arithmetic: The “neuronal recycling” hypothesis. In Stanislas Dehaene, Jean-René Duhamel, Marc D. Hauser, and Giacomo Rizzolatti (eds.), From monkey brain to human brain. A Fyssen Foundation symposium. Cambridge: MIT Press. DOI logoGoogle Scholar
Dehaene, Stanislas, Véronique Izard, Pierre Pica, and Elisabeth Spelke
in press) Core knowledge of geometry in an Amazonian indigene group. Science.
Ginsburg, Herbert P., and Barbara S. Allardice
(1984) Children’s difficulties with school mathematics. In: Barbara Rogoff and Jean Lave (eds.), Everyday cognition: Its development in social context. Cambridge, Mass.: Harvard University Press, pp. 194–219.Google Scholar
Hamilton, William
(1860) Lectures on Logic. Edinburgh: Blackwood & Sons.Google Scholar
Hoeksema, Jack
(1999) Blocking effects and polarity sensitivity. In J. Gerbrandy, M. Marx, M. de Rijke, and Y. Venema (eds.), JFAK. Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday. Amsterdam: Amsterdam University Press (not available in hard copy) www​.illc​.uva​.nl​/j50​/contribs​/hoeksema​/hoeksema​.pdfGoogle Scholar
Horn, Larry R
(1989) A Natural History of Negation. Chicago/London: The University of Chicago Press.Google Scholar
Jespersen, Otto
(1917) Negation in English and Other Languages. Det Kgl. Danske Videnskabernes Selskab, Historisk-filologiske Meddelelser I,5. Copenhagen: Andr. Fred. Høst & søn.Google Scholar
Kneale, William, and Martha Kneale
(1962) The Development of Logic. Oxford: Clarendon Press.Google Scholar
Kratzer, Angelika
(1979) Conditional necessity and possibility. In Rainer Bäuerle, Urs Egli, and Arnim von Stechow (eds.), Semantics from Different Points of View. Berlin-Heidelberg-New York: Springer, pp. 117–147. DOI logoGoogle Scholar
Levinson, Stephen C
(2000) Presumptive Meanings. The Theory of Generalized Conversational Implicature. Cambridge, Mass.: MIT Press.  BoP. DOI logoGoogle Scholar
Pica, Pierre, Cathy Lemer, Véronique Izard, and Stanislas Dehaene
(2004) Exact and approximate arithmetic in an Amazonian indigene group. Science 306. (October 2004): 499–503. DOI logoGoogle Scholar
Seuren, Pieter A.M
(1974) Negative’s travels. In Pieter A.M. Seuren (ed.), Semantic Syntax. Oxford Readings in Philosophy. Oxford: Oxford University Press, pp. 183–208.Google Scholar
in prep.) Language and Logic in Cognition.
Van Fraassen, Bas
(1971) Formal Semantics and Logic. New York-London: Macmillan.Google Scholar
Zwicky, Arnold
(1973) Linguistics as chemistry: The substance theory of semantic primes. In Stephen Anderson & Paul Kiparsky (eds.), A Festschrift for Morris Halle. New York: Holt & Cy, pp. 467–485.Google Scholar