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Logico-Cognitive Structure in the Lexicon

Published online by Cambridge University Press:  01 January 2026

Pieter A. M. Seuren  and
Dany Jaspers
Pieter A. M. Seuren*
Affiliation:
Max Planck Institute for Psycholinguistics
Dany Jaspers*
Affiliation:
KU Leuven HUBrussel
*
[pieter.seuren@mpi.nl]
[dany.jaspers@kuleuven.be]
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Abstract

This study is a prolegomenon to a formal theory of the natural growth of conceptual and lexical fields. Negation, in the various forms in which it occurs in language, is found to be a powerful indicator. Other than in standard logic, natural language negation selects its complement within universes of discourse that are, for practical and functional reasons, restricted in various ways and to different degrees. It is hypothesized that a system of cognitive principles drives recursive processes of universe restriction, which in turn affects logical relations within the restricted universes. This approach provides a new perspective in which to view the well-known clashes between standard logic and natural logical intuitions. Lexicalization in language, especially the morphological incorporation of negation, is limited to highly restricted universes, which explains, for example, why a dog can be said not to be a Catholic, but also not to be a non-Catholic. Cognition is taken to restrict the universe of discourse to contrary pairs, splitting up one or both of the contraries into further subuniverses as a result of further cognitive activity. It is shown how a logically sound Square of Opposition, expanded to a hexagon (Jacoby 1950, 1960, Sesmat 1951, Blanche 1952, 1953, 1966), is generated by a hierarchy of universe restrictions, defining the notion ‘natural’ for logical systems. The Logical Hexagon contains two additional vertices, one for ‘some but not all’ (the Y-type) and one for ‘either all or none’ (the U-type), and incorporates both the classic square and the Hamiltonian Triangle of Contraries. Some is thus considered semantically ambiguous, representing two distinct quantifiers. The pragmaticist claim that the language system contains only the standard logical ‘some perhaps all’ and that the ‘some but not all’ meaning is pragmatically derived from the use of the system is rejected. Four principles are proposed according to which negation selects a complement from the subuniverses at hand. On the basis of these principles and of the logico-cognitive system proposed, the well-known nonlexicalization not only of *nall and *nand but also of many other nonlogical cases found throughout the lexicons of languages is analyzed and explained.

Keywords

complement selectioncontrarietyconceptual fieldsentailmentlexical gapslogical hexagonsquare of oppositionuniverse of discourse

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Type
Research Article
Information
Language , Volume 90 , Issue 3 , September 2014 , pp. 607 - 643
Copyright
Copyright © 2014 Linguistic Society of America

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References

Ariel, Mira. 2008. Pragmatics and grammar. Cambridge: Cambridge University Press.10.1017/CBO9780511791314CrossRefGoogle Scholar
Bach, Kent. 1994. Conversational impliciture. Mind & Language 9. 2. 124–62.10.1111/j.1468-0017.1994.tb00220.xCrossRefGoogle Scholar
Baker, Carl L. 1970. Double negatives. Linguistic Inquiry 1. 2. 169–86.Google Scholar
Bartsch, Renate. 1973. ‘Negative transportation’ gibt es nicht. Linguistische Berichte 27. 1–7.Google Scholar
Béziau, Jean-Yves, and Payette, Gillman (eds.) 2012. The square of opposition: A general framework for cognition. Bern: Peter Lang.10.1007/978-3-0348-0379-3CrossRefGoogle Scholar
Blanché, Robert. 1952. Quantity, modality, and other kindred systems of categories. Mind 61. 369–75.Google Scholar
Blanché, Robert. 1953. Sur l'opposition des concepts. Theoria 19. 89–130.10.1111/j.1755-2567.1953.tb01013.xCrossRefGoogle Scholar
Blanché, Robert. 1966. Structures intellectuelles: Essai sur l'organisation systématique des concepts. Paris: J. Vrin.Google Scholar
Carston, Robyn. 1988. Implicature, explicature, and truth-theoretic semantics. Mental representations: The interface between language and reality, ed. by Kempson, Ruth, 155–81. Cambridge: Cambridge University Press.Google Scholar
Clark, Herbert H. 1970. Word associations and linguistic theory. New horizons in linguistics, ed. by Lyons, John, 271–86. Harmondsworth: Penguin.Google Scholar
Collins, Chris, and Postal, Paul M.. 2014. Classical NEG raising: An essay on the syntax of negation. Cambridge, MA: MIT Press.10.7551/mitpress/9780262027311.001.0001CrossRefGoogle Scholar
Couturat, Louis. 1913. Des propositions particulières et de leur portée existentielle. Revue de métaphysique et de morale 21. 256–59.Google Scholar
Cruse, David A. 1986. Lexical semantics. Cambridge: Cambridge University Press.Google Scholar
Filimonova, Elena (ed.) 2005. Clusivity: Typology and case studies of the inclusive-exclusive distinction. (Typological studies in language 63.) Amsterdam: John Benjamins.CrossRefGoogle Scholar
Fillmore, Charles J. 1982. Frame semantics. Linguistics in the morning calm: Selected papers from SICOL-1981, ed. by The Linguistic Society of Korea, 111–37. Seoul: Hanshin.Google Scholar
Fogelin, Robert J. 1967. Evidence and meaning: Studies in analytic philosophy. London: Routledge & Kegan Paul.Google Scholar
Grice, H. Paul. 1975. Logic and conversation. Syntax and semantics, vol. 3: Speech acts, ed. by Cole, Peter and Morgan, Jerry L., 41–58. New York: Academic Press.Google Scholar
Grice, H. Paul. 1989. Studies in the way of words. Cambridge, MA: Harvard University Press.Google Scholar
Gruber, Jeffrey S. 1976. Lexical structures in syntax and semantics. Amsterdam: North-Holland.Google Scholar
Hamilton, William. 1866. Lectures on metaphysics and logic, vol. 4 (Lectures on logic, vol. 2, 2nd edn., revised), ed. by Mansel, H. L. and Veitch, J.. Edinburgh: Blackwood and Sons.10.1037/12217-000CrossRefGoogle Scholar
Horn, Laurence R. 1972. On the semantic properties of logical operators in English. Los Angeles: University of California, Los Angeles dissertation. [Distributed by the Indiana University Linguistics Club, 1976.].Google Scholar
Horn, Laurence R. 1984. Toward a new taxonomy for pragmatic inference: Q- and R-based implicature. Meaning, form, and use in context, ed. by Schiffrin, Deborah, 11–42. Washington, DC: Georgetown University Press.Google Scholar
Horn, Laurence R. 1985. Metalinguistic negation and pragmatic ambiguity. Language 61. 1. 121–74.10.2307/413423CrossRefGoogle Scholar
Horn, Laurence R. 1989. A natural history of negation. Chicago: University of Chicago Press.Google Scholar
Horn, Laurence R. 1990. Hamburgers and truth: Why Gricean explanation is Gricean. Berkeley Linguistics Society 16. 454–71. Online: http://elanguage.net/journals/bls/article/view/2652.Google Scholar
Horn, Laurence R. 2004. Implicature. The handbook of pragmatics, ed. by Horn, Laurence and Ward, Gregory, 3–28. Oxford: Blackwell.Google Scholar
Horn, Laurence R. 2007. Neo-Gricean pragmatics: A Manichaean manifesto. Pragmatics, ed. by Burton-Roberts, Noel, 158–83. Basingstoke: Palgrave Macmillan:.Google Scholar
Horn, Laurence R. 2012. Histoire d’*O: Lexical pragmatics and the geometry of opposition. In Béziau & Payette, 393–426.Google Scholar
Jacoby, Paul. 1950. A triangle of opposites for types of propositions in Aristotelian logic. The New Scholasticism 24. 32–56.10.5840/newscholas19502413CrossRefGoogle Scholar
Jacoby, Paul. 1960. Contrariety and the triangle of opposites in valid inferences. The New Scholasticism 34. 141–69.10.5840/newscholas196034215CrossRefGoogle Scholar
Jaspers, Dany. 2005. Operators in the lexicon: On the negative logic of natural language. Leiden: Leiden University dissertation.Google Scholar
Jaspers, Dany. 2011. Logic of colours in historical perspective. Logic of colours in historical perspective: HUBrussel.Google Scholar
Jaspers, Dany. 2012. Logic and colour. Logica Universalis 6. 227–48.10.1007/s11787-012-0044-yCrossRefGoogle Scholar
Jaspers, Dany, and Seuren, Pieter A. Μ.. 2014. The square of opposition in Catholic hands: A chapter in the history of 20th-century logic. The square of opposition in Catholic hands: A chapter in the history of 20th-century logic: KU Leuven HUBrussel, ms.Google Scholar
Jespersen, Otto. 1917. Negation in English and other languages. Copenhagen: A. F. Høst.Google Scholar
Jespersen, Otto. 1924. The philosophy of grammar. London: Allen & Unwin.Google Scholar
Kneale, William, and Kneale, Martha. 1962. The development of logic. Oxford: Clarendon.Google Scholar
Larson, Richard, and Jaspers, Dany. 2011. Broad and narrow language faculties. Paper presented at the Workshop on the Evolution of Human Cognition, Georgetown University, Washington, DC, October 18, 2011. Online: http://web.me.com/dany.jaspers/Site/Research_files/LarsonJapsersGEO.pdf.Google Scholar
Levinson, Stephen C. 1983. Pragmatics. Cambridge: Cambridge University Press.10.1017/CBO9780511813313CrossRefGoogle Scholar
Levinson, Stephen c. 2000. Presumptive meanings: The theory of generalized conversational implicature. Cambridge, MA: MIT Press.10.7551/mitpress/5526.001.0001CrossRefGoogle Scholar
Löbner, Sebastian. 1990. Wahr neben Falsch, Duale Operatoren als die Quantoren natürlicher Sprache. Tübingen: Niemeyer.Google Scholar
McCawley, James D. 1972. Grammar and meaning: Papers on syntactic and semantic topics. Tokyo: Taishukan.Google Scholar
McCawley, James D. 1981. Everything that linguists have always wanted to know about logic* but were ashamed to ask. Oxford: Blackwell.Google Scholar
Mostowski, Andrzej. 1957. On a generalization of quantifiers. Fundamenta Mathematica 44. 12–36.10.4064/fm-44-1-12-36CrossRefGoogle Scholar
Noordman, Leo g. m. 1979. Inferring from language. Berlin: Springer.10.1007/978-3-642-67307-8CrossRefGoogle Scholar
Parsons, Terence. 2012. The traditional square of opposition. The Stanford Encyclopedia of Philosophy (Fall 2012 edn.), ed. by Zalta, Edward N.. Online: http://plato.stanford.edu/archives/fall2012/entries/square/.Google Scholar
Ross, John r. 1967. Constraints on variables in syntax. Cambridge, MA: MIT dissertation. [Published as Infinite syntax!, Norwood, NJ: Ablex, 1986.].Google Scholar
Russell, Bertrand. 1946. History of Western philosophy and its connection with political and social circumstances from the earliest times to the present day. London: Allen & Unwin.Google Scholar
Sesmat, Augustin. 1951. Logique II: Les raisonnements, la logistique. Paris: Hermann.Google Scholar
Seuren, Pieter a. m. 1972. Taaluniversalia in de transformationele grammatika. Leuvense Bijdragen 61. 4. 311–70. [Partially republished in English in Seuren 2001:293-311.].Google Scholar
Seuren, Pieter a. m. 1985. Discourse semantics. Oxford: Blackwell.Google Scholar
Seuren, Pieter a. m. 1988. Presupposition and negation. Journal of Semantics 6. 3. 4.175-226. [Reprinted as Chapter 16 m Seuren 2001.].10.1093/jos/6.1.175CrossRefGoogle Scholar
Seuren, Pieter a. M. 1993. Why does 2 mean ‘2’? Grist to the anti-Grice mill. Proceedings of the Conference on Functional Description of Language, Prague, Nov. 24-27, 1992, ed. by Hajičová, Eva, 225–35. Prague: Faculty of Mathematics and Physics, Charles University.Google Scholar
Seuren, Pieter a. m. 2001. A view of language. Oxford: Oxford University Press.Google Scholar
Seuren, Pieter a. m. 2002. The logic of thinking. Koninklijke Nederlandse Akademie van Wetenschappen, Mededelingen van de Afdeling Letterkunde, Nieuwe Reeks 65. 9. 5–35.Google Scholar
Seuren, Pieter a. m. 2006. The natural logic of language and cognition. Pragmatics 16. 1. 103–38. Online: http://elanguage.net/journals/pragmatics/article/view/501.Google Scholar
Seuren, Pieter a. m. 2010. The logic of language: Language from within, vol. 2. Oxford: Oxford University Press.Google Scholar
Seuren, Pieter a. m. 2013. From Whorf to Montague: Explorations in the theory of language. Oxford: Oxford University Press.10.1093/acprof:oso/9780199682195.001.0001CrossRefGoogle Scholar
Seuren, Pieter a. m. 2014. The cognitive ontogenesis of predicate logic. Notre Dame Journal of Formal Logic, to appear.10.1215/00294527-2798718CrossRefGoogle Scholar
Simon, Horst J. 2005. Only you? Philological investigations into the alleged inclusive-exclusive distinction in the second-person plural. In Filimonova, 113–50.Google Scholar
Smessaert, Hans. 2011. The classical Aristotelian hexagon versus the modern duality hexagon. Logica Universalis 5. 2. 1–29.Google Scholar
van der Wouden, Ton. 1994. Negative contexts. Groningen: Groningen University dissertation.Google Scholar
van Fraassen, Bas. 1971. Formal semantics and logic. New York: Macmillan.Google Scholar
Whitehead, Alfred N., and Russell, Bertrand. 1910-1913. Principia mathematica. 3 vols. Cambridge: Cambridge University Press.Google Scholar