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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Cited by
Cited by 9 other publications
Cremers, Crit
2010. NL from Logic: Connecting Entailment and Generation. In Logic, Language and Meaning [Lecture Notes in Computer Science, 6042], ► pp. 94 ff.
Demey, Lorenz
2015. Interactively Illustrating the Context-Sensitivity of Aristotelian Diagrams. In Modeling and Using Context [Lecture Notes in Computer Science, 9405], ► pp. 331 ff.
Jaspers, Dany
2015. The English Tenses, Blanché and the Logical Kite. In The Road to Universal Logic [Studies in Universal Logic, ], ► pp. 319 ff.
Katzir, Roni & Raj Singh
2013. Constraints on the lexicalization of logical operators. Linguistics and Philosophy 36:1 ► pp. 1 ff.
Mondal, Prakash
2016. Toward an Architecture of the Language–Emotion Interface. In Language and Cognitive Structures of Emotion, ► pp. 111 ff.
Seuren, Pieter
2010. A Logic-Based Approach to Problems in Pragmatics. Poznań Studies in Contemporary Linguistics 46:4
Smessaert, Hans
2009. On the 3D Visualisation of Logical Relations. Logica Universalis 3:2 ► pp. 303 ff.
Speranza, J.L. & Laurence R. Horn
2010. A brief history of negation. Journal of Applied Logic 8:3 ► pp. 277 ff.
Speranza, J.L. & Laurence R. Horn
2012. History of Negation. In Logic: A History of its Central Concepts [Handbook of the History of Logic, 11], ► pp. 127 ff.
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