The natural logic of language and cognition
Pieter A.M. Seuren
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.