Propositional and predicate logic-linguistic aspects

Seuren, P. A. M. (2006). Propositional and predicate logic-linguistic aspects. In K. Brown (Ed.), Encyclopedia of Language and Linguistics (vol. 10) (pp. 146-153). Amsterdam: Elsevier.
Logic was discovered by Aristotle when he saw that the semantic behavior of the negation word not is different in sentences with a definite and in those with a quantified subject term. Until the early 20th century, logic remained firmly language-based, but for the past century it has been mainly a tool in the hands of mathematicians, which has meant an alienation from linguistic reality. With the help of new techniques, it is now possible to revert to the logic of language, which is seen as based on a semantic analysis of the logical words (constants) involved. This new perspective, combined with much improved insights into the semantically defined discourse dependency of natural language sentences, leads to a novel and more functionally oriented approach to logic and to a reappraisal of traditional predicate calculus, whose main fault, undue existential import, evaporates when discourse dependency, in particular the presuppositional aspect, is brought into play. Traditional predicate calculus is seen to have a much greater logical power and a much greater functionality than modern predicate calculus. There is also full isomorphism, neglected in modern logic, between traditional predicate calculus and propositional calculus, which raises the question of any possible deeper causes.
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