Logic and semantics in the twentieth century

In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press 562 (2009)
A crucial aspect of the revolution that affected logic at the beginning of the twentieth century concerns the severance of its traditional dependence on the form and structure of natural language. Such a breakdown has had enormous consequences not only for the development of formal logic, but also for the opening of new perspectives in the study of language. This peculiar relationship between mathematical logic and language inquiry is best illustrated by Willard V. O. Quine (1961: 1): Mathematicians expedite their special business by deviating from ordinary language. Each such departure is prompted by specific considerations of utility for the mathematical venture afoot. Such reforms may be expected to reflect light on the ordinary language from which they depart. As a major consequence of its “reforms”, the new mathematical logic has been able to revivify and boost the notion of philosophical and logical grammar, typical of the seventeenth and eighteenth century rationalist tradition. New life has therefore been given to the idea that there exists a common grammatical core shared by every language and determinable a priori, with respect to which diversity and variation are just prima facie features of natural language, hiding its universal logical structure.
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