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A new semantics for first-order logic, multivalent and mostly intensional

✍ Scribed by Hugues Leblanc

Publisher
Springer Netherlands
Year
1984
Tongue
English
Weight
643 KB
Volume
3
Category
Article
ISSN
0167-7411

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✦ Synopsis

Cited by many as distinctive of first-order logic are the bivalence of its statements and the extensionality of its operators, among them the three operators '~', '&', and 'V'. It is to that bivalence and that extensionality, we are told, that the logical entailments and, hence, logical truths peculiar to the logic are due. But first-order logic is a far more diverse thing than its exponents usually allow. As proof I submit here a new semantics for it, one in which statements are susceptible of up to 2 t~~ values, the operators '&' and 'V' are intensional, and yet the logical entailments and logical truths that first-order logic acknowledges are all preserved.

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