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Single Idea 8089

[filed under theme 5. Theory of Logic / A. Overview of Logic / 2. History of Logic ]

Full Idea

Montague's intensional logic was the first really successful attempt to develop a mathematical framework that incorporates the notion of meaning.

Gist of Idea

Montague's intensional logic incorporated the notion of meaning

Source

Keith Devlin (Goodbye Descartes [1997], Ch. 8)

Book Ref

Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.192

A Reaction

Previous logics, led by Tarski, had flourished by sharply dividing meaning from syntax, and concentrating on the latter.

The 15 ideas with the same theme [origins of the various systems of formal logic]:

19369 Lull's combinatorial art would articulate all the basic concepts, then show how they combine [Lull, by Arthur,R]
8686 Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
7622 In 1879 Frege developed second order logic [Frege, by Putnam]
10247 We have no adequate logic at the moment, so mathematicians must create one [Veblen]
11022 Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
18954 Before the late 19th century logic was trivialised by not dealing with relations [Putnam]
5637 Nowadays logic is seen as the science of extensions, not intensions [Scruton]
17786 The mainstream of modern logic sees it as a branch of mathematics [Mayberry]
8087 Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin]
8089 Montague's intensional logic incorporated the notion of meaning [Devlin]
13667 Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro]
13668 Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro]
13669 Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro]
13234 The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
18912 Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]