more from this thinker     |     more from this text

Single Idea 13669

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

Full Idea

In 1910 Weyl observed that set theory seemed to presuppose natural numbers, and he regarded numbers as more fundamental than sets, as did Fraenkel. Dedekind had developed set theory independently, and used it to formulate numbers.

Gist of Idea

Can one develop set theory first, then derive numbers, or are numbers more basic?

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.2)

Book Ref

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.182

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13234 The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]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]