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Full Idea
In the mainstream tradition of modern logic, beginning with Boole, Peirce and Schröder, descending through Löwenheim and Skolem to reach maturity with Tarski and his school ...saw logic as a branch of mathematics.
Gist of Idea
The mainstream of modern logic sees it as a branch of mathematics
Source
John Mayberry (What Required for Foundation for Maths? [1994], p.410-1)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.410
A Reaction
[The lesser tradition, of Frege and Russell, says mathematics is a branch of logic]. Mayberry says the Fregean tradition 'has almost died out'.
Related Idea
Idea 17787 Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
| 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| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |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] |