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Single Idea 13667
[filed under theme 5. Theory of Logic / A. Overview of Logic / 2. History of Logic
]
Full Idea
Skolem and Gödel were the main proponents of first-order languages. The higher-order language 'opposition' was championed by Zermelo, Hilbert, and Bernays.
Gist of Idea
Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 7.2)
Book Ref
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.178
The
15 ideas
with the same theme
[origins of the various systems of formal logic]:
19369
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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
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Montague's intensional logic incorporated the notion of meaning
[Devlin]
|
13667
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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
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The view of logic as knowing a body of truths looks out-of-date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]
|