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5. Theory of Logic / A. Overview of Logic / 2. History of Logic

[origins of the various systems of formal logic]

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The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]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