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Results tagged with lo.logic
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user 51771
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
9
votes
What do we gain with higher order logics?
Bell and Machover don't say (in the quote) anything about statement length, so this doesn't necessarily contradict Gödel.
I can't speak about (universal) shortest proof, but "translating" between high …
- 839
16
votes
Accepted
Status of proof by contradiction and excluded middle throughout the history of mathematics?
I want to echo the other answer, that Brouwer presents the first robust challenge to the Law of Excluded Middle (LEM), but I do want to add some history and background, and maybe recommend a related p …
- 839
7
votes
History of (proposal of) set-theoretic foundations
Not a complete answer, but maybe relevant.
Russell, in Introduction to Mathematical Philosophy (1919) simply states the Peano axioms are the foundations of math without much discussion.
Having reduce …
- 839
10
votes
The logic of Buddha: a formal approach
The 2015 World Congress on Logic and Religion -- which mentions the Bilimoria paper -- also lists a talk "The Logical Nature of the Nalanda Tradition of Buddhism" by Razvan Diaconescu of
Simion Stoilo …
- 839