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Results tagged with lo.logic
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user 1229
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.
18
votes
3
answers
4k
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How would calculus be possible in a finitist axiom system?
I am interested in learning a little more about finitism, currently about which I only know a few encyclopedic paragraphs.
I know that during some time, some mathematicians like Kronecker thought t …
- 2,745
185
votes
11
answers
52k
views
Knuth's intuition that Goldbach might be unprovable
Knuth's intuition that Goldbach's conjecture (every even number greater than 2 can be written as a sum of two primes) might be one of the statements that can neither be proved nor disproved really puz …
- 2,745
26
votes
9
answers
8k
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Why are proofs so valuable, although we do not know that our axiom system is consistent? [closed]
As a person who has been spending significant time to learn mathematics, I have to admit that I sometimes find the fact uncovered by Godel very upsetting: we never can know that our axiom system is co …