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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.
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Probability theory without deductive closure
If you model a human brain as a stochastic reasoning device, you can posit uncertainty as to whether the mechanism of the brain has, at some point in time, reached some logical conclusion and stored i …