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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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Examples in which probabilistic heuristic reasoning fails
There are examples of conjectures in which one can use probabilistic heuristic reasoning to show that they are very likely to be true. For instance, Freeman Dyson used probabilistic heuristic reasonin …
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On mathematical arguments against Quantum computing
I wrote a paper "Why do we live in a quantum world" that assumes that "Quantum mechanics is just an approximation to some deeper theory", which is number 8 in Scott Aaronson's list of eleven objection …