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Results tagged with lo.logic
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user 41139
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.
4
votes
Asymmetric $A \iff B$ proofs
I asked about this before on MSE: https://math.stackexchange.com/q/1500691/101420
There are some arguments that Pythagoras theorem and its converse provide an example of what you're asking. (So given …
- 2,493
16
votes
Taking a theorem as a definition and proving the original definition as a theorem
When I was teaching elementary geometry in high school in Holland 10 years ago, the concept of equivalent definitions was actually part of the curriculum. There the examples were more down to earth: y …