Por Benedict Eastaugh (Munich Center for Mathematical Philosophy-LMU).

Many classical mathematical theorems are computably false: there are “recursive counterexamples” which satisfy their hypotheses but not their conclusions. This is often taken to show that these theorems are constructively unprovable. However, the theoretical standpoint from which recursive counterexamples are defined embeds assumptions that constructivists do not accept. These impossibility results are thus meaningless or invalid from their perspective. In this talk I will argue that reverse mathematics provides a way to internalise recursive counterexamples in weak formal systems acceptable to a range of broadly constructive foundational viewpoints. Although it cannot completely bridge the classical and foundational standpoints, this approach nevertheless brings them closer together.

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