Combining Philosophers

Ideas for Herodotus, Mark Colyvan and Peter Geach

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2 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
17925 Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
     Full Idea: In intuitionist logic double negation elimination fails. After all, proving that there is no proof that there can't be a proof of S is not the same thing as having a proof of S.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)
     A reaction: I do like people like Colyvan who explain things clearly. All of this difficult stuff is understandable, if only someone makes the effort to explain it properly.
17926 Rejecting double negation elimination undermines reductio proofs [Colyvan]
     Full Idea: The intuitionist rejection of double negation elimination undermines the important reductio ad absurdum proof in classical mathematics.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)