Combining Philosophers

Ideas for Anaxarchus, Mark Colyvan and Vittorio Hsle

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2 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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)
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.