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If your system of logic contains a contradiction, then it can be said that any statement in that system "leads to" a contradiction. Thus "proof by contradiction
by plus 4y ago
If your system of logic contains a contradiction, then it can be said that any statement in that system "leads to" a contradiction. Thus "proof by contradiction" can prove any statement in that system.
- miga 4y agoTrying to find a formal system that encodes unbounded infinitary mathematical objects including most of maths, but yet to require that all statements are decidable within a finite number of steps... Is it contradiction in the proof, or rather a contradiction in assumptions? More on logic that permits all that *Bounded* Turing Machine does: https://arxiv.org/abs/2106.13309 https://arxiv.org/abs/2106.13309
- aristofun 4y ago> then it can be said that any statement in that system "leads to" a contradiction Why exactly it "leads to"? I don't get it. Why system can't have a contradiciton for one set of inputs, and not have it for others?