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Neither of the two. A proof by contradiction, as other comments have stated, is: assuming not P1, we reach a contradiction; thus P1 must be true. This is equiva
by butokai 3mo ago
Neither of the two. A proof by contradiction, as other comments have stated, is: assuming not P1, we reach a contradiction; thus P1 must be true. This is equivalent to tertium non datur in classical logic. I’m not sure it’s a valid deduction in your trivalent logic.
- adrian_b 3mo agoAnother poster has provided a link to a definition of "proof by contradiction", which I assume that it is the one that you mean ("A proof by contradiction is a proof of a positive by refutation of the negative."). Unlike in that unambiguous definition, the words used by you are confusing, because "we reach a contradiction" is also applicable to the 2 variants of "Reductio ad absurdum" that I have described. A demonstration like "a proof of a positive by refutation of the negative" is valid only in strictly bivalent logic and invalid in any multivalent logic. The 2 variants of "Reductio ad absurdum" that I have mentioned are also valid in any multivalent logic or modal logic.