"What can’t be false must me true" is what classic logic called "Tertium non datur", and which has absolutely nothing to do with a demonstration by "Reductio ad

"What can’t be false must me true" is what classic logic called "Tertium non datur", and which has absolutely nothing to do with a demonstration by "Reductio ad absurdum", i.e. with "assuming a fact, showing that it would lead to an absurd". A demonstration by "Reductio ad absurdum" can also be done in multivalent logic, for instance in trivalent logic, where a statement can be true or false or neither true nor false, therefore "Tertium non datur" is not applicable. In my opinion, trivalent logic is the simplest kind of logic that is applicable to mathematics or to the real world. Its subset that is bivalent logic is interesting as an object of study but not as a technique that can be useful for practical reasoning or for mathematical demonstrations. If I understood you correctly, you want to distinguish the following 2 kinds of demonstrations, where P1 and P2 are propositions: 1. One demonstrates that "P1 implies not P1". From this it can be concluded that P1 cannot be true. 2. One demonstrates that "P1 implies not P2". But it is known that P2 is true. From these 2 facts it can be concluded that P1 cannot be true. Which of these 2 you call "proof by contradiction"? Probably a better name is needed, because both kinds of demonstrations end in a contradiction, the first contradicts the premise, while the second contradicts an independently known fact. EDIT: Another poster has provided a link to someone who uses the following definition: "A proof by contradiction is a proof of a positive by refutation of the negative." I believe that such a definition refers to a thing so trivial that it does not deserve a special name. Obviously if P is a proposition and it is shown that "not P cannot be true" (refutation of the negative), only in bivalent logic it can be concluded that P must be true. In trivalent logic, that only proves that P is either true or neither true nor false. In real life, bivalent logic is never applicable, as the statements that are neither true nor false are much more frequently encountered than those that are known to be either true or false. So in real life, any "demonstration" by refutation of the negative is almost certainly a logical fallacy.