Question

Explain the following three itemized questions about Indrect Proof (a.k.a. Reductio ad Absurdum): (1) how it works in terms of its unique procedure as a proof, (2) why it constitutes a legitimate proof in spite of its unorthodox procedure by identifying and explaining the two fundamental principles of logic as its underpinnings; and (3) why we accept those two principles.

Answer 1

(1) Reductio ad Absurdum is a form of argument that attempts to disprove a statement by showing it inevitably leads to an absurd conclusion. This means that the statement that we had assumed in the first place must have been false, and hence we have a proof that the statement is false.

(2) Since it's logically verifiable, it's a legitimate proof. It's fundamentally based on the fact that for a statement P, it's not possible that both P and not(P) are simultaneously true.

The other underpinning fact is that if we can reduce a statement to an absurd fallacy, the original statement must be false.

(3) The mathematical definition of a mathematical statement is that its truth value should either be True or False. So, it can't be simultaneously true and false. This is what forms the basis for (2).