Looking at proofs by contradiction and it seems I've run into something that does not sit well with me. I am fine with the law of the excluded middle (thus not an intuitionist) and more fundamentally the Principle of Explosion seems reasonable.
The standard form is:
$(P \wedge \neg Q \implies \bot) \implies (P \implies Q) $
However I've seen a number which claim to be reductio ad absurdem but follow the following format:
$(\neg P \implies \bot) \implies P $
Which seems to be not entirely robust when people use it in a similar way to as follows. Let:
$P = A \wedge B \wedge C$
Then through reductio ad absurdem they find that P is true. Thus any of A, B or C is true.
Think of the infinite primes proof with the original P statement, "If there are infinite primes and cats are plants". I'm concerned about this use. Thanks.