When thinking about philosophy and religion, it becomes clear that logic can only take one so far. For instance, a “perennial” view of the world religions, which I once attempted to entertain, rapidly falls apart on any serious investigation. Religions claim contradictive things vis-a-vis each other, and thus they cannot all be true. It is just a matter of logic that, if Islam is true, Christianity must be false (as Islam denies the divinity of Jesus), though it is logically possible that Islam and Christianity are both false. By analogy, in traditional logic with the square of opposition, “contraries” cannot both be true but both can be false.
Hence, either a “perennial” view embraces logical contradictions or must water down the major religions to such an extent that it must trivialize them all so as to attempt to rid all of the contradictions. Yet if it trivializes them all, that is just another way to infer that these religions are not really true after all. Or if it embraces logical contradictions, this is enough to claim that the “perennial” view is false. By analogy, in logic and pure mathematics, an “indirect proof” (aka reductio ad absurdum*) essentially shows that if a contradiction can be derived from a set of internally consistent premises, then the assumption that led to that contradiction must be false. It’s a common proof making move in number theory and abstract algebra, though it is a valid move when thinking about anything.
Nevertheless, logic alone cannot get us far. It cannot get us true premises. It’s only with true premises that we can then derive new true propositions via valid inferences in logic.
*BTW, you can read my page on Reductio ad Absurdum Arguments: https://amateurlogician.com/reductio-ad-absurdum-arguments/
*ALSO, for math proofs by contradiction: https://www.youtube.com/watch?v=ISjzxdg71rs
