Fundamental Modes of Reasoning.

I would argue that all argument, reason and logic is fundamentally reducible to proof by contradiction and proof by exhaustion. As a toy heuristic argument for the former's fundamentality I will here prove, via contradiction, that everything that can be proved can be proved via contradiction.

1. Suppose some proposition S has a proof P, but is such that it cannot

be proven by contradiction.

2. Suppose ~S

3. Reiterate ~S

4. P

5. Therefore S

6. Contradiction

7. Thus ~~S

8. S

9. But then S is proven by lines 2-8 through contradiction, which contradicts line 1

10. Therefore there does not exist such a proposition S.

Therefore if anything can be proven it can be proven by contradiction.