Every now and then, I'll encounter some wannabe philosopher who likes to argue that logical induction is some totally faith-based assumption with no rational justification. This is false, it is stupidly easy to prove. All we have to do is explore every possible outcome that might occur from making an inductive inference. Watch:
- Imagine a possible world where all swans are white (supposition).
- If all swans are white, then all swans I encounter will be white (because all swans are white).
- If all swans I encounter are white, then induction says that all swans are white (def. of inductive inference).
- Therefore, if all swans are white, then induction worked (it is true that all swans are white, and induction told me so).
- Now imagine a possible world where NOT all swans are white (supposition).
- Suppose also that all swans I encounter happen to be white anyway (supposition; bad luck).
- If all swans I encounter are white, then induction says that all swans are white (3 repeated).
- Therefore, if not all swans are white, then induction failed (it is FALSE that all swans are white, but induction tells me they are).
- If not all swans are white, then one of two things can happen (law of the excluded middle):
- Every future swan I encounter will be white.
- Some future swan I encounter will NOT be white.
- If (1), then I don’t care if not all swans are white. Induction has still worked out correctly in every situation that mattered to me (pragmatism).
- If (2), then oops, I was wrong. Not all swans are white (empirical falsification).
- Therefore, when induction fails, either
- Pragmatism: I don't care.
- Falsification: My mistake will be corrected.
Here, I'll even draw a picture:
