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:
It's very funny that you think the induction, "All swans are white", can be rationally justified while at the same time it is the case that there are black swans. Do better
ReplyDeleteDo you seriously not understand the concept of a "possible world?" Because you sound like you literally don't grasp the concept of a hypothetical...
DeleteI am interested in something, is the inductive method, for example, when we say that all things up to now have been in accordance with naturalism and then conclude that all things are in accordance with naturalism, and something else when believers use this method to, for example, confirm real infinity not it exists because we have never met it and that then proves that the universe has a beginning, I think that this method cannot be applied here.
ReplyDeleteAlrighty! Let's see how this brilliant view applies for anti-induction:
ReplyDeleteObservation: All swans I have ever encountered are white.
Anti-inductive inference: all of the swans I will encounter from now on are black.
Possible World #1: all swans from now on are indeed black.
Possible World #2: there are white swans other than the one I saw but I will never encounter them in my lifetime.
Possible world #3: I will encounter another white swan in my lifetime.
Why don't we apply this? It's so amazing! I've solved the problem of anti-induction!
Do you honestly need me to explain to you why that's absurd?
ReplyDeleteIf all swans are white, then it stands to reason that all swans I encounter will be white. I therefore have a logical basis for forming a hypothesis.
Next time, please try thinking about what you're saying before posting.
But "If x then y" does not allow you to conclude "y, therefore x". The logical basis is fallacious.
DeleteI have never seen a swan before. My friend describes the bird to me, and I reason that all swans must be green, because apples are mostly red, and if all witches are made of wood, then France must be on Mars.
ReplyDeleteNow if all swans really are green, then hoorah! I am correct. If I never encounter a non-green swan, then my logic has made a reliable prediction. If I encounter white or black swans, then I can use the deductive reasoning at my disposal to reason that I was incorrect; may I make better predictions in the future. Thus I have solved the problem of scato-duction
Interesting read. But I object to this:
ReplyDelete"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)."
What was your original statement?
If it was about about all swans that exist, then induction failed, because not all swans you encountered were white.
If it was limited to the swans you encountered until that point ("all the swans I have seen are white"), then it was meaningless, because you just rephrased what happened to you (ie it wasn't a prediction). It merely describes past observations and lacks predictive power. Such a statement is trivial because it only restates what has already been observed without making any future predictions. Induction is intended to extend beyond observed instances to make broader generalizations.
If it was "the next X swans are going to be white, because the first Y were also white", then induction did not fail. But you didn't prove that there was any basis for induction. You might as well say "the next X coin flips will result in all heads, because the first Y also resulted in all heads." Also, if you think past events somehow influence future ones, that statement still relies on the assumption that past observations can reliably predict future occurrences, which is the core of the problem of induction. Without a justification for why the future should resemble the past, this form of induction also lacks a solid foundation.
How would you address the above?