GuyOnInternet
Active Member
- Mar 4, 2022
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The Problem of Induction is the logical gap between "it has happened" and "it will happen." While often treated as a singular riddle, it is more accurately understood as two distinct versions.
Version A: The Failure of Deductive Certainty
"No matter how many times I drop a rock and watch it fall to the ground, I will never know with absolute certainty that the next time I drop a rock it will fall to the ground."
This version is a Troll's Truism, trivially true except so what.
Version B: The Failure of Probability
"No matter how many times I drop a rock and watch it fall to the ground, it never becomes even more likely to be true that the next time I drop a rock it will fall to the ground."
This version is bat-shit crazy. No one actually believes that.
The Logic: Probability is a ratio of known instances (n) to the total possible instances (the future). Since the future is theoretically infinite (∞), any finite number of successful observations divided by infinity always equals zero (P=0).
The Result: Mathematically, your next drop is never more "probable". The tally of the past provides no mathematical leverage over the future; it only provides a psychological expectation.
Now, some people may think an explanation can solve the problem of induction. However, this is not the case.
You may say that now we know why a rock falls when you drop it because of Einstein's Theory that matter warps space. However, according to the problem of induction, we have no good reason to believe that because matter is currently warping space, that matter will continue to warp space in the future.
So, according to the problem of induction, no belief ever becomes even more likely to be true and we will never know anything with any justified confidence. That is annihilationist thinking. The fact of the matter is planes fly, cars drive, etc. The reason people don't jump off of a cliff yet will fly on an airplane is because they reason inductively whether they admit it or not.
Version A: The Failure of Deductive Certainty
"No matter how many times I drop a rock and watch it fall to the ground, I will never know with absolute certainty that the next time I drop a rock it will fall to the ground."
This version is a Troll's Truism, trivially true except so what.
Version B: The Failure of Probability
"No matter how many times I drop a rock and watch it fall to the ground, it never becomes even more likely to be true that the next time I drop a rock it will fall to the ground."
This version is bat-shit crazy. No one actually believes that.
The Logic: Probability is a ratio of known instances (n) to the total possible instances (the future). Since the future is theoretically infinite (∞), any finite number of successful observations divided by infinity always equals zero (P=0).
The Result: Mathematically, your next drop is never more "probable". The tally of the past provides no mathematical leverage over the future; it only provides a psychological expectation.
Now, some people may think an explanation can solve the problem of induction. However, this is not the case.
You may say that now we know why a rock falls when you drop it because of Einstein's Theory that matter warps space. However, according to the problem of induction, we have no good reason to believe that because matter is currently warping space, that matter will continue to warp space in the future.
So, according to the problem of induction, no belief ever becomes even more likely to be true and we will never know anything with any justified confidence. That is annihilationist thinking. The fact of the matter is planes fly, cars drive, etc. The reason people don't jump off of a cliff yet will fly on an airplane is because they reason inductively whether they admit it or not.
