In philosophy we talk about this through the problem of induction, which arises because the three standard options for justifying its validity are unsatisfactory: assuming it is valid as a matter of dogma, proving it is a valid method of finding the truth (which bumps into the problem of the criterion), or proving its validity recursively (i.e. induction works because it’s worked in the past).
It’s not clear that the circular justification of induction is invald.
Circularity is often condemned our of hand, but why? In the context of deductive reasoning circularity implies quodlibet, the ability to pricprove anything. There are infinite arguments of the form “P, therefore P”. Moreover , it would be possible to prove infinitely many contradictions by setting Q=not P.
That’s in the context of deduction. The circular justification of induction doesn’t have the problem of quodlibet, because when you are doing induction you are not starting from an arbitrary claim, you are starting from evidence.
One of the standard approaches is to start from what would be the recursive justification and ground out the recursion by making additional claims, and a commonly needed claim is known as the uniformity principal, which says roughly that we should expect future evidence to resemble past evidence (in Bayesian terms we might phrase this as future and past evidence drawing from the same distribution). But the challenge then becomes to justify the uniformity principal, and it leads down the same path you’ve explored here in your post, finding that ultimately we can’t really justify it
I assume you mean we can’t justify it deductively, as a true axiom. But the hypothesis that regularities continue is a very simple explanatory hypothesis—there’s only way of being the same, but many ways of being different.
It’s not clear that the circular justification of induction is invald.
Circularity is often condemned our of hand, but why? In the context of deductive reasoning circularity implies quodlibet, the ability to pricprove anything. There are infinite arguments of the form “P, therefore P”. Moreover , it would be possible to prove infinitely many contradictions by setting Q=not P.
That’s in the context of deduction. The circular justification of induction doesn’t have the problem of quodlibet, because when you are doing induction you are not starting from an arbitrary claim, you are starting from evidence.
I assume you mean we can’t justify it deductively, as a true axiom. But the hypothesis that regularities continue is a very simple explanatory hypothesis—there’s only way of being the same, but many ways of being different.