Hmm, you'll have to be more precise on what the philosophical account of induction is. To be honest I don't think so, because mathematical induction is a rather strange notion. I'll try to explain it to you, and why it works, as best I can.
Consider the natural numbers 1,2,3, and so forth. They are 'well ordered', which I believe means that take any finite subset of them and there will be a least element. So if you pick a subset, say the numbers between 10 and 20, then there will be a smallest number - in this case 11.
This then allows you to prove something about the smallest element. Say I am able to prove that yes, in fact, 11 is a natural number. Suppose I am then able to prove that if X is a natural number, X + 1 is a natural number. The conjunction of these two statements suffices to prove it for all X greater than the smallest number I started with. As far as I know that is all that mathematical induction is. It is unclear to me how this addresses issues like generalizing universal laws from a limited set of examples. If you want to formalize philosophical notions of induction, which seems to be a good idea, I recommend studying computational learning theory.
That Fredric Shmidtt thing sounds cool. I am excited about what I read in the first couple chapters of an artificial intelligence textbook - namely that the idea of rational agents is being set up as the foundation of A.I.
Consider the natural numbers 1,2,3, and so forth. They are 'well ordered', which I believe means that take any finite subset of them and there will be a least element. So if you pick a subset, say the numbers between 10 and 20, then there will be a smallest number - in this case 11.
This then allows you to prove something about the smallest element. Say I am able to prove that yes, in fact, 11 is a natural number. Suppose I am then able to prove that if X is a natural number, X + 1 is a natural number. The conjunction of these two statements suffices to prove it for all X greater than the smallest number I started with. As far as I know that is all that mathematical induction is. It is unclear to me how this addresses issues like generalizing universal laws from a limited set of examples. If you want to formalize philosophical notions of induction, which seems to be a good idea, I recommend studying computational learning theory.
That Fredric Shmidtt thing sounds cool. I am excited about what I read in the first couple chapters of an artificial intelligence textbook - namely that the idea of rational agents is being set up as the foundation of A.I.
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