Continuing the thoughts on induction I began last week, re: David Stove. If we know that there are 100 swans in the world, and we have seen each swan, recording each as white, then the conclusion "all swans are white" is a matter no longer of induction but of deduction. I'm not sure how it would go formally, but I'm pretty sure you get to that conclusion from those premises. [Even there, one might wonder -- is the first swan that I checked still white? Maybe they can go black as they molt, or something? But let's ignore the impact of the passage of time on swans.] I've seen all swans, all the swans I've seen are white, therefore all swans are white. That's a deduction, so nobody likely objects to calling it a proof.
If so, then let's relax the assumption of completeness: the gradual addition of swans to my data base, the movement from 20 to 30, swans, thus from 20% to 30% of the universe, remains induction, remains something less than proof, BUT is important. For if we're on the same page so far, we may agree that induction is a process that approaches deduction at the limit. It approaches proof-ishness as it proceeds. This takes some of the mystery out of the question, does it not?
But, you will object, we don't know how many swans there are, so the presumption is unrealistic. Well, that hardly makes it unique among philosophical thought-experiments, but perhaps we can relax that too. Simply assume that however many swans there are in the world, their number is finite, and (if it is growing, as given a food supply and a lack of predators it may well be) we can reasonably assume that humans add to a data sample more rapidly than the universe of swans itself increases. In this less demanding situation, it will still be the case that our sample is moving in the direction of universality. Is that enough to make our increasing confidence rational?