On the blog of his "Rationally Speaking" site, American (by adoption) polymath Massimo Pigliucci, reflecting the influence of a certain Scottish polymath, recently wrote that the problem with induction is "that if the only justification for induction is inductive, it is circular. If one cannot find any other justification, then there is no rational basis for induction. It still works, of course, as Hume surely knew... ."
It "works," he concedes, but that is no "justification." The only one he'll recognize for induction is induction itself, and that simply will not do -- because it is "circular." No, induction must be justified by something other than itself. Of course, that something-other-than-itself must also be justified by something other than itself ... and so on. Unless we're prepared to defend infinite regress, we must acknowledge that there comes a point - the foundational one - where we have something that justifies/explains/proves itself. In epistemology, induction is that point.
And is that "circular"? Is it a "tautology"? No. That charge is unfounded at this fundamental level. Consider the difference between the statements "A is A" and "A gazuatron is a gazuatron." The latter is useless as a definition: It's not obvious what a "gazuatron" is - it requires explanation in terms other than itself. But how do we define A - "thing" - in other, more fundamental terms? We can't, because it is the fundamental definition. Without this law of identity, we couldn't have the commutative (A+B=B+A) and associative ([A+B]+C=A+[B+C]) laws of mathematics, among other things. If someone insisted that we define "thing" (and won't accept "a thing apart from everything else"), all we could do is pick up a cup, a pen, a rock - the physical world, the universal foundation.
The failure to recognize a fundamental, non-arbitrary, objective context is the primary problem that bedevils people when they encounter axioms in the epistemology of Ayn Rand and the methodology of Ludwig von Mises. And as such, it is surely a problem not without ethical and political implications. ...
. Suggested reading: Nicholas Dykes' discussion of H.W.B. Joseph's critique of Hume.