The following is lifted shamelessly from the new DFW book, which I’ve been enjoying since I picked it up on Friday. If you’ve read Hume before, or even if you haven’t,¹ you’ll recognize in the story of Mr. Chicken a wonderfully intuitive explanation of the Humean problem of induction (as opposed to the new problem of induction, which includes such things as Goodman’s grue puzzle):

“If you had the right classes in school, however, you might now recall that the rule or principle you want does exist - its official name is the Principle of Induction. It is the fundamental precept of modern science. Without the Principle of Induction, experiments couldn’t confirm a hypothesis, and nothing in the physical universe could be predicted with any confidence at all. There could be no natural laws or scientific truths. The P.I. states that if some thing x has happened in certain particular circumstances n times in the past, we are justified in believing that the same circumstances will produce x on the (n + 1)th occasion. The P.I. is wholly respectable and authoritative, and it seems like a well-lit exit out of the whole problem. Until, that is, it happens to strike you (as can occur only in very abstract moods or when there’s an unusual amount of time before the alarm goes off) that the P.I. is itself merely an abstraction from experience … and so now what exactly is it that justifies our confidence in the P.I.? This latest thought may or may not be accompanied by a concrete memory of several weeks spent on a relative’s farm in childhood (long story). There were four chickens in a wire coop off the garage, the brightest of whom was called Mr. Chicken. Every morning, the farm’s hired man’s appearance in the coop area with a certain burlap sack caused Mr. Chicken to get excited and start doing warmup-pecks at the ground, because he knew it was feeding time. It was always around the same time t every morning, and Mr. Chicken had figured out that t(man + sack) = food, and thus was confidently doing his warmup-pecks on that last Sunday morning when the hired man suddenly reached out and grabbed Mr. Chicken and in one smooth motion wrung his neck and put him in the burlap sack and bore him off to the kitchen. Memories like this tend to remain quite vivid, if you have any. But with the thrust, lying here, being that Mr. Chicken appears now to actually have been correct - according to the Principle of Induction - in expecting nothing but breakfast from that (n + 1)th appearance of man + sack at t. Something about the fact that Mr. Chicken not only didn’t suspect a thing but appears to have been wholly justified in not suspecting a thing - this seems concretely creepy and upsetting. Finding some higher-level justification for your confidence in the P.I. seems much more urgent when you realize that, without this justification, our own situation is basically indistinguishable from that of Mr. Chicken. But the conclusion, abstract as it is, seems inescapable: what justifies our confidence in the Principle of Induction is that it has always worked so well in the past, at least up to now. Meaning that our only real justification for the Principle of Induction is the Principle of Induction, which seems shaky and question-begging in the extreme.”

¹ I take it back. Math majors who have never been exposed to analytical philosophy are required to read some Hume (at least before mailing me to express their righteous indignation). Start with the Enquiry, particularly Section IV. You can even read it for free, if your delightfully argumentative heart so desires.