I resolve an apparently unresolved dispute about how probable uniform experience makes an extrapolation from it, and draw some general lessons about such enumerative induction. Uniform experience does not necessarily confer a high probability on an extrapolation of or generalization from that experience. Rational extrapolation or generalization typically involves a lot of specific background information, though not necessarily a general assumption that nature is uniform or that the future will resemble the past. And new evidence which is highly likely on (...) one hypothesis but highly unlikely on any of its competitors does not necessarily make the former hypothesis highly probable. (shrink)

Does a high degree of confirmation make an inductive argument valid? I will argue that it depends on the kind of question to which the argument is meant to be providing an answer. We should distinguish inductive generalization from inductive extrapolation even in cases where they might appear to have the same answer, and also from confirmation of a hypothesis.

In an enumerative induction we project a property found in all the examined members of a class to a hitherto unexamined member of that class. I consider an unresolved disagreement between Stephen Thomas and John Nolt about how likely the conclusion of one example of such reasoning is, given the premisses. Reflection on their controversy, and on the example, indicates that many textbook commonplaces about enumerative inductions are false. In particular, uniformity of the examined members of a class does not (...) necessarily make it highly likely that the next member will have the target property; this proposition may still be unlikely, or on the other hand be quite definite, depending on our background knowledge. Also, enumerative induction need not rely on any general assumption about the uniformity of nature or the resemblance of the future to the past. (shrink)