Dear Robert & Friends,
"The" problem of induction is many problems.
One problem is what is meant by "induction." Cf. abduction? cf. factual
inference?
One question is whether induction is _ever_ possible. (Another question
is what such a seemingly foolish question could possibly mean.)
If induction is in principle or sometimes possible, another question is
when -- under what circumstances -- is induction possible.
Another question is whether induction takes a general form-- does all
induction follow some general pattern or form -- or are there many
varieties of (efficacious) induction? (This may in part bring us back to
the question, What is meant by "induction"?)
Then there is the _Humean_ version of the problem of induction: if the
concept of causation is incoherent or untenable, how can one ever draw
any inferences about unknown events or about events that have not yet
happened?
Another form of the problem of induction is whether induction can
involve inference from "singular" to "singular" or from "particular" to
"particular" -- i.e., can induction (ever) involve a judgment about the
occurrence or non-occurrence of some (singular?) event based on
observation or knowledge of some other (singular?) event or events
without any reference to a covering generalization, causal law, or
lawlike statement? See J. Pearl for one answer. (But query: What is a
"singular" event?)
Some observers take the view that "the" problem of induction proper
deals with the effort to construct generalizations or the like from
"singulars" or single instances or events. Compare this sentence with
the sentence immediately above.
Another form of the problem of induction is the following: Do animals
engage in induction? Do amoebae do so?
Another question about induction is whether "the" problem of induction
devolves into the question of the "logic" of induction.
Another question is whether induction can or must have "tacit" elements.
I could go on and on. But I won't.
Perhaps what Robert is most interested in (I have erased his original
message, so I'm not sure what his original question was) is what Hume in
particular thought about when he worried about what we now call
"induction." Keep in mind that Hume was, for the most part, a
nominalist. This means that the idea of underlying causes or connections
did not and could not make much sense to him. (But Hume was not always
consistent in his general views. Sometimes he was less nominalist in his
thinking than at other times.) In any case, if Hume was a radical
nominalist, the rising of the sun day after day was something of a
mystery or a puzzle to him. You might well ask whether it should have
been. (Hume himself knew that he was willing to bet his life and all
else that the sun would rise the "next day." {Of course, we will all bet
that someday -- e.g., 80 billion years hence -- it _won't_ rise. But
that's another matter.}) Perhaps the idea of underlying (or not directly
observable) causes is not really so mysterious or implausible after all.
Hume appealed and appeals to many statisticians of a certain stripe
because many statisticians of a certain stripe were or are inclined to
think that "association" or "repetitive pattern" {redundancy!} is all
there is. You are free to say, "That's a crazy idea!" If you do that, it
does not follow that you must conclude that probability and uncertainty
fall out of the picture. Once again: ask Pearl or Shafer for a contrary
view. One can, of course, believe in "causes" and yet believe that
effects and the like are probabilistic; causality, uncertainty, and
probability are entirely compatible. (But this is not necessarily to say
that all induction or inference must involve explicit causal
reasoning.But that's not a can of worms we should open again now.)
I know the above stuff is loose. But forgive me: I am a simple law
teacher.
Yours,
Peter T.
P.S. On a more practical note: all of Hume's popular works are available
on a single CD -- the "Past Masters" series, I think it is. I may be
able to find the exact name of this CD. If you're interested, send me a
private message. But give me lots of time to look for the name.
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