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> Given the truth of finitely many formulae Fa, Fb, Fc,… in a language
> with names a, b, c,… for infinitely many different individuals; it
> would be nice to infer that (for all x)Fx has non-zero probability.
> Hume and Popper say one can’t, and I believe them.

> Nevertheless(!) can one define a language L like, but not necessarily
> identical to, that of ordinary first order logic (though it must have
> names for infinitely many individuals and some wff that are "singular"
> and some that are "universal"); such that a probability P may be
defined
> on a sigma-algebra of sets of wff of L with this property:
> For some universal wff U, there is a finite set S of singular wff, st
> S does not logically imply U,
> but P(U given S) = P({U} intersect S)/P(S) <> 0
> ?

> I feel that I have not worded that very clearly.  My apologies if I
> haven’t.  What I’m trying to ask (of course) is "Can finitely-many
> singular statements ‘give’ a universal statement a non-zero
> probability?"

> PP

     Yes, of course, given the context. The snowflake example comes to
mind. It depends on the way the propositions are worded. You might want
to read "Scientific Reasoning" by Howson and Urbach for a defense of
Bayesianism. They get heavily into the probability. I think Popper is
wrong (even though he is real big in my book) about meaning not being
important in the philosophy of science. I think the Raven’s paradox
supercedes the problem of induction. Of course, this thing didn’t come
along ’till way after Hume’s death (another one in my hall of fame.)
Give Quine a try. He’s great also. Him and Popper disagree with what you
are driving at above, Keep up the good work, PP.

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