Henry Kyburg wrote:
> Hume was perfectly correct in his argument, but what his argument
> demonstrated was that INduction was NOT DEduction. The mystery is why, for
> 250 years, so many philosophers have nevertheless insisted that induction
> should
> satisfy deductive standards. Popper is not an exception: for him "logic" is
> deductive logic, and so the logic of induction is no more than the deductive
> logic of refutation.
I suspect that most of the members of this list would agree that induction is
not deduction. The real issues -- thanks to the work of theorists such as Henry
Kyburg -- are different -- e.g., whether there are general standards of "valid"
or efficacious inductive argument.
>
>
> The latest primrose path is "Bayesianism".
Bayesianism is a primrose path only if one wants to use Bayesian theory to
reintroduce the discredited idea that induction is deduction. Bayesianism is
not necessarily a primrose path if one wants to assert that deduction is
_involved_ in induction.
> ...
>
> Now it could be claimed that all we ever need are posterior probabilities,
> and that probabilities are subjective, so that this is all we CAN do, and to
> do this requires "assumptions" or "prior probabilities. But there is
> an alternative point of view according to which probabilities are based on
> (not "identified with") frequencies, and according to which induction is
> perfectly possible.
There is another option: sometimes prior probabilities are based on frequencies
and sometimes they are based exclusively or principally on something like
"assumptions." Moreover, one should take into account (if this is the case)
that within well-defined domains (e.g., "fair" card games) Bayesianism
reasoning seems to work tolerably well and the necessary probability
calculations might in fact be as well or better done by a computer than by a
human being.
I am not a mathematician or statistician. I am a law teacher. It may be of some
interest to some members of this list that I _always_ saw Bayesianism as a way
of trying to think coherently about (the implications of) my own probability
assessments. As a teacher of the law evidence and as a former lawyer, I never
saw anything surprising or astonishing in the idea that many of the probability
assessments, indeed almost all of them, on which judgments about factual issues
in litigation rest spring from highly subjective or personal opinions or
judgments rather than on rigorously scientific or statistical studies or
observations. I think it is helpful and important to use logical tools that
help keep one's thoughts about probabilities and inferences in some semblance
of order. Witness, for example, what happens otherwise: Professor Alan
Dershowitz argues that evidence that Simpson previously beat his wife before
her death has little probative value because very few wife-beaters go on to
kill their wives.
Sincerely,
Peter Tillers
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