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.
The latest primrose path is "Bayesianism". The idea is that though we
cannot draw categorical conclusions from observational evidence, we CAN
attribute appropriate probabilities to those conclusions. The idea rests on
a confusion. What is the "conclusion"? The conclusion is either "Sentence
S is probable, relative to the evidence (and some other stuff)" or simply
"S". If the conclusion is "Sentence S is probable..." then that is a
DEductive consequence of the evidence and prior probabilities, assuming that
the probability calculus is just part of mathematics, i.e., part of logic.
Bayesianism itself gives us no grounds for accepting a categorical
conclusion like "S". (Note that classical stqtistics does give us such
grounds (relative to a tolerated level of error): to accept or reject a
hypothesis, even if it is a statistical hypothesis, is to adopt a
categorical conclusion S, not to assign a probability to S.)
What is wrong with Bayesianism? It depends on prior probabilities; when we
have justified prior probabilities and we want a posterior probability,
Bayesianism is just right. But sometimes we don't have a prior probability,
and sometimes we want a conclusion concerning frequencies or distributions
or facts. The Bayesian is also dependent on a sharp distinction between
data and hypothesis: the former can, and the latter cannot, be asserted
without a probability modifier.
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.
Example: It is a mathematical (set-theoretical) fact that given any property
P, almost all subsets of a population embody nearly the same proportion of P
as does the original population. Given a sample of the population, we will
rarely go wrong in supposing that the population is similar to the sample in
its relative frequency of P. Put more explicitly: unless we have some
REASON to be skeptical of the sample, we should take it as representative.
If we find 20% P's in our sample, we do not conclude "Probably the
population contains about 20% P's (though that is true) but categorically,
"The population contains about 20% P's." Of course we must be prepared to
abandon this claim in the face of new evidence; but nobody (sensible) ever
claimed that induction was incorrigible.
The issue depends on whether an inductive logic can be developed, and on
whether induction is a more efficient procedure for organizing and
representing knowledge than manipulating probabilities. I'd say the answer
to both questions is 'yes', but that's a matter of conjecture, not
inference.
Some references: Mine: Probability and the Logic of Rational Belief (1961);
The Logical Foundations of Statistical Inference (1974); A survey, about
1970: Probability and Inductive Logic; related: Epistemology and Inference,
1983. For related material, see Isaac Levi, Gambling with Truth, and also
his Enterprise of Knowledge.
Cheers,
Henry
