Robert,
It's been some time since I was a philosophy student, but here's my
understanding of the state of Hume's critique. Post-Kant, our
understanding of Hume's critique of induction is that it simply states
that induction is not an *analytic* form of inference. That is, it is
not a form of inference that is true by virtue of the form of the
inference, in the way that logical deduction is.
The fact that induction is not as firmly founded as deduction, though,
shouldn't really disturb us, since part of the reason that deduction
is firmly founded is that deduction does not, in some sense, actually
produce information; it simply reveals what is implicitly there
already.
I don't have any primary sources at my fingertips now, but the Oxford
Companion to the Mind, in its entry on "Analytic Proposition" gives:
"Thus, Kant, taking judgements expressed by propositions to have the
form 'A is B' defined an analytic judgement as one where 'the
predicate B belongs to hte subject A as something which is (covertly)
contained in the concept A.'.... An analytic statement thus cannot be
denied without contradiction and is logically necessary.....[this]
leads to speaking of analytic propositions as true in virtue of the
meanings of words."
under INDUCTION we have
"It is clear from this account that ampliative inferences [those whose
conclusions are not already implicit in their premises] are by
definition not deductions and hence not deductively valid.....That
gives rise to the so-called problem of induction, but from a purely
logical standpoint it can appear to be a matter of lamenting the fact
htat not all of the inferences which we make have the rigour and
compulsion of deductions, coupled, perhaps with the insinuation that
only deductive inferences are rationally grounded. But, against the
insinuation, it is far from obvious why good reasons for a conclusion
must preclude its negation on pain of contradiction. It is clearly
possible to distinguish good from bad reasoning which is not in this
way absolutely compelling."
So I don't think you should worry about this too much, unless you want
to write a dissertation in philosophy instead of engineering....
Hope this is helpful,
Best,
Robert
