popper-logic-scientific-discovery

But let us now consider the view that (8) is false, or in other words,
that
is valid, and consequently
and also the following:
( + )
p(a ia j)>p(a i)p(a j)
p(a j, a i)>p(a j),
p(a n, a 1a 2 ... a n − 1) >p(a n)
appendix *vii 381
This view asserts that once we have found some k i to possess the
property A, the probability increases that another k j possesses the same
property; and even more so if we have found the property in a number
of cases. Or in Hume’s terminology, ( + ) asserts ‘that those instances’ (for
example, k n), ‘of which we have had no experience, are likely to resemble those, of which
we have had experience’.
The quotation, except for the words ‘are likely to’, is taken from
Hume’s criticism of induction. 4 And Hume’s criticism fully applies to
( + ), or its italicized verbal formulation. For, Hume argues, ‘even after the
observation of the frequent constant conjunction of objects, we have no reason to draw
any inference concerning any object beyond those of which we have had experience’. 5
If anybody should suggest that our experience entitles us to draw
argument may indeed be valid if it is used critically—against a theory which entails the
impossibility of knowledge, or of learning from experience. But one must be very careful
in using it. Empirical knowledge in some sense of the word ‘knowledge’, exists. But in other
senses—for example in the sense of certain knowledge, or of demonstrable knowledge—it
does not. And we must not assume, uncritically, that we have ‘probable’ knowledge–
knowledge that is probable in the sense of the calculus of probability. It is indeed my
contention that we do not have probable knowledge in this sense. For I believe that what
we may call ‘empirical knowledge’, including ‘scientific knowledge’, consists of guesses,
and that many of these guesses are not probable (or have a probability zero) even though
they may be very well corroborated. See also my Postscript, sections *28 and *32.
4 Treatise of Human Nature, 1739–40, book i, part iii, section vi (the italics are Hume’s). See
also my Postscript, note 1 to section *2 and note 2 to section *50.
5 loc. cit., section xii (the italics are Hume’s). The next quotation is from loc. cit., section vi.