>1. Do you think induction _needs_ a "justification"? If a justification is not
>supplied, should we say that induction is illegitimate? Or should we begin by
>assuming that induction sometimes works and that we should continue to believe
>that it works (sometimes) unless someone shows that it does not work or cannot
>work? Is it your position that induction is impossible?
This is a very difficult question, the answer to which depends largely
upon what you mean by "need". Perhaps somebody who continued in their
study of philosophy (instead of going switching to computer science as I
did) would have more to say about this.
Personally, I give induction the status of a working assumption that I
adopt for lack of an alternative. Planning and acting are neutral
activities in a world where induction fails; they have no effect on my
expected utility. However, planning and acting are quite useful in a
world where induction succeeds. So, it seems to make sense to continue
to plan and act as if I could count on induction holding since I can
only benefit from such activities.
This leads to the somewhat odd conclusion that acting as if induction
were true may be rational even if one cannot establish that induction is
valid. In this sense, induction might not need justification.
However, this a fairly off the cuff comment. While I'm quite confident
of the difficulties with formal arguments for the validity of induction,
I admit that I'm less confident and less well-read in how to deal with
the aftermath.
>2. Does deduction need a justification? If so, would a deductive justification
>of deduction be circular? Would only a non-deductive justification (e.g., an
>inductive justification?) of deduction be non-circular? Should we assume that
>deduction is invalid unless someone can demonstrate the contrary?
Well, any reasoning system needs axioms and we generally pick axioms
that are self-evident. A world in which deduction is not valid is
unthinkable to us and one wonders if thought itself would be possible in
such a world. Even as on outsider to such a world, it's not clear how
one could ever hope to make a truthful statement about it.
While we could give induction the status of an axiom, I see two
problems:
1) The failure of induction is quite within the scope of our
imagination. We can talk about a universe (perhaps not our own) in
which induction fails and we can make somewhat sensible statements about
such a universe.
2) We can imagine ways that such an axiom could be false. What happens
if we have as an axiom that the world is predictable and then we
suddenly observe chaos?
Induction is a strange beast.
--
Ron Parr email: [EMAIL PROTECTED]
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Home Page: http://robotics.stanford.edu/~parr
