Ron Parr wrote:
> 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.
It sounds like we are back to Pascal's Wager, but now we have induction
starring in the role formerly played by God!
I enjoy philosophy as a spectator sport as much as the next person, and I
remain in awe of those such as Ron Parr who continue to follow Hume in their
extreme skepticism about induction. They display true courage of their lack
of convictions -- in the face of what seems so overwhemingly obvious to the
rest of us, that induction works often but not always. The same is true of
my car, and I'm quite happy with it.
In a practical sense, we cannot put greater trust in _deduction_, because of
our fallible premises and rules, not to mention our fallible inferencing. As
I understand it, the rationale for induction is just about as weak and
circular as the rationale for deduction:
"In the 1950s, Nelson Goodman dissolved the traditional problem of induction
by pointing out that the validity of deduction consists in conformity to
valid deductive principles at the same time that deductive principles are
evaluated accroding to deductive principles. Justification is then just a
matter of finding a coherent fit between inferential practice and
inferential rules. Similarly, inductive inference does not need any general
justification but is a matter of finding a set of inductive principles that
fit well with inductive practice after a process of improving principples to
fit with practice and improving practice to improve with principles. Instead
of the old problem of coming up with an absolute justification of induction,
we have a new problem of compiling a set of good inductive principles."
(p400, Paul Thagard, "Induction" in the _MIT Encyclopedia of Cognitive
Sciences_, MIT Press, 1999.)
I think it's time that we accepted that induction is just as rational as
deduction. Whether we do or not, the interesting "problem of induction" is
not whether induction is "true" or "rational", "axiomatic" or
"self-evident", but rather _when_ does it work and how far. There are
massive literatures in statistics, psychology, machine learning, and UAI (to
name but a few) that address this important problem and have generated many
interesting and useful results, theoretical and empirical. At this point,
Hume is a true red herring.
(To David Poole)
The lesson I draw from Goodman's Grue-Bleen paradox is that model simplicity
is a key issue in induction, explanation, and learning -- a point at least
as old as William of Occam. While some logicians may enjoy confusing
themselves and others on this issue, scientists with even a smattering of
knowledge about color know very well why blue and green are more useful
constructs for understanding and predicting the world than grue and bleen.
Max
> >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]
> --------------------------------------------------------------
> ------------
> Home Page: http://robotics.stanford.edu/~parr
>
