Ronald,
>When you apply Bayes rule, you are assuming that future outcomes will be
>drawn from the same distribution as past outcomes, i.e. you are assuming
>that induction works.
Not true! ALL I am assuming is basic, timeless Bayes Rule.
I am beginning with a prior distribution which places some mass on "simple
universe," some mass on "unlearnable universe," and some mass on "edge of
chaos universe evolving a self-understanding." Then I am conditioning on
data from what is observable to me in the present, which is all the data we
ever have. This gives me a posterior distribution on all three hypotheses.
"Simple universe" gets thrown out immediately, leaving me with
non-negligible mass on "unlearnable" and "edge of chaos." For me (maybe
not for you) there is far more mass on "edge of chaos."
None of this involved time at all. In the very most unlearnable of the
unlearnable hypotheses, the past, present and future have absolutely
nothing to do with each other. The present materialized exactly as it is
right now, including my memories of my childhood and this quaint idea I
seem to have that I'm learning, and is going to dissolve again in an
instant. For me (maybe not for you) this hypothesis has very low posterior
probability, because the likelihood of my seeing something I can understand
so well as a temporally evolving universe is quite high under the "edge of
chaos" hypothesis and miniscule under this "very, VERY unlearnable"
hypotheiss.
>Therefore, you cannot use Bayes rule to justify
>induction without falling into the trap of circular reasoning.
This is not circular at all. It's just Bayes rule. I'm starting with a
prior, conditioning on what I see, and ending up with a posterior.
Under "very VERY unlearnable" I have a very vague distribution on what's
going to happen an instant from now. Under "edge of chaos" I have a pretty
good idea for a while into the future.
>More generally, Bayes rule is not an escape from the requirement that we
>reason non-circularly. If you construct a hypothesis that is
>self-reinforcing, then you have constructed template which can be used to
>justify anything.
I cannot justify anything.
I can't justify belief in the tooth fairy, or that I will wake up tomorrow
morning with purple spots all over my body, or that the sun won't rise
tomorrow. I can't prove them wrong, but they have very low evidential
support.
Kathy
