Date: Thu, 2 Oct 1997 08:10:17 -0400
To: bhaskar-AT-jefferson.village.Virginia.EDU
From: Doug Porpora <porporad-AT-duvm.ocs.drexel.edu>
Subject: BHA: Math and probability


Hi everyone,

John,

I'm intrigued by the ontological status of mathematics too. Although it
seems like mathematics is something we invent, there are mathematical
properties we only discover. That such properties need to be discovered
implies that they have a reality independent of us.  Of course, if
mathematics is a reality independent of us, where does it exist?  And it
seems strange to think that whatever mathematical system we might happen to
invent already existed somewhere waiting for us.  Although I am not
entirely satisfied with the solution, it seems to me that some ideas like
mathematics are emergently material -- that is, they have objective or
material properties.

Re probability, I'm not sure, but it seems that probability is subsumable
under set theory.  Probability refers to sets of possible outcomes.  If so,
then as some have suggested, probability may result either
epistemologically or ontologically.  Epistemologically, we may just be
asking, given what we know, how likely a certain outcome is.
Ontologically, as in the case of the urn, the probability of drawing six
black balls from an urn with a particular mix is equivalent to a ratio of
sets:  the ratio of the set of outcomes of size six in which all balls are
black to the set of all outcomes of size six.

In that case, the probability is a feature not of our ignorance but of the
actual mix in the urn. There is a sense too in which we can still speak of
probability in the past.  If we have just drawn six balls from an urn
containing six black balls and a thousand white balls, then, in the domain
of actuality, the probability of our having drawn six black balls is one.
In the domain of the real, however, we can marvel at the wild improbability
of our having drawn six black balls from that particular mix.  In that
case, the improbability of the actual outcome might be something in need of
explanation. Physicists have recently been puzzling over probability in
just this sense in the case of the so-called anthropic coincidences of
cosmology.

doug

doug porpora
dept of psych and sociology
drexel university
phila pa 19104
USA

porporad-AT-duvm.ocs.drexel.edu




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