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From: david@fisher.UUCP (David Rubin)
Newsgroups: net.religion.jewish
Subject: Re: Proof of Outlandish Propositions
Message-ID: <722@fisher.UUCP>
Date: Mon, 5-Aug-85 09:28:20 EDT
Article-I.D.: fisher.722
Posted: Mon Aug  5 09:28:20 1985
Date-Received: Tue, 6-Aug-85 09:46:33 EDT
References: <293@mit-athena.UUCP>
Distribution: net
Organization: Princeton University Department of Statistics
Lines: 52

> I would  like to see  Rosen prove that  the universe can  be described
> mathematically.   This assumption is fundamental   in  all science and
> works well.   But this is  merely phenomenology and  not proof.   Also
> the assumption seems to  break down in  certain domains of physics and
> many mathematicians cringe  at what the  field theorists call   proof.
> You  may   consult Shlomo Sternberg and  Arthur   Jaffe about this  at
> Harvard.    Further, the  Hilbert,   Bernays,  Goedel   formulation of
> mathematics  fails in   some  sense  because  any mathematical  system
> interesting  enough to describe the universe   is incomplete which  is
> distressing if you believe math can provide a  complete description of
> the universe  (although Weinberg has a  slightly   different opinion -
> see Gravitation and cosmology).  I have  heard both Andrew Gleason and
> David Kazhdan at Harvard make this point.

I cannot answer whether Rosen indeed believes the universe can be so
defined, but it appears to me that such criticisms confuse mathematics
with science.  The latter is fundamentally empirical, not logical, in
nature; self-consistency (the standard of logical/mathematical systems)
is given far less weight than consistency with observation.  Mathematics
is used by the scientist as a means, not an ends in itself, in an attempt
to describe the pattern of all observations as compactly as possible.
The scientist will often have many explanations that fit the data
available to him, in which case he will favor the simplest one that does
not conflict with the data and still remains "testable" (subject to
refutation).

Thus, the empiricist/scientist does not presume that there exists some
explicit mathematical formulation of the laws of the universe, but
rather that mathematical formulations may successfully approximate
those laws to such an extent as to provide some mechanism to
accurately predict future phenomena.  For what is "understanding" of a
system if not the ability to foresee its behavior?  Science, in the
end, PROVES nothing, for that is not its intent; it stands or falls on
how well it DESCRIBES.

As Martillo implies, religous endeavors can assume mathematical (i.e.,
logical) qualities; this is especially characteristic of Rabbinic 
Judaism, which proceeds from a set of assumptions (frequently disputed)
to arrive at a conclusion.  However, this does nothing to refute those
who would approach cosmic matters empirically, rather than by religous
doctrine or mathematical analysis.

An overly simplified synthesis of how these differing approaches
might influence dogma follows: the religous would declare that God
exists, the logical might declare either way, depending upon their
assumptions and the quality of their logic, and the empirical would
not declare either way, save perhaps to declare the issue unresolvable
(divine action being indistinguishable from other phenomena: is it
God (however defined), or does our model merely need an overhaul?).

					David Rubin
			{allegra|astrovax|princeton}!fisher!david