From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: Semantics of Set Theory
Organization: Boise State University
Date: Mon, 4 Jan 1993 21:53:31 GMT

In article <C0CHy7.6Hx@umassd.edu> pmsc13sg@UMASSD.EDU writes:
>[This is a reply to e-mail from Chris Holt <chris.holt@newcastle.ac.uk> 
>(Dec.28). His message was a reply to my Dec. 25 post. He has given permission 
>to quote his e-mail.]
>
>In article <BztroA.6Bz@umassd.edu>, pmsc13sg@UMASSD.EDU (Stephen Grossman) 
>writes
>
>>Can anyone help me distinguish the "argument" of Randall and [Zeleny] from the
>>ravings of mental patients? It seems much ado about nothing, a way for the
>>intellectually challenged to pass the day until nurse brings another sedative.
>
>CH	It depends on what you know (and believe) about math. foundations. If 
>you understand basic ZF set theory, as described, for example, in Fraenkel, 
>Bar-Hillel, and Levy, then you start having an inkling about where they're 
>coming from. Quine's NF was an attempt to get around the class hierarchy of 
>russell. Nowadays, many people think you shopuld start in category theory, 
>modeling logics in toposes. But if you don't know math, it's a bit rash to 
>dismiss it all as ravings.
>
>In my experience, objectivist writings ignore the entire area because the 
>authors were math. incompetent; but tastes differ.
>
>SG	Philosophy is the context of science. Science (inc/math) cannot prove 
>nor refute philosophy. Philosophy is the study of the basic facts of existence 
>whereas science is the study of non-basic facts.

This is an appalling assertion: see below.

 Studying the philosophy of 
>math is proper, once a specific philosophy has been proven as the context. 
>Randall and Holmes bypassed the need for philosophy by using math in place of 
>philosophy.

Perceptive of you to notice that.  By the way, I am one person,
Randall Holmes.

 They flirt with metaphysics in a manner suggesting that math 
>bases meta instead of the proper hierarchy: meta bases math.

I'm afraid not (from the Objectivist standpoint).  Rand's theory of
concept formation depends on mathematics.

 And rational 
>knowledge is hierarchical (eg, arithmetic prior to alegebra).

Certainly.  But your understanding of the hierarchy is defective.
Mathematics carries its own metaphysics around with it, in the form of
symbolic logic and set theory, which in turn founds such practical
disciplines as arithmetic and algebra.  Mathematics, if taken
seriously, is a self-sufficient philosophical system (relative to its
own internal needs; there remains the question of how it is related to
the physical world).

 It may even be 
>that Randall and/or Zeleny have parts of an objective philosophy of math (tho 
>improbable).

How generous of you to grant the bare possibility.

 That would be irrelevant since it would need some, particular 
>philosophy for validation.

See above.

 Even the most abstract science cannot justify 
>science. Science has far too much prestige in the modern world. It must be 
>subordinate to philosophy, hopefully an objective philosophy, but to SOME 
>philosophy. Philosophy must not be made consistent with science. It is science 
>which must be made consistent with philosophy. Science always contains an 
>implicit philosophy which must be judged without any reference to
science.

Science does in fact contain an implicit philosophy.  Most explicit
attempts at philosophy of science (especially recent ones) have very
little to do with the implicit principles which actually make science
work.  Some of these are embodied in mathematics, which is explicitly
heavily used by science, and makes its own implicit philosophical
commitments much clearer than science does.  This implicit philosophy
should not be judged "without reference to science"; one of the most
powerful arguments for the validity of the underlying philosophy of
science (whatever it is) is that science _works_. 

One of the danger signals that our understanding of the implicit
philosophy of science is defective is that the working philosophy of
most mathematicians (realism, so-called "platonism") is incompatible
with the "official" (empiricist and nominalist) philosophy of science.
The historical function of the "official" philosophy, which has helped
to make science a success, has been to keep philosophers from screwing
up the workings of the system.  Science allows no one to dictate to it
that certain facts are "basic" and beyond its purview; it will no more
allow this privilege to Objectivists than to churchmen.  The implicit
philosophy of science is _part of science_ (except for the part
inherited from mathematics), just as the implicit philosophy of
mathematics is part of mathematics.

Uncovering explicitly what the working philosophy of science is would
be a worthy endeavour, but it would be a service to science, and would
not make some other discipline the master of science.

[...]

>Apart from the intellectual fraud, philosophy causes science.

This is a doubtful proposition; influences have run in both directions.

>________________________________________________________________________________
>	"In that world, you'll be able to rise in the morning with the spirit
>you had known in your childhood: that spirit of eagerness, adventure and cer-
>tainty which comes from dealing with a rational universe."
>                                                              AYN RAND
>--------------------------------------------------------------------------------
>Stephen Grossman <PMSC13SG@UMASS.EDU>
>================================================================================


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu