From: pmsc13sg@UMASSD.EDU (Stephen Grossman)
Subject: Re: Semantics of Set Theory
Reply-To: pmsc13sg@UMASSD.EDU
Organization: UMASS DARTMOUTH, NO. DARTMOUTH, MA.
Date: Mon, 4 Jan 1993 19:54:06 GMT

[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. 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. They flirt with metaphysics in a manner suggesting that math 
bases meta instead of the proper hierarchy: meta bases math. And rational 
knowledge is hierarchical (eg, arithmetic prior to alegebra). It may even be 
that Randall and/or Zeleny have parts of an objective philosophy of math (tho 
improbable). That would be irrelevant since it would need some, particular 
philosophy for validation. 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. 
	I studied phil. of language under a professor who permitted students to 
debate philosophy while demanding blind faith in an unexamined "science" of 
language (There is no science of language). When I inferred the philosophy 
implicit in this "science" of language it was consistent with her philosophy. 
She strongly resisted the implications of this "coincidence." I noted that she 
would have rejected any science of language inconsistent with her philosophy 
but got no reply. Apart from the intellectual fraud, philosophy causes science.
________________________________________________________________________________
	"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>
================================================================================
Newsgroups: sci.philosophy.tech