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- Newsgroups: sci.philosophy.tech
- Path: sparky!uunet!pmafire!mica.inel.gov!guinness!opal.idbsu.edu!holmes
- From: holmes@opal.idbsu.edu (Randall Holmes)
- Subject: Re: Semantics of Set Theory
- Message-ID: <1993Jan4.215331.18751@guinness.idbsu.edu>
- Sender: usenet@guinness.idbsu.edu (Usenet News mail)
- Nntp-Posting-Host: opal
- Organization: Boise State University
- References: <BztroA.6Bz@umassd.edu> <C0CHy7.6Hx@umassd.edu>
- Date: Mon, 4 Jan 1993 21:53:31 GMT
- Lines: 121
-
- 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
-