[FOM] The meaning of `set'
Muller F.A.
F.A.Muller at phys.uu.nl
Mon Feb 20 06:46:57 EST 2006
Dear all,
All postings about the similarities between
finite and infinite sets, the colloquial use
of the word `set', about the acceptability
of the axioms of ZFC or extensions of it,
and more, orbit around one deep philosophical
problem: the problem of meaning, of what
meaning `is', of how expressions obtain
meaning.
Since Wittgenstein it has become a triviality
to say that our use of expressions is
constitutive for their meaning. But only
very recently has Paul Horwich made an attempt
to propound a theory of meaning based on this
triviality. The word `theory' is meant here
in the sense in which philosophers use it,
so mathematicians are warned there are
differences with how they use the word
`theory'. Nonetheless the mentioned theory
of meaning can be formulated as having
five postulates; on the basis of those
postulates then several outstanding problems
in the philosophy of language can be
solved.
Important for readers of this list is
that this theory has been applied to
mathematics, in particular to the word
`set' and to set-theory in general.
For those who are interested, here are
the references:
`The Implicit Definition of the Set-Concept'
Synthese 138 (2004) 417-451
`Deflating Skolem'
Synthese 143 (2005) 223-253
I submit that without a clear view of how
expressions obtain meaning in language,
the discussions concerning the topics mentioned
in the opening paragraph of this posting
are destined NOT to go to the heart of the
matter.
Many things said by for example Harvey Friedman
about the set-concept fit the view expressed
above and expounded in the two references seamlessly.
Salute,
--> F.A. Muller
**********************************************
Inst History & Foundations of Science & Math.
Utrecht University
f.a.muller at phys.uu.nl
**********************************************
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