re: Axioms and Meaning

From: Mitchell J Porter (mjporter@U.Arizona.EDU)
Date: Sat Jul 28 2001 - 11:54:09 MDT

Precedence: bulk

Lee Corbin said

> More importantly, some maps are so
> detailed that they explicitly denote some object or
> relationship in the real world.
> This last claim is very controversial

Since there can be no controversy about the existence of
detailed maps, you must mean 'intrinsically', not 'explicitly'.

But symbols which are isomorphic to their referents still have
their meaning only by convention. If two rocks have similar shapes
it doesn't mean that one refers to the other... What isomorphisms
do is make the 'decoding' of symbols easier, by making it

The closest thing to a 'natural symbol' would have to be
some phenomenon which one learns to interpret as an indicator
of another phenomenon: "Where there's smoke, there's fire."
The interpretation of language is just an instance of this:
"Where there's symbols, there's communicative intent."

> My question: what about an axiom system? Are all the
> meanings (as in symbolic logic) only conventional? How
> does this relate to Godel's theorem?

Of course, my answer is going to be: yes, all the meanings
are conventional. But there *is* structure, so therefore
there is some sort of systematic mapping present. The real
question is, onto what? If it's onto 'mathematical or
logical facts', then you have to be some sort of realist
about the number two, the property of noncontradiction,
and so on. If not (if you want to be a nominalist materialist,
for example), then it seems like you have to take the road
of formalism... axiom systems are just games with rules,
and aren't actually about anything.

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