[FOM] Absolute truth vs. relative meaning and formal nature of mathematics
A. Mani
a_mani_sc_gs at yahoo.co.in
Mon Feb 6 19:22:55 EST 2006
On Tuesday 07 February 2006 01:16, Vladimir Sazonov wrote:
> Mathematics is rather a lot of various
> formal systems and related intuitions some of which can have relatively
> universal character, but never absolutely universal.
I agree with most of what you say. But it should be noted that given a level
of development of mathematical knowledge, there are common universals between
them. Not that they become defining universals for mathematics but at least
for something minimal *. Any statement of formal consistency either
proof-theoretic or model-theoretic is a weak concept of truth. Again things
like 'admissible rules' have truth in them. There are relevant concepts of
truth evolving ... but 'absolute' may mean something like a minimal cover in
a concept lattice.
* For example the difference between the function symbol and its
interpretation on a domain is universal to mathematics. This anti-Fregean
perspective is not always maintained in other domains.
A. Mani
Member, Cal. Math. Soc
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