[FOM] Absolute truth vs. relative meaning and formal nature of mathematics

[A. Mani]

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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