[FOM] Platonism and Formalism

Vladimir Sazonov V.Sazonov at csc.liv.ac.uk
Fri Sep 26 14:43:13 EDT 2003

Torkel Franzen wrote:

> Karl Podnieks says:

>   >Which properties of structures and methods used in mathematics and
>   >metamathematics are leading to the illusion that the natural number
>   >system is a stable and unique mathematical structure that exists
>   >independently of any axioms and cannot be defined by using axioms?
>   I think the more interesting question is how the (Sunday) conviction
> arises that the properties of the natural numbers are somehow
> indeterminate or ineffable! I hope to arrive at a better understanding
> of this (but not of course to convince anybody of anything contrary
> to their Sunday meditations).

It is Platonism, "the unique" absolute standard model of PA independent 
on anything  - what is mysticism and meditation. I think that anybody 
just with normal critical style of thinking cannot accept that 
something is determinate, without any scientifically sound explanation 
what does it mean, without reference to any superbeliefs. One reason 
that this happens with thinking people is the pressure of a wrong and 
long-standing tradition. History of Science knows many such examples. 
(Say, absolute time seems self-evident and even confirmed by our 
everyday experience, whereas the accurate analysis of this hypothesis, 
even without any advanced experiments, makes it doubtful.) 
Of course, for some of us superbeliefs have some highest value. 
These people cannot be convinced. This is a borderline which is almost 
impossible to overcome. It is unfortunate that such a mysticism 
concerning existence of mathematical objects is alive until now. 

Vladimir Sazonov

> ---
> Torkel Franzen
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