[FOM] Indispensability of the natural numbers
V.Sazonov at csc.liv.ac.uk
Wed May 19 10:37:41 EDT 2004
Steven Ericsson-Zenith wrote:
> Vladimir Sazonov said:
>> Mathematicians do not need to have
>>a metatheory. They just deduce their theorems (with the help
>>of some intuition, of course).
> and then said:
>>Whatever are our beliefs, the mental concept of the natural numbers
>>is something vague, anyway. It is only illusion of something solid.
> I would like to understand how you sustain this position since the
> first appears - at least to me - to contradict the second position.
I do not see any contradiction.
> A metatheory would seem essential if you are to resolve the
> inadequacies of "illusion" - for example, what *exactly* do you mean
> by "illusion"?
I have no *exact* understanding of what illusion is.
According to Webster's English Dictionary in the Internet:
illusion is "perception of something objectively existing in such
a way as to cause misinterpretation of its actual nature".
The actual nature of natural numbers (I mean - in general - not
in concrete examples) is our thoughts of them. Our thoughts are
sufficiently objective. We can communicate on them one with another.
But our perception of our thoughts on N that this imagined entity
is solid is our illusion.
I do not need any metatheory (as you suggest) to realize this,
although I do not exclude the possibility that some metatheoretical
considerations might illuminate some questions discussed here.
See also my answer to Timothy Y. Chow which probably should
clarify my position for you.
> Dr. Steven Ericsson Zenith
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