[FOM] Indispensability of the natural numbers

[Vladimir Sazonov]

Steven Ericsson-Zenith wrote:
> Vladimir Sazonov provides the following metatheory:
> 
>>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.
> 
> 
> And then says:
> 
>>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.
> 
> 
> Is this not a contradiction?  It appear to me that you metatheorise.

Of course, *any* kind of argumentation concerning the nature of
natural numbers and illusions on them could be considered as
(meta)theorising in a very broad and *informal* sense, although
I would not use the term "(meta)theorising" here.

Do you realize that in the second paragraph above from my posting
I mean rather a *formal* metatheory and confirm that "some
metatheoretical considerations might illuminate some questions
discussed here".

Is this really a contradiction?


In the next posting Steven Ericsson-Zenith wrote:
 > Vladimir Sazonov said:
 >
 >>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".
 >
 >
 > Appeal to common usage does not help us here.


Does not help absolutely? Should not we start with something
simple, and only after achieving a good understanding on this
level to go to the second, etc? There is a lot of mess and
mutual misunderstanding even on the first level and
*inappropriate* appealing to metatheories (about formal systems)
on this level makes things even more messy and leads us to a
vicious circle.

If you know what to say on the following part below, please do that.
My way of thinking is probably slightly different. But I presented
something more concrete in my answer to Timothy Y. Chow. In particular,
I tried to explicate why solidness of N (or, actually, of the meaning
of "and so on") is illusive.


 > It seems to me, on further review, that you are missing an important
 > aspect of this question.
 >
 > An understanding of the nature of apprehension and the "process" of
 > prediction in inference - abduction, induction and deduction - in which
 > illusion is simply a part - demands that we provide comprehensive
 > metatheory. And in this manner we can, in fact, provide an exact
 > definition of what illusion is.
 >
 > With respect,
 > Steven
 >


Best wishes,

Vladimir

> 
> With respect,
> Steven