[FOM] Indispensability of the natural numbers
V.Sazonov at csc.liv.ac.uk
Thu May 20 12:28:51 EDT 2004
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
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
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,
> With respect,
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