Norman Samish wrote:
> 
> Thanks to all who replied to my question.  This question has
> bothered me for years, and I have hopes that some progress can
> be made towards an answer.
> 
> I've heard some interesting concepts, including:
> (1) "Numbers must exist, therefore 'something' must exist."
> (2) "Something exists because Nothingness cannot non-Exist."
> 
> Perhaps the above two are equivalent.
> 
> With respect to (1) above, why must numbers exist?  

I am not sure that any definitive answer can be given to this
question. A possible argument is that the existence of numbers
by themselves is much easier to accept than the existence of
"usual material things" in a classical sense. Of course, even
if it was really a weakest assumption, it is not granted.

The idea behind "numbers must exist" is that "God Himself
cannot make that two plus two equates something different of
four". Another way to say it is that "even if there were nothing
(or no thing) there would remain that whenever/wherever there
would be something in which natural numbers could be thought of,
the Fermat conjecture should be true". If natural numbers did
not exist, this necessity would immediately apply to them
whenever and wherever they appear. I would say that the set of
such necessities is not different from natural numbers themselves.
Of course, it is too strong to claim that natural numbers exist
individually and one independently of another. The arguement is
that "arithmetics" as a whole exists by itself (and as something).

> With respect to (2) above, why can't "nothingness" exist?
 > The trivial answer is that even "nothing" is "something."
> However, I don't think that this addresses the real question.  
> 
> A state of pure "NO THING" would forbid even the existence
> of numbers,

Yes. It should even forbid the existence of a "Fermat theorem
constraint" and it is hard to imagine (at leat for me) that such
a constraint could not exist. So it is not so puzzling (at least
to me) that something exist.

> or of empty space, or of an empty set.  It would
> be non-existence.  
> 
> Non-existence seems so much simpler than the infinity of
> things, both material and immaterial, that surrounds us.

"Material and immaterial things that surround us" most probably
only appear so to us. To explain the existence of something could
also be a too strong (and unachievable) requirement. Only the
perception of the existence of something requires an explanation.

> So why are things here?  (I'm grateful that they are, of course.)
> 
> Is this a self-consistent, if unanswerable, question?

Like "Who created the world?", this formulation involves possibly
unnecessary and misleading prejudices. At least: the existence of
"thing*s*" and the existence of an "here".

Georges.

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