FOM: infinity of the universe

[holmes@catseye.idbsu.edu]

>> Dear All,
>> 
>> If the universe is infinite then there are enough objects to 
>> support an interpretation of the mathematics of the natural numbers

>Let me pay tribute to this sort of writing and ask 
>Mr. Holmes the following

What sort of writing?

>And what if the universe is not infinite ? 

Then things are different.  The world is much simpler to describe
if it is infinite, and it is desirable to adopt simplifying hypotheses
where possible.

>How can we know is it finite or infinite ? 

The philosophical principle of sufficient reason strongly suggests that
the world is infinite; is there any reason for there to be any particular
finite number of objects?

If there is a finite number of objects then the number of objects is 
either odd or even.  How can we know if it is odd or even?  Is there any
reason to believe it is one or the other?

There are many things which are true which I do not, cannot, and never
will know.  This is true even on the level of physical reality.  I do
not know and cannot establish whether there are sentient beings
discussing the philosophy of mathematics somewhere within 1 billion
miles of Betelgeuse.  Nonetheless, either there are such beings or
there are not.  Limitations on what I can know do not constitute
limitations on what can be true.

>If it is infinite is it actually or potentially ? 

Actually.

>If it is only potentially what is the size of this potential ? 

See above.

>If it is infinite is there a place for (my favorite) unicorns ? 
>    (remark: as a unicorn is just a certain finite combination of 
>     elements it can arguably be implemented somewhere)

It is a common fallacy to suppose that a logical consequence of the
infinity of the universe is that every possible configuration occurs
somewhere in the infinite universe.  But if unicorns are physically
possible (a doubtful assertion) and the physical universe is of
infinite extent (which is what current cosmological theory, supported
by indirect observations, suggests) then unicorns exist with
probability 1 (which is not the same as saying that they do certainly
exist), but also with overwhelming probability do not exist anywhere
near us.

And God posted an angel with a flaming sword at | Sincerely, M. Randall Holmes
the gates of Cantor's paradise, that the       | Boise State U. (disavows all) 
slow-witted and the deliberately obtuse might | holmes at math.boisestate.edu
not glimpse the wonders therein. | http://math.boisestate.edu/~holmes

PS Dr. Holmes thanks Dr. Kanovei for providing the occasion to write this
posting -- it was a lot of fun! (though I am being perfectly sincere).