Mohsen Ravanbakhsh wrote:
> /Why?  "Mathematical" means nothing but not self-contradictory. 
>  Sherlock Holmes stories are mathematical.  That doesn't mean Sherlock 
> Holmes exists in some Platonic realm.
> /
>  
> Brent,
>  
> What do you mean by that? 

Mathematics is just assuming some axioms and rules of inference and then 
proving theorems that follow from those.  There's no restriction except that it 
should be consistent, i.e. not every statement should be a theorem.  So you can 
regard a game of chess as a mathematical theorem or even a Sherlock Holmes 
story.  You may suppose these things "exist" in some sense, but clearly they 
don't exist in the same sense as your computer.

>I do not get your point.
> Anyway I do not insist that it should be realizable. But I have examples 
> in which we need them!
> Consider the use of Pythagoras theorem in nature. There are many cases 
> in which the distance between two points should be irrational.

Only under the assumption that space has a Euclidean metric - which is begging 
the question.  From the operational viewpoint, all measurements yield integers 
(in some units).  Real numbers are introduced in the Platonic realm to insure 
that some integer equations have solutions.  Similarly imaginary numbers are 
introduced to complete the algebra.  They are all our inventions - except some 
people think the integers are not.

Brent Meeker


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