🚀 go-pugleaf

In article <344@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:

>This is the question. Continuous models are the simplest to work with
>mathematically, but are the simplest possibility as models of physical
>reality? I do not think so.

It isn't clear to me that any such distinction can be made.

>There is good reason to suspect that no completed infinite totalities
>exist.

I know of none.  Name some.

 The continuum that appears in formal mathematical systems is different
>then what mathematicians mean by `the continuum'. The latter is a speculative
>philosophical idea that cannot be formalized mathematically.

If it is a speculative philosophical idea, it isn't mathematics.  This
sounds like gibberish.

>For example the real numbers definable in any consistent formal system
>are countable.

Completely false, and downright silly to boot.

I presume you meant something like there are countable models of
the first order theory or something like that.

>particular formal system. 

>Whether *all real numbers* exists or this phrase has any mathematical
>meaning is itself a speculative philosophical question.

In a word, bunk.


-- 
     Gene Ward Smith/Brahms Gang/IWR/Ruprecht-Karls University 
               gsmith@kalliope.iwr.uni-heidelberg.de