John Mikes wrote:
> Brent M,
> please spare me  the arithmetic class.
> I scribbled an example which may be wrong. So noted and I am ashamed.
> I was referring to the concept of (our) /'axioms'/ - products of human 
> thinking to make our edifice of the cognitive inventory we carry *- 
> VALID*. I opened the possibility that a quite different view may exist 
> with maybe different 'axioms' - without going into theorizing about such.
> And I won't.
> I still hold that EVERYTHING is not restricted to our human ways - not 
> in logic, not in our so called possibilities, not in anything.

Sorry.  I quite agree with you.  I regard logic and mathematics as our 
inventions - not restrictions on the world, but restrictions we place on how we 
think and talk about the world.  We can change them as in para-consistent 
logics.

Brent

> Best regards
>  John Mikes
> 
> On Sat, Aug 16, 2008 at 3:42 PM, Brent Meeker <[EMAIL PROTECTED] 
> <mailto:[EMAIL PROTECTED]>> wrote:
> 
> 
>     1Z wrote:
>      >
>      >
>      > On 15 Aug, 20:12, "John Mikes" <[EMAIL PROTECTED]
>     <mailto:[EMAIL PROTECTED]>> wrote:
>      >
>      >> As for 1Z's axioms:
>      >> In my vocabulary axioms are artifacts invented to make our theories
>      >> workable. If 1 + 1 is NOT 2,
>      >
>      > How would that turn out the case?
>      >
>      >> you can say goodby to math.
> 
>     We define arithmetic so 1+1=2, but that's a particular model for
>     dealing with
>     distinguishable, discrete things.  It doesn't apply to everything,
>     e.g. (1
>     member of the U.S. 400m relay team) + (1 member of the U.S. 100m
>     sprint team) =
>     (1 member of the U.S. Olympic team).  And given quantum entanglement and
>     indistinquishability of particles it may only apply *approximately*
>     to things
>     like apples and oranges.  So if 1+1=/=2 it just means you tried to
>     apply a model
>     where it doesn't work.
> 
>     Brent Meeker
> 
>      >> Furthermore I dislike the use of the word 'infinite' - in TEXTS
>     I  rather
>      >> use: 'unlimited'.
>      > >
>      >
> 
> 
> 
> 
> 
> > 


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