[Beowulf] OS for 64 bit AMD

[Joe Landman]

Richard Walsh wrote:


> This is the definition I have always thought was the most fundamental.  
> The word
> is used colloquially most of the time.  In fact, the truth of an axiom 
> is always debatable.

One of the great dangers of dealing with language as a modality for 
communication is the concept of a definition, and the varied 
interpretations one can have of a definition.  The imprecision in a 
language lends itself to grey areas, such as

  J: Axiom == X
M: Axiom == Y

M/J: X != Y

Of course, the problem is that even with precise languages stuff like 
this happens (to wit Goedel's completeness bits).

> We simply come to rest on a idea so that we can proceed to 
> act/compute/design/think
> etc.  ... but we must always be aware of the potential for 
> overreaching.  Perhaps the
> most basic axiom is that of the notion of identity (one cannot count 
> without it), but
> we all know that in fact no two things are identical. 

:)

Do we really?  I expect an electron looks like every other electron (but 
never having seen one, this is of course a guess).  A foundation of our 
observational sciences include being able to discern between different 
and identical things.

>We carry on with 
> it anyway
> because the implications (all of mathematics) are so useful and 
> interesting.

I suspect that it is a little more rigorous than that.  We develop 
formalisms that allow us to test things reductio ad-absurdium to help 
define things better.  This allows us to build up rigorous and 
(hopefully) testable hypotheses.

Then again, I like the simplicity of "we do math because it is useful".



-- 
Joseph Landman, Ph.D
Founder and CEO
Scalable Informatics LLC,
email: landman at scalableinformatics.com
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