[Beowulf] OS for 64 bit AMD
landman at scalableinformatics.com
Wed Apr 6 11:36:19 EDT 2005
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
> 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
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
web : http://www.scalableinformatics.com
phone: +1 734 786 8423
fax : +1 734 786 8452
cell : +1 734 612 4615
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