My understanding of "axiom", both by definition and through context,
is not something you assert because you /believe/ it is true, rather
it is an inescapeable acknowledgement of a fundamental truth. It is
an assertion of the irreducability of a fact, such as 1+1=2.
Newton's Principia Mathematica is a good example of the intrinsic
fallacy of attempting to reduce or refute an axiom. In this rather
unweildy tome, he spent some 70 pages trying to "prove" that 1+1=2.
The "proof" ultimately involved symbology and abstractions of an order
far greater that the fact they purported to prove. It was also seen to
be self-referential, meaning that the initial assertion is used in the
proof, an obvious (axiomatic?) non-sequiteur. His failure actually
highlights the essential nature of an axiom, and also speaks to the
necessity of asserting these axioms as a foundation to any treatise
in logic or philosophy.
>"Existence exists" is very tempting, but the only one of Rand's axioms
>that I have seen demonstrated to my satisfaction is that I am aware of
>my own existence. (That goes back at least to Descartes's "cogito
>ergo sum.") As for "things are what they are," that may be valid, but
>it's not terribly useful: it doesn't give us any necessary connection
>between what is and what we perceive, or say anything about the ways
>in which things change.
>
>Vicki
>rosenzweig@acm.org
> ----------
It's tempting to insist that axioms should somehow help us divine the
fundamental nature of existence (I know /I/ wish it were so), but they
can't, and they're assertion isn't meant to. They're not transparent
windows into reality, they're the solid and very opaque cornerstones
of it.
At the risk of being presumptuous, I beleive the author wished to assert
the axiomatic nature of these items to provide a "formal" framework to
point to, to keep uncoordinated ramblings and abject silliness out of
scientific or philosophical discourse.
But what the hell do I know, anyway?
Dan Plante
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The Metasystem Transition History of the "Dan Plante" System
initial conditions = data (conception)
control of data = information (conception to puberty)
control of information = knowledge (puberty to marriage)
control of knowledge = wisdom (marriage to divorce)
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