Re: virus: C of V: Another Religion

Vicki Rosenzweig (
Fri, 31 Jan 97 10:15:00 PST

The problem is that, historically, things have been asserted
as axioms because people thought them to be fundamental
truths, and have then turned out not to be. Euclid's Fifth
Postulate, about parallel lines, is a classic example of this.
Many people thought it was a fundamental truth about math
and/or the universe for a long time, when in fact it isn't even
true about the surface of the earth, and your choice of axioms
here determines the kind of geometry you'll get, but there are
several internally-consistent possibilities.

Similarly, while it's tempting to take 1+1=2 as an axiom, first we
have to know what 1 and 2 are counting. 1 particle plus 1 particle
doesn't always create 2 particles, for example: 1 electron plus
one proton produces one neutron. As for pure entities, there are
valid and useful mathematical systems in which 2 + 2 =0.

I learned a long time ago to be wary of definitions. I learned this
from Spinoza. It isn't what he was trying to teach, and when I caught
him at it I flung the book across the room: he tried to sneak in
Anselm's "proof" of the existence of God as a definition.

From: owner-virus
To: virus
Subject: Re: virus: C of V: Another Religion
Date: Thursday, January 30, 1997 5:45PM

At 10:16 AM 1/30/97 PST, Vicki Rosenzweig wrote:
>Alternatively, axioms are the things you assert because you believe
>them to be true but cannot prove them. For example, Euclidean
>geometry asserts the existence and properties of parallel lines;
>other geometries make different assertions, and one of them is a
>better description of the planet on which we live than Euclid's.

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.
> ----------

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

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)