From: Samantha Atkins (email@example.com)
Date: Thu Aug 12 2004 - 12:01:11 MDT
It takes quite a bit of teasing out to clarify what is meant by a
statement like "the universe is a manifestation of mathematics".
IMHO, it would be more accurate to say something like that reality
interacts and manifests in ways that we can describe via mathematics -
a grasping for the "orderliness" or "algorithm-like" nature. Saying
it is a manifestation of mathematics seems to go much further than
this. One could as well say "only information exists" or as a
variant, "reality is virtual". Some very interesting arguments can
be and have been made for such, but all of the provide a shaky
foundation for a philosophical system to rest upon.
While Geddes did not call it an axiom it is the basis of his
Metaphysics so it stands in the place where one would expect an axiom.
That mathematics has empirical suitability is not really astonishing
at all. Mathematics is a formal way of stating/capturing algorithms,
relationships and regularities. It will map to any system containing
relationships and regularities. Math is the abstraction of the way
logically coherent systems work. If it did not map well to the
Universe then the Universe would be incoherent chaos. That it isn't
doesn't make it permissible to claim that such coherence itself is a
manifestation of the abstraction for expressing, capturing,
manipulating coherent algorithms and relationships..
On Tue, 10 Aug 2004 04:36:23 -0400, Eliezer Yudkowsky
> Samantha Atkins wrote:
> > Anyone can slap together conclusions they desire to belief and claim
> > they all fit together in a well formed and well supported whole. The
> > TOE that can be thus written is not the TOE.
> > Starting by statement axioms is fine if the axioms actually have some
> > clearly and foundational meaning. But how the hell does some blather
> > like "All reality is a manifestation of pure mathematics" qualify?
> > What do you mean by "pure mathematics" and "manifestation" in that
> > incredible construct? For a philosophical system the starting axioms
> > should be irreducible, not general conclusions, hypothesis or theories
> > themselves.
> I don't claim to know how or why it is so, but it seems obvious enough that
> our physical universe is a manifestation of that which we name
> "mathematics" - maybe even in the sense of our physical universe being a
> model which satisfies an axiomatic system, but I'm still studying
> mathematical logic so it's too early for me to speculate coherently about that.
> Geddes credits the speculation that all is math and all math exists to
> Tegmark, Geddes didn't make it up himself. Nor did Tegmark devise it; if I
> recall correctly "all is math" goes back to Pythagoras, and I don't know
> who first speculated that everything exists. I agree that a statement like
> "all is number" is unsuitable for use as an axiom, but Geddes did not call
> it an axiom. It would only be an "axiom" if Geddes were making logical
> deductions conditional upon it, without asserting that the axiom itself
> were true or false. In modern-day mathematics, axioms are strictly empty
> of empirical content. That's what makes them axioms. (All the more
> ironic, then, if our universe is a model satisfying an axiomatic system;
> everything that we call an "empirical" fact would simply be a consequence,
> relative to our location, of the axioms in which we happen to be embedded.)
> Those who believe the universe is math are driven to that conclusion by
> the astonishing empirical suitability of math as a system for describing
> the universe and the internal consistency of physics - it's clear that this
> is a very basic thing, but to call it an axiom is inappropriate. That is
> not the right name for basic things we don't understand.
> Incidentally, Geddes's statements about MWI in QM are wrong. MWI does not
> interact with the "everything exists" hypothesis, nor is MWI *in QM* a
> consequence of the "everything exists" hypothesis.
> Also, Geddes, kindly do not call it "Yudkowsky's arrow of morality" for I
> never said such a thing.
> Eliezer S. Yudkowsky http://intelligence.org/
> Research Fellow, Singularity Institute for Artificial Intelligence
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