From: Eliezer Yudkowsky (sentience@pobox.com)
Date: Tue Aug 10 2004 - 02:36:23 MDT
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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