On 21 Jul 2011, at 20:30, meekerdb wrote:
On 7/21/2011 11:03 AM, Jason Resch wrote:
On Thu, Jul 21, 2011 at 10:54 AM, meekerdb <[email protected]>
wrote:
On 7/21/2011 2:27 AM, Bruno Marchal wrote:
Axiomatics are already in Platonia so of course that forces
computation to be there.
The computations are concrete relations.
If the are concrete then we should be able to point to them.
If your mind is a computer, you don't even need to point to them,
everything you see and experience is direct evidence of the
existence of the computation implementing your mind.
Also, I don't think the "point test" works for everything that has
a concrete existence. How would a many-worlder point to the other
branches of the wave function, or an eternalist point to the past?
How would an AI or human in a virtual environment point to the
concrete computer that is rendering its environment?
They don't need axioms to exist. Then the numbers relation can be
described by some axiomatic.
And one can regard the numbers as defined by their relations. So
the "fundamental ontology" of numbers is reduced to a description
of relations.
Is a chair the same thing as a description of a chair, or an idea
of a chair?
The is no need to suppose they exist in the sense of tables and
chairs.
Assume both matter and number relations exist. With comp, the
existence of number relations explains the existence of matter,
That's the question. It seems that comp requires more than the
existence of number relations, it requires the existence of a UD or
equivalent.
Not at all. The UD is a collection of number relation, and its
existence is a theorem in elementary arithmetic.
It requires the existence of all computation.
That is Sigma_1 truth. That is contained in a tiny fragment of
provable truth in elementary arithmetic.
I see no reason to suppose these exist, at least not in any
conventional meaning of 'exist'.
It exists in the sense of "even numbers exist".
It certainly doesn't follow from my saying "Yes" to the doctor that
I believe they exist.
It does follow.
It also has the problem that it explains too much - the white rabbit
problem.
But that is *the* interesting things. Matter become a mathematical
problem. You can refute comp by showing that there is too much white
rabbits. But the logic of self-reference shows that it is not trivial.
The logic S4Grz1, X1* and Z1* explains already why the white rabbits
might be very rare, perhaps even more rare than with QM.
but the existence of matter does not explain the existence of
number relations.
It may not explain them, but it exemplifies them. And in fact
that's how we learn what numbers are and how to count - long before
we learn Peano's axioms and Cantor's diagonalization.
That is normal. We are embedded in the reality of numbers, and cannot
see the numbers before seeing matter. This is explain in the theory.
It is therefore a simpler theory to suppose the existence of number
relations is fundamental and the appearance of matter is a
consequence, than to suppose both exist independently of each other.
Simpler, yes. But then, "God did it" and "Everything exists." are
simple too. An explanation with no predictive power isn't much of
an explanation.
It predicts physics and consciousness. Quantitively and qualitatively.
OK, it has not YET find a new particle, and that might take time. But
the theory explains much more than physics has ever explain, and this
with much fewer assumptions.
Bruno
http://iridia.ulb.ac.be/~marchal/
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