On 18 Jun 2014, at 05:53, Russell Standish wrote:
On Tue, Jun 17, 2014 at 06:54:25PM +0200, Bruno Marchal wrote:
On 17 Jun 2014, at 10:42, Russell Standish wrote:
On Tue, Jun 17, 2014 at 10:27:02AM +0200, Bruno Marchal wrote:
On 16 Jun 2014, at 00:57, Russell Standish wrote:
On Sun, Jun 15, 2014 at 01:33:14PM +0200, Bruno Marchal wrote:
On 14 Jun 2014, at 12:13, Russell Standish wrote:
Changled title again, as this has wandered a lot from tronnies.
On Sat, Jun 14, 2014 at 10:08:08AM +0200, Bruno Marchal wrote:
If there were a reason why a primitive matter was needed
(to select
and incarnate consciousness), there would be number X
and Nu which
would emulate validly "Brunos and Davids" finding that
reason, and
proving *correctly* that they don't belong only to
arithmetic, which
would be false, and that is a mathematical
contradiction, even if
Why is it false? Why couldn't the numbers X and Nu belong both
to
arithmetic and the primitive matter?
That could happen, but that could also not happen.
Then the proof is not false.
Yes, it is. If the proof was correct, it could not happen.
Are you trying to suggest that you've derived a contradiction
here? If
so, then I don't see it.
Are you OK with the fact that the existence of primitive matter is
consistent with arithmetic, but that the non existence of primitive
matter is also consistent with arithmetic?
Yes.
OK.
If yes, the contradiction comes from the fact that the zombies (in
this context) in arithmetic would be able to validly prove the
existence of primitive matter, when assuming Peter Jones could
*validly* argues (= proves) that there is primitive matter and
simultaneously say "yes" to the doctor.
Why is that a contradiction?
In fact there are two contradictions.
I explain the contradiction which is relate to about.
'To prove A', classically, is equivalent to showing that ~A leads to
a contradiction, that is ~A is inconsistent. This mirrors the fact
that []A is the same as ~<> ~A.
To prove the existence of anything is equivalent to prove that its non
existence leads to a contradiction, or "0=1".
So you cannot prove *validly* the existence of Primitive Matter (PM,
hereafter) and keep your belief (above) that the non existence of
primitive matter is consistent with arithmetic.
"validly" means that all models (or consistent extensions) satisfy
what you prove. This is usually guaranty by the relevant soundness and
completeness theorem.
There is a more direct contradiction.
By definition or "primitive matter" it cannot be proved to exist. It
would be proved from what?
Something "primitive" means something which has to be assumed.
And why do you say that anybody (whether zombie or not) can *prove*
the existence of primitive matter? We don't know that for a fact.
I played the devil advocate. I put my foot in Peter Jones' food, and
imagine he could convince us of the existence of primitive matter, and
from that I get a contradiction.
In the case such a "valid" proof exist, it is just trivial to make a
mechanical procedure to find it, that's why I said any zombie can find
it. Validity is a recursive/decidable/total-computable/sigma_0 notion,
unlike provability, which is sigma_1 (partial-computable, semi-
decidable), and consistency, which is pi_1 (like Riemann Hypothesis).
If no, then you have to tell me which of 0, s(0), s(s(0)), ... *is*
primitive matter (only the standard numbers, as only them belongs to
all models of the arithmetical theories (RA, PA). But you can't do
that, as we already know at this stage that the appearance of the
primitive matter involves infinities of arithmetical relations.
We cannot decide to put 0 and its successors in the primitively
material without doing a category error.
It seems like we're talking finitism here, rather than primitive
matter. But in any case, I answered yes, above. The properties of
arithmetic shouldn't depend on the existence of primitive matter.
All right,
Best,
Bruno
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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
Latest project: The Amoeba's Secret
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