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?
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.
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.
That cannot be
validly related to the proof found by Bruno and David in the UD, as
you can conceive that arithmetical truth is independent of the
presence of absence of primitive matter.
Of course, but if you so conceive,
This follows from logic alone.
then presumably Bruno and David
never correctly find a reason why primitive matter is needed.
Indeed. That's the very point.
Bruno
Not really, because you've only proved a non inconsistency of the
assumption
"arithmetical truth is independent of the presence of absence of
primitive matter", not its truth.
?
We have a model of PA without primitive matter. Indeed the usual (N,
0, +, *) structure.
We have a model of PA with primitive matter. We add new constants in
the language, plausibly a second type of variable (but that's is not
necessary here) and let them denote primitively physical objects (or
object we decide to assume such, continuing to play the role of Peter
Jones (here I am really the Devil advocate). We don't even need to add
any axioms although here a large spectrum of choice exist to extend
arithmetic with primitive matter (whatever that is, but usually
related to what we observe, like that moon or those bosons).
This shows the obvious: PA, by itself don't talk about primitive
matter, no more than it can say any specific thing about non standard
numbers or real numbers or sets). It talks on natural numbers and
their relations.
So we cannot in PA, or in arithmetic, proves the existence of
primitive matter, or its non-existence.
But if Peter Jones succeeded in convincing me *validly* (and thus all
Bruno Marchal in all computations/models of (sigma_1) arithmetic) of
the existence of some primitive matter, then such a *valid* argument
would be a proof (by the completeness theorem of Gödel) which can be
translated in arithmetic, and that would make inconsistent PA + ~PM,
where PM is for "it exists primitive matter". That contradicts the
consistency of arithmetic without PM, as above.
Intuitively, it is even more shocking, as it would mean that the p-
zombies of Peter Jones would "convince" validly all the p-zombies of
Bruno Marchal, in all models of arithmetic, that primitive matter
exist (when above we have a model with none). That is inconsistent
with the fact that there are models of PA without primitive matter.
So yes, it seems to me that this shows that Peter Jones' argument,
when made precise enough to be valid, for maintaining a role of
primitive matter for actual consciousness, leads to a contradiction.
So Peter argument has to be necessarily ineffective, making "primitive
matter" into a god-of-the-gap. Which is what step 8 is supposed to show.
This is similar with the argument based on Gödel against mechanism.
Once precise and valid enough, the machine can diagonalize and refute
them. This was well seen by Judson Webb(*).
I recommend that book, which has been reedited:
http://www.amazon.com/Mechanism-Mentalism-Metamathematics-Finitism-Synthese/dp/9027710465
abstract:
This book grew out of a graduate student paper [261] in which I set
down some criticisms of J. R. Lucas' attempt to refute mechanism by
means of G6del's theorem. I had made several such abortive attempts
myself and had become familiar with their pitfalls, and especially
with the double-edged nature of incompleteness arguments. My original
idea was to model the refutation of mechanism on the almost
universally accepted G6delian refutation of Hilbert's formalism, but I
kept getting stuck on questions of mathematical philosophy which I
found myself having to beg. A thorough study of the foundational works
of Hilbert and Bernays finally convinced me that I had all too naively
and uncritically bought this refutation of formalism. I did indeed
discover points of surprisingly close contact between formalism and
mechanism, but also that it was possible to undermine certain strong
arguments against these positions precisely by invoking G6del's and
related work. I also began to realize that the Church-Turing thesis
itself is the principal bastion protecting mechanism, and that G6del's
work was perhaps the best thing that ever happened to both mechanism
and formalism. I pushed these lines of argument in my dissertation
with the patient help of my readers, Raymond Nelson and Howard Stein.
I would especially like to thank the latter for many valuable
criticisms of my dissertation as well as some helpful suggestions for
reorganizing it in the direction of the present book.
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
(http://www.hpcoders.com.au/AmoebasSecret.html)
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