On 30 Apr 2015, at 13:42, David Nyman wrote:
On 30 April 2015 at 09:10, Bruno Marchal <marc...@ulb.ac.be> wrote:
Platonia runs all possible CPU, and it is a certainty that all those
computer and execution of computers exists in Platonia (which is a
very little platonia compared to the one used in physics and
analysis).
On the contrary, some people might argue that a physical computation
is only an approximation of those in Platonia, and that there are no
computers in the physical reality.
I'm happy to offer myself as a candidate for "some people" in this
regard. It's all too easy to overlook the fact that, *on strictly
materialist assumptions*, there is no independent justification for
regarding physical activity as 'performing a computation', or some
approximation thereof, other than as a convention. On the assumption
that everything reduces hierarchically to some canonically primitive
level, all action must proceed relentlessly from the bottom up and
with complete indifference to our perceptual or conceptual
convenience.
I agree, but this is not entirely obvious. You can get this by UDA-
MGA, but without this or similar, a materialist could remain non-
eliminativist, and say that very plausibly his brain is doing the
"right informatoion treatment" as he considered that his headache
(which he assures you is not there by convention) does result from its
brain doing the right computational information treatment, and that
this is possible to explain (for example with G/G*, etc.). Of course
we know that this works only if the physical reality is itself
emergent, and that is why comp makes the mind-body problem two times
more difficult than for a materialist, as we have to justify
consciousness but also matter.
Here we are in a place where I think you type of argument can still be
used to criticize comp itself. Comp explains matter, but someone can
reason along your line and pretend that it still fail to explain
entirely consciousness. It just push the bottom on an arbitrary Turing
universalm level, and makes everything into dreams, some cohere enough
to give matter and consciousness, but consciousness looks like it is
still explained in term of (infinities) of 3p relations, as the view
from inside can be invoked by the materialist (forgetting that by
using comp, he must explain matter too).
Of course, the standard riposte here is that this is all very well
but such things as the 'software' level of explanation remain as a
requirement for *human* understanding. But in the context of the
mind-body problem (and particularly on the assumption of physical
primitiveness) that would be to immediately beg all the questions
that want an answer.
OK.
I should have thought that this would be particularly obvious to
anyone favouring the view that mathematics, and hence the notion of
computation itself, is nothing more than a free invention of the
(presumably all-too-physical) human mind.
Yes. But this can't work, of course. That is why we have to postulate
a Turing universal reality independent of the human mind. Luckily we
have a lot of them, like arithmetic (assumed by everyone) or
combinators, etc. Note that once we have one of them, the independent
reality of all the others is acquired. You can defined 0, 1, 2, ...
with the combinators and prove that 2+2=4, and similarly, you can
defined the combinators in arithmetic, and show that they do what they
have to to do.
But then the rest is still related to a multilevel graded and layered
sotware theory. The only thing very new here, is that incompleteness
forces the machine do introduce the distinction between justfiable,
relatively justifiable; knowable, probable, true, dreamed, consistent,
etc.
It is an arithmetical fact that the logic of----provable('2+3=5') & 2
+ 2 = 5-----is different from the logic of ---provable('2+2=5')---.
mathematicians and even many logicians does not like so much the
intensional part of computer science and logic, and modal logic where
decried for a long time. Quine said that they were born in sin, and he
raises some difficulties. But today, we know that incompleteness
reintroduce two mathematical modal logic having a clear extensional
meaning, yet being intensional in meaning, and worst, (but this is
ignored except from a minority like Goldbaltt, Boolos, Artemov, ...),
that incompleteness forces the machine to recognize the Theaetetus
distinctions between []p and []p & p. Not only does they have
different modal, intensional, logics (G and S4Grz) but they have quite
distinct features: G models the 3-I (the 3p thing that you let the
doctor re-implement it in the artificial brain). S4Grz models the
knowledge of a non nameable 1-I, like it is normal for the 1-notion to
be. The knower as no name, no 3p description *from* its first person
point of view. (we know better, but only for mich simpler theory that
we trust, like PA). Typically, the machine *should* say No to the
doctor, or violate its intuition by betting on some substitution
level, and becoming a practical computationalist.
Consciousness seems to appear with the law that p implies
bewesibar('p') when p is computable (sigma_1). p -> []p is true
Löbianity, self-consciousness is when that fact is recognize by the
machine. p -> []p is provable. This entails a form of self-awareness
[]p -> [][]p, as []p is sigma_1. But this is mirrored in the S4Grz
logic, which obeys that law too.
I will come back on this.
Bruno
David
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