On 16 Feb 2014, at 21:56, David Nyman wrote:
On 16 February 2014 16:17, Bruno Marchal <[email protected]> wrote:
On 16 Feb 2014, at 15:32, David Nyman wrote:
On 16 February 2014 09:39, Bruno Marchal <[email protected]> wrote:
<snip>
From "thought cannot act on matter" we arrive at "thought cannot
refer to matter", and well, this is almost the consequence of step
8, as it says that the notion of matter has nothing to do with a
material reality. Then we can still refer to the moon, but we know
it is a sort of collective lawful "hallucination", or more exactly a
mean on a set of 3p well defined computation.
Yes, at least it seems that thought cannot refer to the sort of
matter of which it would be an epiphenomenon!
<snip>
It illustrates, perhaps better than step 8, the difficulty of
wanting a primitive matter having a primitive ontological reality
capable of singularizing a conscious person capable to refer to it.
I have to think more about this.
In effect, might step 8 be regarded as a reductio of the premise
that the laws of matter to which we can refer and those of any
putative ur-matter can be in any way coterminous? Under CTM, it is
consistent to suppose that the observable laws of matter must derive
from some principled notion of computation. At the outset we grant
the assumption that such a notion of computation must ultimately be
grounded in primitive physical activity. Accordingly, we propose a
system of such physical activity that is initially acceptable as
grounding some set of computational relations corresponding to a
conscious subject and hence to the physical laws observable by such
a subject. Then we show that we can systematically change the
physical contingencies such that every last vestige of these
relations is evacuated even while all relevant physical events
continue to go through. This in effect provides a reductio of the
original premise, under CTM: That the observable physical laws can
be supposed to derive directly from a more primitive physical
activity and simultaneously from any principled notion of
computation consistently extractable from such activity. Since both
cannot be the case, we must opt for one or the other.
OK.
However, one distinction between arithmetic / computation as an
ontology, and some kind of putative ur-physics, is that it is more
difficult to discern any principled motivation whatsoever to derive
"reference" in a primitive physics. A typical response to this
reference problem is to justify CTM by smuggling an ad hoc notion
of computation into physics.
Yes. That is why at first sight I took the discovery of the quantum
universal machine as a blow for comp. I thought that the quantum
formalism provided a notion of physical computability, but it
brought only a notion of physical computation, which is not excluded
with computationalism (it is a sort of direct exploitation of the
statistical nature of the computations below our substitution level).
Could you elaborate a little on the distinction you see between
physical computability and physical computation?
May be I should not have, as we can use the intensional Church's
thesis, for the UD. But we can formally make a difference, and some
can exploit it.
In fact the difference between computation and computability is more
general than between physical computation and physical computability.
Computability a priori concerns only the class of functions that we
can compute.
It has been proved that such class is the same for all know universal
system, from Babbage machine to the quantum computer. But each system
computes in a priori very different ways. Combinators are computed by
following two simple reduction laws (like Kxy = x, Sxyz = xz(yz)),
arithmetic computes by adding and subtracting one, register machine
compute by erasing or adding one in some register, quantum
computations processes on waves, etc.
But all systems can imitate all systems. Combinators and their
reduction can implement a program computing like a quantum processor
(althou with a superexponential slow down, which does not matter in
the UD*, though).
Now for some reason, I didn't get that immediately, and for a time I
believed that QC could violate the intensional Church thesis, notably
due to strict parallelization, use of arbitrary complex coefficients,
and entanglement. I was just wrong.
In fact, even if some quantum computation was necessary for the mind
to exist, comp should still able to justify this, by a necessary back
and forth above and below the substitution level, which indeed must
already play some role in the stabilization of the histories (the
measure). In fact comp predicts already the existence, formally, of
comp-quantum computations. But it is an open problem if it is
isomorphic to quantum computation. Today, it is even an open problem
if such comp-quantum-computation violates Church thesis (which I find
not quite plausible, to be sure).
Bruno
It is ad hoc in the sense that "physical computation" is still no
more than primitive physics, so now computation itself becomes an
epiphenomenon of physics and consciousness therefore an
epiphenomenon of an epiphenomenon. If not a blatant contradiction,
this strikes me as quite close to a reductio.
It makes arithmetic an epiphenomenon of physics, and it makes
physics an epiphenomenon of physics.
Computation (as emulated in arithmetic) on the other hand offers,
at least, a principled system of internally-recursive self-
reference that could motivate the layers of connectivity between
the ontological base and the level of indexical "physical reality".
With a big price of "reducing" physics to a "unique" calculus of
self-reference on the consistent, and/or "true", or both extensions.
This makes sense only if the arithmetical or quasi-arithmetical []p
& p, []p & <>t, (and []p & p & <>t) obeys knowledge and probability
logic respectively, and that is the case when p is restricted on
sigma_1 sentences (which emulates UD*).
Bruno
David
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