David Deutsch wrote (at the Fabric Of Reality mailing list):
>Preprint available at http://xxx.lanl.gov/abs/math.HO/9911150
>
>*Machines, Logic and Quantum Physics*
>
>Authors: David Deutsch, Artur Ekert, Rossella Lupacchini
(hereafter DEL).
>Abstract: Though the truths of logic and pure mathematics are objective and
>independent of any contingent facts or laws of nature, our knowledge of
>these truths depends entirely on our knowledge of the laws of physics.
>Recent progress in the quantum theory of computation has provided practical
>instances of this, and forces us to abandon the classical view that
>computation, and hence mathematical proof, are purely logical notions
>independent of that of computation as a physical process. Henceforward, a
>proof must be regarded not as an abstract object or process but as a
>physical process, a species of computation, whose scope and reliability
>depend on our knowledge of the physics of the computer concerned.
Very nice and very pedagogical paper. I disagree with
the philosophy, though.
(I like also a lot the FOR book, I find the argument for the multiverse
convincing and I share Deutsch's appreciation for Popper, but there too
I am not convinced by the philosophy. In particular I disagree with
Deutsch's view on Church's thesis).
Here I will make short remarks on the abstract and about the beginning
of the paper *Machines, Logic and Quantum Physics* by DEL.
> Abstract: Though the truths of logic and pure mathematics are
> objective and independent of any contingent facts or laws of
> nature, ...
I agree, but when DEL add:
>our knowledge of
>>these truths depends entirely on our knowledge of the laws of physics.
I could have agree with the idea that our knowledge of these truth
depends on the laws of physics, but I don't understand how
our knowledge of these truth could depend on *our knowledge* of the laws
of physics. Indeed most elementary truth in math has evolved independently
of our knowledge of physics. And it seems also that the knowledge
of *modern physics* depends on our knowledge of mathematics. It is a little
like to say that to understand Pythagore's theorem you need to understand
quantum mechanics. It is the contrary IMHO. Although I agree there are
strong evidence that my brain obeys Schroedinger Equation, I don't need
to be able to solve Schr. Eq. for using my brain. I don't even need
to know I have a brain.
Now it happens that I do not even believe that our knowledge of these
logical and mathematical truth depends on the laws of physics.
I am defending the quite opposite thesis, mainly
that the laws of physics depends on the knowledgeability of these logical
and mathematical truth.
I manage to show that by a kind of arithmetical "turing-tropic" principle
in my thesis
http://iridia.ulb.ac.be/~marchal
I quote the beginning of DEL's paper *Machines, Logic and
Quantum Physics*:
> Genuine scientific knowledge cannot be certain, ...
I agree. Even logic and math cannot give
certain knowledge, as Descartes realises a long time ago.
> ..., nor can it be justified a priori.
Why ?
This is a pessimistic axiom. If this was true, there would be
no hopes explaining the very existence of the ``empirical world".
That principle forces us to take that existence for granted.
I don't see any logical or empirical reason to do that.
It is quite (logically) possible (consistent) that someone
find an a priori axiom (perhaps inspired by physical observation)
and derive from it a new sort of realm from which he is able to
explain the origin of the physical laws. And, as Wheeler makes it
clear in his ``law without law", such realm cannot be physical
(if not we face an infinite regress).
Well. That is what I have done in my thesis. And other people
like Tegmark, Schmidhuber, Jacques Mallah, Hal Finney, James
Higgo, Chris Malloney, Russell Standish, and many others
are yet searching such realms and justifications:
see
http://www.escribe.com/science/theory/
I know that David Deutsch critisizes Wheeler's idea (that physics
is not fundamental after all!) in his paper
``On Wheeler's notion of 'Law without Law' in Physics",
Deutsch, D., Foundations of Physics, Vol. 16, N° 6, pp. 565-572, 1986.
But, quasi explicitly, Deutsch imposes the fundamental nature
of physics. Another misleading idea is his maintaining that mathematical
truth are analytical. But since the Godelian failure of logicism,
this is not tenable. Even the simple axioms of elementary arithmetics
need some form of non trivial introspection.
The DEL paper extends in some way Landauer's idea that
information is physical. (Why don't you refer to it?).
In my thesis I show that
1) if we are Turing emulable (it is the
computationalist hypothesis in psychology) then physics
*must* be derivable from the psychology of machines via
computer science and self-reference logic; and
2) I illustrate a beginning of such
a derivation of physics (in the chapter 5).
Only if we are *not* Turing emulable (that is not even quantum
turing emulable!) are DEL's conclusion consistent.
Physics must be informatical or computationalism (which is explicitly
postulate by David Deutsch) should be false.
Bruno
Bruno MARCHAL Phone : +32 (0)2 650 27 11
Universite Libre Fax : +32 (0)2 650 27 15
de Bruxelles
Avenue F.D. Roosevelt, 50 IRIDIA, CP 194/6
B-1050 BRUSSELS Email : marchal.domain.name.hidden
Belgium URL :
http://iridia.ulb.ac.be/~marchal
Received on Thu Dec 02 1999 - 02:56:13 PST