At 10:54 18/06/04 -0400, Stephen Paul King wrote:
Thank you for bringing this book to our attention. I will see if I can get a copy ASAP. I am very interested in how Changeux deals with the epiphenomena problem, if he even addresses it.
Not really, Changeux is eliminarivist both on mind and mathematics! He takes that as high-level pure (implicitely 3-person) description of natural phenomena.
I have read the Smullyan book and found that it strenghend my insistence that we need to give a more detailed explanation as to how, at least, the appearence of physical implementations are necessary; he did not address physicality at all.
Obviously. It is just an introduction to the Godel-Lob logic G of Self-Reference.
I would bet he is not aware of my proof that if we are digitalisable machine then
physics is (re)define as the measure one on the consistent extensions (UDA),
and he is probably still less aware of its arithmetical translation
(the machine interview) and the derivation of QL. Today provability logicians
and quantum logicians seems not really aware of each others, and all logicians
and even probably all mathematicians are not really interested in fundamental
Still, Smullyan is aware that G could be useful in (theoretical) artificial
intelligence; he even asserts that G has a psychological appeal.
To tell you how "grave" is the situation ;) : Smullyan, like 99,99999999%
of the scientists, and like 99,999999999% of the laymen since Aristotle,
believes in a physical reality. Actually there is an explicit passage where
Smullyan says so by giving a "typical" platonic dualist, even modal, account
of the difference between math and physics. Let me quote him, but before
let me recall that, in classical (also called boolean) propositional logic, a
tautology is a formula true in all possible worlds, where a world is an
assignement of 1 or 0 to propositional letters. For example,
((NOT A) OR ((NOT B) OR A)
has always the truth value 1, independently of the truth value given to A or to B, as I hope people can verify by building the truth table.
After having explain along this way what a tautology is, Smullyan says:
<< This is related to Leibniz's notion of possible worlds. Leibniz claimed that of all possible worlds, this one was the best. frankly I have no idea whether he was right or wrong in this, but the interesting things is that he considered other possible worlds. Out of this, a whole branch of philosophical logic known as possible world semantics has developed in recent years---notably by the philosopher Saul Kripke---which we will discuss in a later chapter. Given any possible world, the set of all propositions that are true for that world, together with the set of propositions that are false for that world, constitute the state of affairs holding for *that* world. A tautology, then, is true, not only for this world, but for *all* possible worlds. The physical sciences are interested in the state of affairs that holds for the *actual* world, whereas pure mathematics and logic study *all* possible states of affairs. >>
Smullyan confuses physics with what I call "geography"!. I guess quantum many-worlders have good evidence that physics is related to the interference of the many worlds. Also modern laws of physics are most of the time derivable from being invariant for a (symmetrical) transformation ... among "states of affairs". And computationalists *know* much more: physics is as mathematical as mathematics and machine psychology: physics entirely emerges from the interference between all states of affairs (actually: maximal sequences of states of affairs)... as anticipated by sound machines.
Note also that Smullyan uses (but does not study nor exploit) the Thaetetus trick by defining knowledge by true belief: a reasoner knows p if he believes p and p is true.
Note also Smullyan can be quite perverse! Indeed, he proposes a "self-referential" interpretation of G*---which arithmetically never talks about itself but *about* some machine. It makes look G* a very queer (although consistent but not self-referentially correct) machine.
But the book has an infinite charm, and is very much easier than Boolos 1993 (classical treatise on G) or Smorinski 1985 (classical textbook).
Hopefully your explanation of G and G* will help.
It is really the explanation of my thesis which you need, I am afraid I can hardly explain better G than Smullyan. But ok I will try. You can find in my url links to this list where I made previous attempt. If someone has an idea if we can send mails mixed with simple drawings, that would help ...
One question to leave you with: If it can be proved that a physical implementation of quantum computation exist in Nature (in microtubles to be specific), what effect would this have in your thinking? (I am very aware of Tegmark's paper (http://www.consciousness.arizona.edu/hameroff/papers/decoherence/decoherenc e.html ) but have found a possible loophole that seems to allow coherence to occur in long enough durations for quantum computations to take place.)
It would change nothing.
Why? Because the only assumption I am using is that we are (turing) emulable,
and all known physical unitary transformations (solutions of SWE) are turing
emulable (albeit "slowly" but this does not matter in UD*, given than the first person
cannot be aware of the slowness (and even of any "actualness" of an execution)
of the UD. Cf UDA.
(If the brain is a quantum machine following a NON computable unitary evolution like Nielsen's one, that is something like e^(i.Omega t), with Omega being the Chaitin number of some universal machine, then it could change things, but then comp would be false, and we go out of my working hypothesis ;) BTW, with comp, the existence of such a non comp unitary evolution is highly undecidable.
----- Original Message ----- From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, June 18, 2004 6:06 AM Subject: Connes, Changeux and Comp
> Hi all, > > I am rather busy finishing my (french, alas again) paper on the debate > between the french biologist J.P. Changeux and the french mathematician > Alain Connes. > Actually the book has been translated: > http://www.amazon.co.uk/exec/obidos/ASIN/0691004056/wwwlink-software-21/202-7192216-8003069 > Changeux is a materialist elimininativist. He believes in monistic > materialism. Mathematics, according to him, is exclusively a construction > of the human brain. > Connes is platonist for mathematical truth, but seems to accept some form > of physical realism, so that he accepts a form of platonistic dualism (an > invention of Aristotle, not Plato: it is the position of realism with > respect to both math and physics). Connes acknowledges that his position > entails the mystery of the relation between math and physics (the > unreasonable effectiveness of math in physics). Obviously the comp hyp can > reconcile them, but at the price of dismissing physical realism. I > recommend the book. It makes clear the inevitability of a clash between two > forms of realism in science. It is also interesting that Connes uses the > term of "bifurcation" both in relation with Everett's quantum mechanics and > Godel's theorem; that's a point which is made utterly clear in the comp > approach I follow for the fundamental questions. > > I hope also you have been able to buy the little and cheap book "Forever > Undecided" by Smullyan, which > has been re-edited recently, but seems to be again out of print. I will > make some critical comments about it soon. I definitely consider that book > as a royal introduction to the modal logic G, which, as you (should) know > is the basic material on which the technical comp derivation of physics is > extracted. (Well the beginning of the derivation, of course ...). Be sure > you have no more problem with the Universal Dovetailer Argument, and please > don't hesitate to send last minute objections ;) > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ > >