How about: "self"? is it a good enoug "1st person" "soul"?
Here you put your finger on something quite important but rather hard to explain without saying more on the incompleteness phenomenon. We will certainly come back on this more than once. The idea is that there are many notion of selves for the sound machine. (I recall I am always talking about a machine which proves theorem of arithmetic, and by definition a machine is sound if she proves true theorems). Then the third person self is defined by a correct functional description of the machine at the right level (which exist for us by comp, and which can be made explicit for simple machine like Peano-Arithmetic, ...). It is a third person self, a little like when you say "I have a mouth" ... I remember now that I did use the term soul for this notion of *third* person (or self) in the provocative view of comp: "comp means you can save your soul on a disket". Stathis made me think that the word soul is perhaps better used for the first person self.
In a nutshell, the third person self is the one which will be described by the Godelian beweisbar provability predicate Bew(x), (and then by the modal logical systems G and G* (for those who remember, I will re-explain later)). The first person self will be defined by applying the Theaetetus trick on the third person self, that is on bew. So the first person will be defined by a new predicate saying "Bew(x) and True(x)". But the predicate Truth(x), by Tarski theorem, cannot be defined in the language of the machine. Still, by using G (and G*) we can defined such a box (but detail will be given at time).
Now the machine is sound, which means the machine proves only true proposition of arithmetic. So, obviously the first and third person are equivalent. But the incompleteness theorems will entail that neither the 3-machine self, nor 1-machine self can *prove* that equivalence. Such subtle nuances will be made cristal transparent by the explicit use of G and G*. I recall that G is a formal theory complete for the provable discours,by the machine, on the propositional provability logic of itself (the machine itself). G* is a formal theory complete for the true discours,by the machine, on the propositional provability logic of itself (the machine itself). That is: G* contains the true but unprovable sentences on and by the machine. What appears here, with the box [0] for the 3-person and [1] for the 1-person:
G* proves [0] = [1], but G does not prove it.
Well I guess this was difficult for those who doesn't know enough logic and my intend was to explain more before. So don't worry if you don't understand.
Remember that the popular book by Smullyan "Forever Undecided" has been reedited, and is a not too bad introduction to the modal logic G. It could help.
Old (in this list) definition of G and G* can be found here http://www.escribe.com/science/theory/m1417.html and in the neighborhood.
Bruno
John M ----- Original Message ----- From: "Bruno Marchal" <[EMAIL PROTECTED]> To: "Stathis Papaioannou" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Friday, April 30, 2004 9:37 AM Subject: Re: Are we simulated by some massive computer?
> Ok Stathis, thanks for the precision. > Anyway you give me the temptation to identify the soul by the first person. > We will be able to prove (with the comp hyp) that not only the soul exists > but (I forget to say) also that from the *correct* soul point of view, the soul > is NOT a machine. > But perhaps the word "soul" is to charged with emotion, and perhaps > we should stick on the expression "first person". > 'course, it is just a matter of vocabulary. (But then humans are able > to fight themselves during centuries for matter of vocabulary ... :( > > Bruno > > > > > At 22:23 30/04/04 +1000, Stathis Papaioannou wrote: > > >On 29 April 2004 Bruno Marchal wrote: > > > >>At 23:16 28/04/04 +1000, Stathis Papaioannou wrote: > >> > >> > >>>There is a single idea underlying much of the confusion in discussions > >>>of personal identity: the belief in a soul. > >> > >>Indeed. > >> > >> > >>>I use this term for a quality or substance which resides in a person > >>>throughout his life and is somehow responsible for his identity, and > >>>which (here is the problem) is not captured by a complete description of > >>>the person's physical and psychological state. Often, it is a hidden > >>>assumption. > >> > >> > >>That's a nice definition of the soul, quite similar to the provable > >>properties > >>of the "first person", once we will define it precisely (in the Thaetetus > >>way). And comp will > >>entails, *as a theorem*, the existence of the soul, then! > > > >Actually, I didn't mean to use "soul" as a synonym for consciousness or > >subjective experience, which is why I said it was something not captured > >by a complete description of a person's physical *or psychological* state. > >Subjective experience differs from other empirical data in that it can > >only be fully understood in a first person context, but I do not see why > >this should disqaulify it from being a fit subject for scientific study. > >Cognitive psychologists write rigorous scientific papers of which they are > >very proud, and they seem to have replaced the behaviourists (who thought > >consciousness was at best unimportant and at worst non-existent) in most > >academic psychology departments. > > > >What I meant by "soul" was something beyond reason or empirical fact, > >whether of the first or the third person variety; something magical or > >supernatural, in other words. > > > >Stathis Papaioannou > > > >_________________________________________________________________ > >Find love today with ninemsn personals. Click here: > >http://ninemsn.match.com?referrer=hotmailtagline > > http://iridia.ulb.ac.be/~marchal/
http://iridia.ulb.ac.be/~marchal/
