Le 06-juin-06, à 20:50, [EMAIL PROTECTED] a écrit :

> Given a
> (countably infinite) sequence of functions f1, f2, ..., you say that
> fn(n)+1 must either be in the sequence OR not in the sequence.

I am just showing constructively that if f1, f2,f3, ... is a well 
defined sequence of computable functions from N to N, then the 
"diagonal" function g (i.e. the one defined by g(n) = fn(n)+1) for each 
n) cannot belong to the sequence f1, f2, f3, ...
The proof is constructive in the sense that if you give me some fk 
equal to g, I can generate a contradiction from that. The contradiction 
being that g(k) will be equal to g(k)+1.

> But I will take some of my rare spare time (which I always have by
> diagonalization)

I hope you will explain to me how you do that :)

> to think some more about this absoluteness of
> computability and Church Thesis, etc. and try to understand this and
> solve the puzzle of where your straw-man argument is wrong.

OK, I let you think a little more then.

> Speaking of straw-men, it seems you are saying that machines simply
> running programs, without axioms and inference rules, are like zombies.

Where am I saying that?

>   Zombies are how I would traditionally think of machines, but you seem
> to be saying that the axioms and inference rules somehow breathe life
> into the machine.

Not really. Axioms and inference rule just makes it possible for the 
machine to develop (third person describable) beliefs. The relation 
between computation and proof are subtle. Let us be sure everyone 
understand Church thesis (and its non constructive price) before moving 
on the subject of theories and chatting machines. I could say things 
but it will adds confusions at this stage.
Also zombie is a concept in the philosophy of mind, but we are not yet 
really talking about that.

OK, i give the solution tomorrow. All right? (answer only if you prefer 
I give you more time, or else to make any other comments of course, but 
by default I give the answer tomorrow).



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