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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Sat, 17 Jun 2006 14:11:12 +0200

Le 15-juin-06, à 21:03, Jesse Mazer a écrit :

*>
*

*> Tom Caylor wrote:
*

*>
*

*>>
*

*>> So apparently we are still missing something. You need to tell us
*

*>> *why* this is not the right reason. The set of instructions for g is
*

*>> precisely a big "case" statement (if you will) on n, like this:
*

*>>
*

*>> switch n:
*

*>> begin
*

*>> case 1:
*

*>> set of instructions for f1:
*

*>> case 2:
*

*>> set of instructions for f2:
*

*>> case 3:
*

*>> set of instructions for f3:
*

*>> ...
*

*>> end (after an infinite number of cases)
*

*>>
*

*>> This is an infinitely long program. You need the whole program to
*

*>> define g, not just the portion you need for a given input. Is there a
*

*>> finite version of g? I don't see how.
*

*>>
*

*>> Tom
*

*>
*

*> I haven't been following the all details of this discussion, so
*

*> apologies if
*

*> I get things confused...but aren't those f1, f2, f3 etc. supposed to
*

*> correspond *only* to turing machine programs which actually halt and
*

*> give
*

*> you a finite number as an output? If so, then although we can write
*

*> down the
*

*> list of all possible turing machine programs, there is no way to
*

*> figure out
*

*> which programs on this list correspond to one of your functions and
*

*> which
*

*> don't without solving the halting problem.
*

Note that even if you could solve the halting problem (perhaps with

some oracle) you would still not been able to solve the problem of

distinguishing the code/program of a total comp function from the code

of a strictly partial comp function.

I have proved that insolubility of code-of-total/code-of-partial

distinction again and again without using the insolubility of the

halting problem.

Of course I proceed in that way to make things as simple as possible.

Showing the insolubility of an harder problem (tot/partial) is of

course simpler than showing the insolubility of a simpler problem (the

halting problem).

Another reason is that the set R of the total fi (the constructive

reals) and the set P of the Fi will provide neat description of the

first person plenitude and the third person plenitude, and relate all

this to "Smullyan's heart of the matter".

Bruno

http://iridia.ulb.ac.be/~marchal/

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Received on Sat Jun 17 2006 - 08:12:29 PDT

Date: Sat, 17 Jun 2006 14:11:12 +0200

Le 15-juin-06, à 21:03, Jesse Mazer a écrit :

Note that even if you could solve the halting problem (perhaps with

some oracle) you would still not been able to solve the problem of

distinguishing the code/program of a total comp function from the code

of a strictly partial comp function.

I have proved that insolubility of code-of-total/code-of-partial

distinction again and again without using the insolubility of the

halting problem.

Of course I proceed in that way to make things as simple as possible.

Showing the insolubility of an harder problem (tot/partial) is of

course simpler than showing the insolubility of a simpler problem (the

halting problem).

Another reason is that the set R of the total fi (the constructive

reals) and the set P of the Fi will provide neat description of the

first person plenitude and the third person plenitude, and relate all

this to "Smullyan's heart of the matter".

Bruno

http://iridia.ulb.ac.be/~marchal/

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Received on Sat Jun 17 2006 - 08:12:29 PDT

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