>
>
> The problem with this is that there cannot be a characteristica
> universalis, its possibility is disproved by the incompleteness
> theorems and the halting theorem and other related results.
>
> Regards,
> Mike
>
>
This is really interesting. What are the two theorems mentioned?

Thanks
P


The halting theorem states that one cannot write a program that
determines if an arbitrary program halts

Proof is easy by diagonalisation.

Suppose we have such a program.  Make a new program just like the
first with the place where it prints HALTS by an infinite loop.,
Replace the DOES NOT HALT with a stop instruction.

Give revised program to the tester.  If the program halts it does
into a loop, and if it does not halt it stops.  Contradiction so the
program does not exist

>
==John ffitch

This the most succinct explanation I've ever read, very good.

On 24 Oct 2012, at 11:01, John ffitch wrote:

> The halting theorem states that one cannot write a program that
> determines if an arbitrary program halts
> 
> Proof is easy by diagonalisation.
> 
> Suppose we have such a program.  Make a new program just like the
> first with the place where it prints HALTS by an infinite loop.,
> Replace the DOES NOT HALT with a stop instruction.
> 
> Give revised program to the tester.  If the program halts it does
> into a loop, and if it does not halt it stops.  Contradiction so the
> program does not exist
> 
>> 
> ==John ffitch

Dr Victor Lazzarini
Senior Lecturer
Dept. of Music
NUI Maynooth Ireland
tel.: +353 1 708 3545
Victor dot Lazzarini AT nuim dot ie