On Fri, 22 Sep 2000 10:04:40 +0200 (SAST) Peter van Heusden <pvh at egenetics.com> wrote:
> A) Suppose you write a program whose purpose is to examine another
> program and decide whether the program halts. Let's call this program
> H. If a program halts, H does not halt. If the program does not halt, H
> halts.
>
> B) Feed H to itself. Now there are two possibilities:
>
> B.1) H decides that H halts, in which case H does not halt. Oops!
>
> B.2) H decides that H does not halt, in which case H halts. Oops again!
>
> Now, a computer can't solve this problem. My question is, can anyone?
? If I'm not mistaken, Hegel's distinction between bad and true infinity 'solves' (hahhahahhha) this problem. A bad infinity is where one finite H is defined through not being something else (H halting other programs - determinate negation). The true infinity is when it returns to itself (H fed to itself) - it forms an impossible circle and the 'vanishing mediator' of H is the 'remainder' - which, of course, is nothing (Hegel's pure being)... the essence of H is its own self-relating negativity... quality, quantity, quantum...
ken