Re: An instance of Russell's paradox?

"A.T." wrote:
>
> Hello,
> I have been studying Prolog for a while, and stumbled across several
> difficulties which I seem to be unable to overcome on my own. Since I
> am doing it all solely for the purpose of understanding FOL (and
> Russell's PM straight after that) I have let myself choose Sci.Logic as
> the addressee of my questions. Hopefully, someone can kindly spare a
> while for me on this.
>
> 1. Can all algorithms be enumerated,

Yes. An algorithm can be expressed in finite terms in a formal
language. Therefore there are no more than countably many of them.

> or will that be another
> formulation of Russell's paradox

Diagonalize out of your enumeration to prove that not all functions are
algorithmic.

> (with the list of all algorithms being
> another way of expressing the set of all sets)?

No, just a confusion.

(I'm amused by Eagleson's "I hope I am clear.")

--
I don't know who you are Sir, or where you come from,
but you've done me a power of good.
.

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