Re: An instance of Russell's paradox?

In article <1125408987.204762.38660@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"A.T." <andrzej-tomaszewski@xxxxx> wrote:

>Ms Knox wrote:
>
>[snip]
>
>> All *partial* functions (or all Turing Machines, etc.) can be
>> enumerated, and there is no diagonalisation problem with that.
>
>I see.
>
>> The set of just all *total* functions (or always-halting TMs, etc.) can
>> not be enumerated for the reason you give: the diagonalisation of any
>> list of total functions will be another total function which is
>> different from every one in the list.
>
>Right, I see.
>
>Ms Knox, may I also ask you to kindly make some remarks regarding the
>other two questions I posted, namely, the question suggesting the
>infinite generalization of the arity of every predicate (I got this
>idea from Quine, but I lost trace of the actual source),

Sorry, that's something I'm neither knowledgeable about nor interested
in. Do you recall what benefit(s) there might be in making this
extension? ISTM that giving up finite expressions would be giving up a
lot.

>as well as the
>question pertaining to the actual difference between an atom and a
>predicate in philosopher(socrates) transformed into [philosopher,
>socrates], where the predicate is(?) really the first atom of the
>analogous list form of a proposition (the problem is, I really see no
>difference whatsoever).

Firstly, there is a difference. In Prolog, the [a b c] representation
of lists is actually syntactic sugar for the binary (and nullary) term
".":
.(a, .(b, .(c, .())))

Similarly, in Lisp the (a b c) representation of lists is sugar for
(a . (b . (c . NIL))))

Secondly, in Prolog the =.. predicate converts between an arbitrary term
such as philosopher(socrates) and the prefix list representation of it.
These are *not* interchangeable. Internally to a Prolog implementation
terms may indeed be represented as some sort of list, but that is wholly
different from the *external* representation of Prolog "[...]" lists
using '.' terms.


>As always, I am most greatful for your time. Thank you very much indeed
>for writing.
>
>Kindest regards,
>Tom
>
>> [snip]

--
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| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
.

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