Re: An instance of Russell's paradox?

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), 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).

As always, I am most greatful for your time. Thank you very much indeed
for writing.

Kindest regards,
Tom

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