Re: Ross Finlayson what about the Prolog Liar Paradox ?

[ Followup-To: set ]

In comp.theory Ross Finlayson <[email protected]> wrote:

[ ... ]

> Since Chrysippus for modal, temporal, relevance logic,
> there's the like of "Hume's connexions", where something
> like John Stuart Mill would be so familiar to quasi-modal
> repeteurs.

> The model-theory and the proof-theory are equi-interpretable.

> Then, "theories-of-one-relation" like set-theory or class-theory
> or part-theory or partition-theory, or order-theory or ordering-theory,
> like set theory, for example ZFC with:

> an ordinary vacuity, the empty set,
> an ordinary infinity, the inductive set,

> those being both expansion-of-comprehension and
> restriction-of-comprehension, since axioms are of at least two kinds,
> then for various rulialities/regularities that compete:

> well-foundedness, sets having e-minimal elements,
> well-ordering, orderings having e-minimal elements,

> then besides the usually not included alike Martin's axiom:

> well-dispersion, both e-minimal and e-maximal, the illative or univalent,

> then the rest of the axioms of ZFC being expansion of comprehension
> or composing sets, quite naively, then at least one of those,
> doesn't matter much, being called a schema instead of an axiom
> for first-order-izibility,

> that's ZFC, the set theory, then for its accounts modeling the
> descriptive set theory's account of geometry and for the objects
> of real analysis, usually also axiomatizing

> least-upper-bound existence of the rational field,
> measure 1.0 of the unit in the real field,

> since those aren't derived in the usual way, with line-reals first
> providing least-upper-bound and measure 1.0, then yes,
> I've heard of ZFC, and NBG and GBN, and ZFC with classes.

That sentence is far too long.  Splitting it over many (what look like)
paragraph breaks doesn't help.  In fact, it is so long that any meaning
it may have can only be extracted from it by laborious analysis, so
excessively laborious that it is fair to accuse the sentence of being
meaningless.

That you may be debating the inane and meaningless yourself is not an
acceptable pretext.

> It's good to know these things and be thorough and conscientious,
> instead of being a vacuous moron of the ordinary sort.



> In school when were shown that an error in reasoning could result
> seemingly correct answers that were wrong, it was in the setting
> of a calculus course, where one of the expressions was a quotient
> with the divisor being an expression in the difference of a constant
> and a variable, thusly, if the variable was equal the constant,
> then that would be dividing by zero, which is undefined, then a
> resulting evaluation resulted 0 = 1, which was wrong. Then there
> was addressed limits from the left and limits from the right and
> discontinuities and removable discontinuities, about the thorough sort
> of account.

> The point here is that the gap in definition about the objects of
> mathematics is different than ex falso quodlibet, since singularities in
> a singularity theory are branches in a multiplicity theory,
> and it's simply erroneous to break the definition, and erroneous to have
> carried the derivation, ex falso quodlibet is erroneous.

-- 
Alan Mackenzie (Nuremberg, Germany).