Re: Post Axiom Syndrome

george wrote:
> Ross A. Finlayson wrote:
> > Consider the Liar paradox. With primary
> > objectives of consistency, that no untrue statements are provable, and
> > completeness, that all true statements are provable, a statement as the
> > liar is basically false, it's not true, but then of course its
> > statement is that its false, so its not false, but not true, false in a
> > different or circular sense.
>
> It's none of the above. There is simply NOTHING you can do
> with the Liar if you are going to insist that everything has
> to have a truth-value. But there is, of course, no reason to
> insist upon that. As soon as you learn that 1/0 is undefined,
> "undefined" is COMPLETELY legitimate and there is simply nothing
> anybody can do about that.
>
> > The Liar is not so bad, but with further primary objectives in an
> > encompassing theory of mathematical logic, unrestricted comprehension
> > and quantifiers lead to a variety of states or modes of statement that
> > that basically reflect the Liar.
>
> THAT viewpoint is just plain STUPID. The Liar was ALREADY THERE,
> in natural language. It is not like you are going to be able to
> get away from it by going to something MORE comprehensive (like
> FOL). Of course, FOL is so weak that most people think that
> natural language is stronger than it, but what do they know.

On the contrary, my brother, that viewpoint is not stupid.

That your knee-jerk reaction to something you don't understand is to
call it stupid is an aspect of your personality, I can understand that
even when I disagree with you. That doesn't reflect well on you for
the variety of times that you've later changed your mind.

ZF is inconsistent, because something like X: for any x, x E X, is
simple to define, and quantification involves a choice function over U.

I think you would do well to read Hegel's definitions of Being and
Nothing, they are short monographs.

Your finite axiomatic system that is not the null axiom system is
incomplete, there are true things, inarguably across all frames of
reference, of which it is ignorant. Then, if a motivation of
determining a theory within mathematical logic is that it prove all
true things, be complete, and disprove all false things, be consistent,
then it must be complete, perhaps for it so to be consistent.

Several hundred years ago, the square root of negative one was
undefined. Are you so quick to think that 1/0 is undefined? 1/0 is
one divided by zero, i is the square root of negative one. Where there
are a variety of complex number systems that simplify the use of
complex and hypercomplex numbers, there are as well a variety of
systems to treat 1/0, a realized unit scalar infinity, and it is seen
in some modern analytical results, for example where a variety of
solutions exist.

A model is to a theory as a class is to a set, they're each pointless.
What's the class of all classes? Is the model of all models not a
model? Is the order type of all ordinals an ordinal?

ZF is inconsistent. Can you get past that?


Ross

.

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