Wikileaks says Wednesday is the End for Hillary.

[xorcist at sigaint.org]

>> "AXIOM: A proposition regarded as self-evidently true,
>
>
> 	Axioms being self-evidently true means that if you choose to
> 	DENY them, you need to USE them in the denial process
> 	anyway, therefore proving that they ARE true. Try assuming that
> 	the so called identity principle is not 'true' and see where
> 	you get.

No, one simply denies them. But, even if one HAD to USE them, that would
not prove them. I might use several axioms to derive a contradiction. If
one of my axioms IS the law of non-contradiction, I can then exclude one,
or more of the axioms to rectify the situation, including the principle of
non-contradiction.

I'm not aware of any systems of logic that deny the law of identity. It
is, of course, quite foundational. But since you claimed that axioms can
be proven: well go ahead and prove it, then. After all, the burden of
proof is never on the skeptic.

But this all began not with a disagreement over the law of identity, but
over the law of non-contradiction. The principle of non-contradiction IS
denied, by example, in the philosophical school of dialetheism. It is used
in mathematics, as well, in formal paraconsistent logics, which can not
only be inconsistency-tolerant, but also have more states to a proposition
than merely "true" and "false."

These, and other multi-value logics, generally, are useful in a wide area
of mathematics, physics, electronics and so on.

In these complex systems they are quite useful. Why should we not use them
in other complex areas of thought?

Simply because you're not aware of them? Well then, OK. So then we have to
AGREE on which system to use first, then.

"QED"

>
> 	I don't need to invoke internet authority or the sacred
> 	wikipedia scriptures xorcist. I can explain what an axiom in my
> 	own words.

I don't either. I've explained several times that axioms are assumptions,
or if you prefer, propositions, and are not subjected to PROOF. You
disagreed, so I quoted sources.

Your statement about axioms was quite wrong. They are not subject to proof.
You're now trying to walk  that back and play a different angle -- one
that I handed to you -- that of self-evidence.

Quite good. Let's continue.

>
> 	And even going by that definition, if axioms are self-evidently
> 	TRUE, then people who don't 'agree' that they are true are
> 	self-evidently...troubled.

They are self-evident only from a certain way of thinking. For example, in
geometry, a point is axiomatic. An infinitely small object with no
dimension. This is an intellectual abstraction that is self-evident and
meaningful only from the perspective of that intellectual simplification
used in geometry.

Physically, there is nothing with no dimension. From an idealized,
abstracted, way of thinking the existence and meaning of a point is
self-evident. From a physical perspective, it is utter rubbish.

What perspective you have, the way you're approaching a subject, informs
which axioms you'll use as the foundation of your reasoning.

> 	(and by the way, your first source is about mathematics, not
> 	logic or philosophy in general)

I'm quite aware of that. So? Formal logic, as studied and used by
philosophy, is a branch of mathematics.

And in any case, in philosophy, and informal logic, axioms cannot be
proven, as you have stated.