Re: Well Ordering the Reals

Hi,

I promote the null axiom theory towards completeness in a theory, and
for other reasons. An "axiomless" system of natural deduction is
without the "non-logical", or "proper" axioms, for example the axioms
of Zermelo-Fraenkel set theory, while still having first-order
predicate logic and its axioms that resolve to tautology, identity,
equality.

Some of the "axioms" of ZF I think are very well "theorems" of the null
axiom theory, FNAT the Finlayson Null Axiom Theory, or the NAT, an
Axiom Free Theory or AFT, a set, number, geometrical, and physical
theory.

There is basically nothing then (or) not nothing ad infinitum to
generate a fundamental sequence of sorts and then inference of things
infinite, ie "paradoxes" are used to impose structure, and alternative,
of sorts, besides some initial sequencing.

There is some notion of paraconsistency, that is, inconsistency, in the
dialethic dually-self-intraconsistent ur-element, thus that the
inconsistency is negligeable because the opposite of the truth in that
sense is a truth, for example, in problems with the LEM, the law of
excluded middle. Similarly completeness follows.

Basically, the agreement on any one true fact, and all its
implications, where that is basically restricted to numbers, a null
axiom, leads to something for nothing.

That seems whimsical, perhaps, even absurd.

Ross

.