That paradigm is to derive results in the context of an

axiomatic system.

A set of neutrosophic axioms [OMEGA] is called neutrosophic

axiomatic system, where the neutrosophic deducing and the neutrosophic inference (neutrosophic implication) are used.

The great Austrian mathematician Kurt Godel shook up the academic world by proving for any computable

axiomatic system powerful enough to describe the arithmetic of the natural numbers that, one, if the system is consistent, it cannot be complete ("incompleteness theorem"), and two, the consistency of the axioms cannot be proved within the system.

I think that is a false assumption, which led to a false interpretation that in turn led to an

axiomatic system that does not resemble reality very much.

No consistent

axiomatic system proves all mathematical truths.

There is no set of all sets--it leads to contradictions both in naive set theory and in the

axiomatic system Badiou chooses--hence there is no totality of Being, no ontological absolute.

and establishing the consistency of each

axiomatic system.

The transition from classical mechanics to quantum mechanics has meant a significant change in the

axiomatic system and main laws of classical mechanics.

27] that "An

axiomatic system is in general constructed in order to axiomatize a certain scientific discipline previously given in a pre-systematic, "naive", or 'genetic' form".

We framed the results of this analysis as an

axiomatic system, explicitly based on the non-Aristotelian premises of Korzybski (1941), and stated in a mathematical language of known structure--an algebraic dialect of the WIE mathematical theory of sets.

Consequently, an

axiomatic system 'is a formation of our arbitrariness still not made up out of thin air, a creation of the researcher still not without relationship with reality' (Schumpeter 1908, p.

He presents an

axiomatic system in which there are principles taken by the knower as prior and primary, embodying what is first in nature.