Neutrosophy

The neutrality of this article is disputed.

Neutrosophy is a theory developed by Florentin Smarandache following on from the work of Basarab Nicolescu and Stéphane Lupasco. This theory considers every notion or idea together with its opposite or negation and the spectrum of "neutralities" (i.e. notions or ideas located between the two extremes, supporting neither nor ). The and ideas together are referred to as . The theory claims that every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium.

Table of contents

1 Origins
2 Extensions
3 See also
4 References
5 External links

Origins

Neutrosophy, neutrosophic logic, neutrosophic sets, etc., were invented in the 1980s by Smarandache, after he coined the word from the Latin neuter and the Greek sophia, to mean "knowledge of neutral thought".

Smarandache promotes neutrosophy heavily. He organized the "First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and Statistics" in 2001 and published the conference's proceedings. One book about neutrosophy was published by American Research Press, a small publisher closely aligned with Smarandache. Additionally, some articles by Smarandache and Jean Dezert were included in the Journal of Multiple-Valued Logic, Volume 8, Number 3, issue dedicated to neutrosophy and neutrosophic logic, and Numbers 5-6. This journal is now known as the Journal of Multiple-Valued Logic and Soft Computing. Other journals that published on neutrosophics are International Journal of Social Economics (University of California at Fresno), Libertas Mathematica (University of Texas at Arlington), Proceedings of the Second Symposium / Romanian Academy of Scientists, American Branch (City University of New York), Bulletin of the Transilvania University of Brasov (Romania), Abstracts of papers presented to the International Congress of Mathematicians (Beijing, China) and Abstracts of papers presented to the meetings of the American Mathematical Society (University of California at Santa Barbara meeting).

Extensions

Smarandache extended neutrosophy to neutrosophic logic (or Smarandache logic), neutrosophic sets, and so forth.

In bivalent logic, the truth value of a proposition is given by either one (true), or zero (false). Neutrosophic logic is a multi-valued logic, in which the truth values are given by an amount of truth, an amount of falsehood, and an amount of indeterminacy. Each of these values is between 0 and 1. In addition, the values may vary over time, space, hidden parameters, etc. Further, these values can be ranges.

In the neutrosophic logic every logical variable x is described by an ordered triple x = (T, I, F) where T is the degree of truth, F is the degree of false and I the level of indeterminacy.

(A) To maintain consistency with the classical and fuzzy logics and with probability there is the special case where T + I + F = 1.

(B) But to refer to intuitionistic logic, which means incomplete information on a variable proposition or event one has T + I + F < 1.

(C) Analogically referring to Paraconsistent logic, which means contradictory sources of information about a same logical variable, proposition or event one has T + I + F > 1.

Thus the advantage of using Neutrosophic logic is that this logic distinguishes in philosophy between relative truth that is a truth in one or a few worlds only noted by 1 and absolute truth denoted by 1+. Likewise neutrosophic logic distinguishes between relative falsehood, noted by 0 and absolute falsehood noted by -0 in non-standard analysis.

For example, a neutrosophic answer to the question "Is the pope a Catholic?" might be "80-90% true, 36-42% false, and 2-7% indeterminate". Note that these values need not sum to 100%. Smarandache claims that it can serve as a generalization of many other logics, such as: fuzzy logic, intuitionistic logic, paraconsistent logic, boolean logic, etc.

In neutrosophic set theory, propositions of the form "x is an element of S" are answered in terms of neutrosophic truth values. Hence, each element has a membership-degree, an indeterminacy-degree, and a non-membership degree. These are claimed to generalise paraconsistent sets and intuitionistic sets, amongst others.

There are some papers which describe applications at Smarandache's home page.

References

C. Ashbacher, Introduction to Neutrosophic Logic, American Research Press, 2002.
L. Wos, Auomated Reasoning: 33 Basic Research Problems, Prentice-Hall, 1988.

External links

Florentin Smarandache: A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability.
Florentin Smarandache: Neutrosophy
Journal of Multiple-Valued Logic and Soft Computing