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Thesis-antithesis-neutrothesis, and neutrosynthesis.

1. Introduction.

In neutrosophy, <A>, <antiA>, and <neutA> combined two by two, and also all three of them together form the NeutroSynthesis. Neutrosophy establishes the universal relations between <A>, <antiA>, and <neutA>.

<A> is the thesis, <antiA> the antithesis, and <neutA> the neutrothesis (neither <A> nor <antiA>, but the neutrality in between them).

In the neutrosophic notation, <nonA> (not <A>, outside of <A>) is the union of <antiA> and <neutA>.

<neutA> may be from no middle (excluded middle), to one middle (included middle), to many finite discrete middles (finite multiple included-middles), and to an infinitude of discrete or continuous middles (infinite multiple included-middles) [for example, as in color for the last one, let's say between black and white there is an infinite spectrum of middle/intermediate colors].

2. Thesis, Antithesis, Synthesis.

The classical reasoning development about evidences, popularly known as thesis-antithesis-synthesis from dialectics, was attributed to the renowned philosopher Georg Wilhelm Friedrich Hegel (1770-1831) and later it was used by Karl Marx (1818-1883) and Friedrich Engels (1820-1895). About thesis and antithesis have also written Immanuel Kant (1724-1804), Johann Gottlieb Fichte (1762-1814), and Thomas Schelling (born 1921). While in ancient Chinese philosophy the opposites yin [feminine, the moon] and yang [masculine, the sun] were considered complementary.

Thesis, Antithesis, Neutrothesis, Neutrosynthesis.

Neutrosophy is a generalization of dialectics (which is based on contradictions only, <A> and <antiA>), because neutrosophy is based on contradictions and on the neutralities between them (<A>, <antiA>, and <neutA>). Therefore, the dialectical triad thesis-antithesis-synthesis is extended to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis. We do this not for the sake of generalization, but for better reflecting our world. A neutrosophic synthesis (neutrosynthesis) is more refined that the dialectical synthesis. It carries on the unification and synthesis regarding the opposites and their neutrals too.

Neutrosophic Dynamicity.

We have extended in [1] the Principle of Dynamic Opposition [opposition between <A> and <antiA>] to the Principle of Dynamic Neutropposition [which means oppositions among <A>, <antiA>, and <neutA>]. Etymologically "neutropposition" means "neutrosophic opposition".

This reasoning style is not a neutrosophic scheme, but it is based on reality, because if an idea (or notion) <A> arises, then multiple versions of this idea are spread out, let's denote them by [<A>.sub.1], [<A>.sub.2], ..., [<A>.sub.m]. Afterwards, the opposites (in a smaller or higher degree) ideas are born, as reactions to <A> and its versions [<A>.sub.i]. Let's denote these versions of opposites by [<antiA>.sub.1], [<antiA>.sub.2], ..., [<antiA>.sub.n]. The neutrality <neutA> between these contradictories ideas may embrace various forms, let's denote them by [<neutA>.sub.1], [<neutA>.sub.2], ..., [<neutA>.sub.p], where m, n, p are integers greater than or equal to 1.

In general, for each <A> there may be corresponding many <antiA>'s and many <neutA>'s. Also, each <A> may be interpreted in many different versions of <A>'s too. Neutrosophic Dynamicity means the interactions among all these multi-versions of <A>'s with their multi-<antiA>'s and their multi-<neutA>'s, which will result in a new thesis, let's call it <A'> at a superior level. And a new cycle of <A'>, <antiA'>, and <neutA'> restarts its neutrosophic dynamicity.

Practical Example

Let's say <A> is a country that goes to war with another country, which can be named <antiA> since it is antagonistic to the first country. But many neutral countries <neutA> can interfere, either supporting or aggressing one of them, in a smaller or bigger degree. Other neutral countries <neutA> can still remain neutral in this war. Yet, there is a continuous dynamicity between the three categories (<A>, <antiA>, <neutA.), for countries changing sides (moving from a coalition to another coalition), or simply retreating from any coalition.

In our easy example, we only wanted to emphasize the fact that <neutA> plays a role in the conflict between the opposites <A> and <antiA>, role which was ignored by dialectics.

So, the dialectical synthesis is extended to a neutrosophic synthesis, called neutrosynthesis, which combines thesis, antithesis, and neutrothesis.

Theoretical Example.

Suppose <A> is a philosophical school, and its opposite philosophical school is <antiA>. In the dispute between <A> and <antiA>, philosophers from the two contradictory groups may bring arguments against the other philosophical school from various neutral philosophical schools' ideas (<neutA>, which were neither for <A> nor <antiA>) as well.

Received: 12 February, 2015 Accepted: 20 Febrauary, 2015

Acknowledgement

The author would like to thanks Mr. Mumtaz Ali, from Quaid-i-Azam University, Islamabad, Pakistan, for his comments on the paper.

References

[1.] Florentin Smarandache, Law of Included Multiple-Middle & Principle of Dynamic Neutrosophic Opposition, EuropaNova & Educ. Publ., BrusselsColumbus (Belgium-USA), 136 p., 2014.

[2.] Florentin Smarandache, and Mumtaz Ali, Neutrosophic Triplet Groups, mss., 2013.

[3.] Fu Yuhua, Creating Generalized and Hybrid Set and Library with Neutrosophy and Quad-stage Method, mss. 2015.

Florentin Smarandache

University of New Mexico, 705 Gurley Ave. Gallup, NM 87301, USA, E-mail: smarand@unm.edu
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Author:Smarandache, Florentin
Publication:Neutrosophic Sets and Systems
Article Type:Report
Date:Mar 1, 2015
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