Set Theory and Logic

1003 Submissions

[8] viXra:1003.0269 [pdf] submitted on 8 Mar 2010

The Smarandache's Class of Paradoxes

Authors: C. Le
Comments: 4 pages, edited by C. Le, and translated into German by Bernd Hutschenreuther

The Smarandache's Class of Paradoxes are semantic paradoxes of the form "All is <A>, the <nonA> too!", where <nonA> is what is not <A>. As a particular case, replacing <A> but an attribute (or, in general, by an idea) it is well know the Smarandache semantic paradox: "All is possible, the impossible too!" which is the motto of the Paradoxism movement in arts, letters, and sciences.
Category: Set Theory and Logic

[7] viXra:1003.0224 [pdf] submitted on 7 Mar 2010

Introduction to Neutrosophic Logic

Authors: Charles Ashbacher
Comments: 145 pages

As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by where I do not use some topic from those courses.
Category: Set Theory and Logic

[6] viXra:1003.0171 [pdf] submitted on 6 Mar 2010

Deducibility Theorems in Boolean Logic

Authors: Florentin Smarandache
Comments: 4 pages

In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.
Category: Set Theory and Logic

[5] viXra:1003.0167 [pdf] submitted on 6 Mar 2010

A Class of Recursive Sets

Authors: Florentin Smarandache
Comments: 7 pages

In this article one builds a class of recursive sets, one establishes properties of these sets and one proposes applications. This article widens some results of [1].
Category: Set Theory and Logic

[4] viXra:1003.0119 [pdf] submitted on 6 Mar 2010

Funny Problems!

Authors: Florentin Smarandache
Comments: 6 pages

Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and afterwards. They have a more educational interest because make the students think different!
Category: Set Theory and Logic

[3] viXra:1003.0117 [pdf] submitted on 6 Mar 2010

Linguistic Paradoxes and Tautologies

Authors: Florentin Smarandache
Comments: 12 pages

Classes of linguistic paradoxes are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such paradoxes one grammatically adjusts the sentences.
Category: Set Theory and Logic

[2] viXra:1003.0065 [pdf] submitted on 6 Mar 2010

Logic: a Misleading Concept. a Contradiction Study Toward Agent's Logic Ontology

Authors: Feng Liu, Florentin Smarandache
Comments: 10 pages

The paper presents a fresh new comprehensive ideology on Neutrosophic Logic based on contradiction study in a broad sense: general critics on conventional logic by examining the essence of logic, fresh insights on logic definition based on Chinese philosophical survey, and a novel and genetic logic model as the elementary cell against Von Neumann oriented ones based on this novel definition. As for the logic definition, the paper illustrates that logic is rather a tradeoff between different factors than truth and false abstraction. It is stressed that the kernel of any intelligent system is exactly a contradiction model. The paper aims to solve the chaos of logic and exhibit the potential power of neutrosophy: a new branch of scientific philosophy.
Category: Set Theory and Logic

[1] viXra:1003.0062 [pdf] submitted on 6 Mar 2010

Intentionally and Unintentionally. On Both, A and Non-A, in Neutrosophy

Authors: Feng Liu, Florentin Smarandache
Comments: 7 pages

The paper presents a fresh new start on the neutrality of neutrosophy in that "both A and Non-A" as an alternative to describe Neuter-A in that we conceptualize things in both intentional and unintentional background. This unity of opposites constitutes both objective world and subjective world. The whole induction of such argument is based on the intensive study on Buddhism and Daoism including I-ching. In addition, a framework of contradiction oriented learning philosophy inspired from the Later Trigrams of King Wen in I-ching is meanwhile presented. It is shown that although A and Non-A are logically inconsistent, but they are philosophically consistent in the sense that Non-A can be the unintentionally instead of negation that leads to confusion. It is also shown that Buddhism and Daoism play an important role in neutrosophy, and should be extended in the way of neutrosophy to all sciences according to the original intention of neutrosophy.
Category: Set Theory and Logic