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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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