1) Sorites Paradox (associated with Eubulides of Miletus (fourth century B.C.):

Our visible world is composed of a totality of invisible particles.

a) An invisible particle does not form a visible object, nor do two invisible particles, three invisible particles, etc.
However, at some point, the collection of invisible particles becomes large enough to form a visible object, but there is apparently no definite point where this occurs.

b) A similar paradox is developed in an opposite direction. It is always possible to remove a particle from an object in such a way that what is left is still a visible object. However, repeating and repeating this process, at some point, the visible object is decomposed so that the left part becomes invisible, but there is no definite point where this occurs.

Generally, between <A> and <Non-A> there is no clear distinction, no exact frontier. Where does <A> really end and <Non-A> begin? One extends Zadeh's "fuzzy set" term to the "neutrosophic set" concept.

2) Uncertainty Paradox: Large matter, which is under the 'determinist principle', is formed by a totality of elementary particles, which are under Heisenberg's 'indeterminacy principle'.

3) Unstable Paradox: Stable matter is formed by unstable elementary particles (elementary particles decay when free).

4) Short Time Living Paradox: Long time living matter is formed by very short time living elementary particles.

References:

[1] Marie-Helene Boyer, "Re: How are possible the Smarandache Uncertainty, Unstable, etc. Paradoxes?", MAD Scientist, Washington University School of Medicine, St. Louis, Missouri,

http://www.madsci.org/posts/archives/972501333.Ph.r.html.

[2] Chong Hu, "How are possible the Smarandache Uncertainty, Unstable, etc. Paradoxes?", MAD Scientist, Washington University School of Medicine, St. Louis, Missouri, http://www.madsci.org/posts/archives/972501333.Ph.q.html.

[3] Chong Hu, "How do you explain the Smarandache Sorites Paradox?", MAD Scientist, Washington University School of Medicine, St. Louis, Missouri, http://www.madsci.org/posts/archives/970594003.Ph.q.html.

[4] Amber Iler, "Re: How do you explain the Smarandache Sorites Paradox?", MAD Scientist, Washington University School of Medicine, St. Louis, Missouri, http://www.madsci.org/posts/archives/970594003.Ph.r.html.

[5] Leonardo Motta, editor, "A Look at the Smarandache Sorites Paradox", Second International Conference on Smarandache Type Notions In Mathematics and Quantum Physics,

University of Craiova, Craiova, Romania, December 21 - 24, 2000;

In the web site at York University, Canada, http://at.yorku.ca/cgi-bin/amca/caft-04.

[6] Gheorghe Niculescu, editor, "On Quantum Smarandache Paradoxes", Second International Conference on Smarandache Type Notions In Mathematics and Quantum Physics,

University of Craiova, Craiova, Romania, December 21 - 24, 2000;

In the web site at York University, Canada, http://at.yorku.ca/cgi-bin/amca/caft-20.

[7] Florentin Smarandache, "Invisible Paradox" in "Neutrosophy. / Neutrosophic Probability, Set, and Logic", American Research Press, Rehoboth, 22-23, 1998.

[8] Florentin Smarandache, "Sorites Paradoxes", in "Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry", Xiquan Publishing House, Phoenix, 69-70, 2000.

[9] Louisiana Smith and Rachael Clanton, advisor Keith G. Calkins, "Paradoxes" project, Andrews University, http://www.andrews.edu/~calkins/math/biograph/topparad.htm.