edited by Leonardo F. D. da Motta

   Look at this Sorites Paradoxes (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.

 Between <A> and <Non-A> there is no clear distinction, no exact frontier. Where does <A> really end and <Non-A> begin? We extend Zadeh's fuzzy set term to neutrosophic concept.


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

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