The Smarandache Class of Paradoxes
by
C. T. Le
Arizona State University, Tempe

Let <A> be an attribute, and <Non-A> its negation. Then: Paradox 1. ALL IS <A>, THE <Non-A> TOO. Examples: E11: All is possible, the impossible too. E12: All are present, the absents too. E13: All is finite, the infinite too. Paradox 2. ALL IS <Non-A>, THE <A> TOO. Examples: E21: All is impossible, the possible too. E22: All are absent, the presents too. E23: All is infinite, the finite too. Paradox 3. NOTHING IS <A>, NOT EVEN <A>. Examples: E31: Nothing is perfect, not even the perfect. E32: Nothing is absolute, not even the absolute. E33: Nothing is finite, not even the finite. Remark: The three kinds of paradoxes are equivalent. They are called: The Smarandache Class of Paradoxes. More generally: Paradox: ALL (Verb) <A>, THE <Non-A> TOO (<The Generalized Smarandache Class of Paradoxes>) Replacing <A> by an attribute, we find a paradox. Let's analyse the first one (E11): <All is possible, the impossible too.> If this sentence is true, then we get that <the impossible is possible too>, which is a contradiction; therefore the sentence is false. (Object Language). But the sentence may be true, because <All is possible> involves that <the impossible is possible>, i.e.< it's possible to have impossible things>, which is correct. (Meta-Language).

Of course, from these ones, there are unsuccessful paradoxes, but the proposed method obtains beautiful others. Look at pun which remembers you Einstein:

All is relative, the (theory of) relativity too! So: 1. The shortest way between two points is the meandering way! 2. The unexplainable is, however, explained by the word: "unexplainable"! References [1] Ashbacher, Charles, "'The Most Paradoxist Mathematician of the World', by Charles T. Le", review in Journal of Recreational Mathematics, USA, Vol. 28(2), 130, 1996-7.

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The Smarandache Class of Paradoxes

Date received: October 2, 2000