## THE SMARANDACHE CLASS OF PARADOXES, Vol. 1

### edited by Charles T. Le

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:

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.

[2] Begay, Anthony, "The Smarandache Semantic Paradox", Humanistic Mathematics Network Journal, Harvey Mudd College, Claremont, CA, USA, Issue #17, 48, May 1998.

[3] Le, Charles T., "The Smarandache Class of Paradoxes", Bulletin of the Transylvania University of Brasov, Vol. 1 (36), New Series, Series B, 7-8, 1994.

[4] Le, Charles T., "The Smarandache Class of Paradoxes", Bulletin of Pure and Applied Sciences, Delhi, India, Vol. 14 E (No. 2), 109-110, 1995.

[5] Le, Charles T., "The Most Paradoxist Mathematician of the World: Florentin Smarandache", Bulletin of Pure and Applied Sciences, Delhi, India, Vol. 15E (Maths & Statistics), No. 1, 81-100, January-June 1996.

[6] Le, Charles T., "The Smarandache Class of Paradoxes", Journal of Indian Academy of Mathematics, Indore, Vol. 18, No. 1, 53-55, 1996.

[7] Le, Charles T., "The Smarandache Class of Paradoxes / (mathematical poem)", Henry C. Bunner / An Anthology in Memoriam, Bristol Banner Books, Bristol, IN, USA, 94, 1996.

[8] Mitroiescu, I., "The Smarandache Class of Paradoxes Applied in Computer Sciences", Abstracts of Papers Presented to the American Mathematical Society, New Jersey, USA, Vol. 16, No. 3, 651, Issue 101, 1995.

[9] Mudge, Michael R., "A Paradoxist Mathematician: His Function, Paradoxist Geometry, and Class of Paradoxes", Smarandache Notions Journal, Vail, AZ, USA, Vol. 7, No. 1-2-3, 127-129, 1996.

[10] Popescu, Marian, "A Model of the Smarandache Paradoxist Geometry", Abstracts of Papers Presented to the American Mathematical Society, New Providence, RI, USA, Vol. 17, No. 1, Issue 103, 96T-99-15, 265, 1996.

[11] Popescu, Titu, "Estetica paradoxismului", Editura Tempus, Bucarest, 26, 27-28, 1995.

[12] Rotaru, Ion, "Din nou despre Florentin Smarandache", Vatra, Tg. Mures, Romania, Nr. 2 (299), 93-94, 1996.
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[14] Smarandache, Florentin, "Mathematical Fancies & Paradoxes", The Eugene Strens Memorial on Intuitive and Recreational Mathematics and its History, University of Calgary, Alberta, Canada, 27 July - 2 August, 1986.

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[16] Tilton, Homer B., "Smarandache's Paradoxes", Math Power, Tucson, AZ, USA, Vol. 2, No. 9, 1-2, September 1996.

[17] Weisstein, Eric W., "Smarandache Paradox", CRC Concise Enciclopedia of Mathematics, CRC Press, Boca Raton, FL, 1661, 1998.

[18] Zitarelli, David E., "Le, Charles T. / The Most Paradoxist Mathematician of the World", Historia Mathematica, PA, USA, Vol. 22, No. 4, # 22.4.110, 460, November 1995.

[19] Zitarelli, David E., "Mudge, Michael R. / A Paradoxist Mathematician: His Function, Paradoxist Geometry, and Class of Paradoxes", Historia Mathematica, PA, USA, Vol. 24, No. 1, #24.1.119, 114, February 1997.