THE SMARANDACHE CLASS OF PARADOXES

                           

Let <A> be an attribute, and <Anti-A> its negation.  
Then:

Paradox 1.  ALL IS <A>, THE <Anti-A> TOO.
  Exemples:
  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 <Anti-A>, THE <A> TOO.
  Exemples:
  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>.

  Exemples:
  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 <Anti-A> TOO

(<The Generalised 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>, 
wich 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]   Weisstein, Eric W. "Smarandache Paradox." From MathWorld-
-A Wolfram Web Resource. 
http://mathworld.wolfram.com/SmarandacheParadox.html 
     [2]  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.
     [3]  Begay, Anthony, "The Smarandache Semantic Paradox",
<Humanistic Mathematics Network Journal>, Harvey Mudd College,
Claremont, CA, USA, Issue #17, 48, May 1998.
     [4]  Le, Charles T.,  "The Smarandache Class of Paradoxes",
<Bulletin of the Transilvania University of Brasov>, Vol. 1 (36),
New Series, Series B, 7-8, 1994.
     [5]  Le, Charles T.,  "The Smarandache Class of Paradoxes",
<Bulletin of Pure and Applied Sciences>, Delhi, India, Vol. 14 E
(No. 2), 109-110, 1995.
     [6]  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.
     [7]  Le, Charles T.,  "The Smarandache Class of Paradoxes",
<Journal of Indian Academy of Mathematics>, Indore, Vol. 18, No.
1, 53-55, 1996.
     [8]  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.
     [9]  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.
     [10]  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.
     [11]  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.
     [12]  Popescu, Titu,  "Estetica paradoxismului", Editura
Tempus, Bucarest, 26, 27-28, 1995.
     [13]  Rotaru, Ion, "Din nou despre Florentin Smarandache",
<Vatra>, Tg. Mures, Romania, Nr. 2 (299), 93-94, 1996.
     [14]  Seagull, Larry,  "Clasa de Paradoxuri Semantice
Smarandache" (translation), <Abracadabra>, Salinas, CA, USA, 
Anul 2, Nr. 20, 2, June 1994.
     [15]  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.
     [16]  Vasiliu, Florin,  "Paradoxism's main roots",
Translated from Romanian by Stefan Benea, Xiquan Publishing
House, Phoenix, USA, 64 p., 1994;  review in <Zentralblatt fr
Mathematik>, Berlin, No. 5, 830 - 17, 03001, 1996.
     [17]  Tilton, Homer B., "Smarandache's Paradoxes", <Math
Power>, Tucson, AZ, USA, Vol. 2, No. 9, 1-2, September 1996.
     [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.




                   SMARANDACHE'S LINGUISTIC PARADOXES


     Abstract.
  Classes of linguistic paradoxes are introduced with examples
and explanations.  
  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.

     Let <N>, <V>, <A> be some noun, verb, and attribute
respectively, and <Non-N>, <Non-V>, <Non-A> respectively their
antonyms.  For example, if <A> is <small> then <Non-A> is <big>
or <large>, etc.
Also let <N'>, <N''>, etc. represent synonyms of <N> or even <N>,
and so <V'>, <V''>, etc.
or <A'>, <A''>, etc.
Let <NV> represent a noun-ed verb, and <NV'> a synonym, etc.
  Then, one defines the following classes of linguistic paradoxes
and semi-paradoxes:


     1.   <Non-N> is a better <N>.
          <Non-A> is a better <A>.
          <Non-V> is a better <V>.
  Examples:  
Not to speak is sometimes a better speech.
Not to complain is a better complain.
Unattractive is sometimes better than attractive.
Slow is sometimes better than fast.
No government is a better government.
A non-ruler is a better ruler.
No news is good news.
Not to stare is sometimes better to look.
Not to love is a better love.
Not to move is sometimes a better move.
Impoliteness is a better politeness.
Not to hear is better than not listening.
No reaction is sometimes the best reaction.
Not to show kindness is a better kindness [welfare].
She is better than herself.
No fight is a better fight [i.e. to fight by non-violent means].


     2.   Only <N> is truly a <Non-N>.
          Only <A> is truly a <Non-A>.
  Examples:
Only a rumor is truly a gossip.
Only a fiction is truly a fact.
Only normal is truly not normal.
Nobody is truly a 'somebody'.  
Only fiction is truly real.
The friend is the most dangerous hidden enemy.
Only you are truly not you [=you act strangely].
Only mercy can be truly merciless.
If you spit at the sky, it will fall in your face.
Only gentleness is truly wild.


     3.   This is so <A>, that it looks <Non-A>.
  Examples:  
This is so true, that it looks false!
This is so ripe, that it looks spoilt.
This is so friendly, that it looks hostile.
He seemed so trustworthy, that he looks untrustworthy.
This is so fake, it looks real!
This is so proper, that it looks improper.
This is so beautiful, that it looks unreal.
This is so simple, that it looks difficult.
The story was so real, that it looked fiction.
Can't see the trees for the forest.


     4.   There is some <N> which is <A> and <Non-A> at the same
          time.
  Examples:    
There are events which are good and bad at the same time.
There are laws which are good and bad at the same time.
There are some news which are real and wrong at the same time.
There are some insects which are helpful and dangerous at the
same time. [like the spider]
There are men who are handsome and ugly at the same time.
There are classes that are fun and boring at the same time.
There are some ministers which are believers and mis-believers at
the same time.
There are moments that are sweet and sour.
There are games which are challenged and not competitive at the
same time.
Food which are simultaneously hot and cold.
The game was exciting, yet boring [because we were losing].
People are smart and foolish at the same time [i.e., smart at
something, and foolish at other thing].


     5.   There is some <N> which <V> and really <Non-V> at the
          same time.
  Examples:    
There are people who trick and do not really trick at the same
time.
There are some people who play and don't play at the same time.
Some of life's experiences are punishments and rewards at the
same time.
Exercise is exhausting but also invigorating.
There are children who listen and do not really listen at the
same time.
There are teachers who teach and don't teach at the same time.
There are people who spell and misspell at the same time.
Nice and rough people concomitantly.
Politicians who lie and tell the truth all the time!


     6.   To <V>, even when <Non-V>.
  Examples:  
A sage thinks even when he doesn't think.
I exist when I don't exist.
A clown is funny even when he isn't being funny.
To die of thirst surrounded by water.  [saltwater]
To be a poet and not know it.
A mother worries even when she doesn't worry.
To believe even when you don't believe.
Is matching even when not-matching.
I sleep even when I am awake.
Always running around.
To dream, even when not sleeping.


     7.   This <N> is enough <Non-N>.
  Examples:
This silence is enough noise.
This vacation from work is hard work.
The superiority brings enough inferiority.  [=listlessness]
This day is my night.
This diary is enough non-diary.
This sleep is enough awake.
This sweet truthfulness is enough sarcasm.
This table of four is enough for six people.
I had enough.
This job is enough recreation [when enjoying the job].


     8.   <Non-V> sometimes means <V>.
  Examples:  
Not to speak sometimes means to speak.
Not to touch sometimes means to touch.
The preserve peace sometimes means going to war.
To destroy life (as in viruses) sometimes means to preserve life.
Not to listen sometimes means to listen.
Two feet forward sometimes means standing still.
Not to litter sometimes means to litter.
Speeding is sometimes not speeding [in case of emergency].
Not to show anger is sometimes to show anger.


     9.  <N> without <N>.    
  Examples:  
Hell without hell.
The style without style.
The rule applied:  there were no rule!
Our culture is our lack of culture.
Live without living.
Some people are so afraid of death, that they do not live.
Work without work.
Can't live with them, can't live without them.
Death without death [for a Christian dying is going on to eternal
life].
Guilt without guilt [sometimes is guilty but doesn't feel
guilty].


     10.  a) <N> inside/within the <Non-N>.
  Examples:  
Movement inside the immobility.
Silence within the noise.
Slavery within the freedom.
Loneliness within a crowd.
A circle within a circle.
The wrestling ring inside a squared section.
To find wealth in poverty [i.e., happiness and love].


          b) <Non-N> in the <N>.
  Examples:  
Immobility inside the movement.
Noise inside the silence.
The eye of the storm.
Government.  Bureaucracies.
Inequality inside the equality.
Single inside the marriage.
Anger inside the happiness.
Warmth in the cold.
Cold in the heat.
Laughing without being happy.
Has not gotten anywhere.
Poverty in wealth [no poverty or love in a wealth family].

                       
     11.  The <A> of the <Non-A>.
  Examples:  
The shadow of the light.
Music of silence.
Relaxing of exercise effect.
The restrictions of the free.
Life through death.
The sound/loudness of the silence.
I can see the light at the of the tunnel.
The slave of freedom [someone who couldn't give up his freedom,
not even in marriage].


     12.  <V> what one <Non-V>.
  Examples:  
To see what one can't see.
To hear what one can't hear.
To taste what one can't taste.
To accept what on can't understand.
To say what one can't say [to tell a secret].
To wait patiently when one doesn't know how to wait.
To breath what one can't breath.
To feel what one can't feel.
To appreciate what one dis-appreciates.
To believe what one can't believe [faith].
To smell what one can't smell.


     13.  Let's <V> by <Non-V>.
  Examples:  
Let's strike by not striking [=Japanese strike].
Let's talk by not talking; [means to think].
To vote by not voting at all.
To help someone by not helping [using experience as a teacher].
Let's justify by not justifying.
Let's win by not winning.
Let's strip by not stripping [to make bare or clear].
Let's fight by not fighting [Ghandi's Motto].


     14.  <N> of the <Non-N>.
  Examples:  
The benefits we get from non-benefits.
The smoke we got from non-smokers.
The rewards we get from hard work.
The service we get from non-service.
The god that comes from bad.
The pleasure we get from the pain.


     15.  <Non-A> is <A>.
  Examples:  
The bad is good [because makes you try harder].
The good is bad [because doesn't leave any room for improvement].
Work is a blessing.
The poor is spiritually rich.
Sometimes ugly is beauty [because beauty is in the eyes of the
beholden]. 
You have to kiss a lot of frogs before you find a prince.
Hurt is healing.
"There is no absolute" is an absolute.
Not to commit any error is an error.


     16.  A <Non-N> <N>.
  Examples:  
A positive negative [which means: a failure enforces you to do
better]
A sad happiness.
An impossible possibility.
Genuine imitation leather.
A loud whisper.
A beautiful disaster  [which means beauty can be found anywhere].
A bitter sweet.
A harsh gentleness [a gentleness that is very firm with you].
A guiltless sinner [someone who doesn't regret sinning].


     17.  Everything has an <A> and a <Non-A>.
  Examples: 
Everything has a sense and a non-sense.
Everything has a truthful side and a wrong side.
Everything has a beginning and an ending.
Everything has a birth and a death.
Everything has its time and a non-time.
Everything has an appearance and a non-appearance.
Everything around you resolves and also dissolves.
Everybody has a good side and a bad side.
Everyone has a right and a wrong.


     18.  <V> what <Non-V>.
  Examples:  
To be what you are not.
One needs what one doesn't need.
Expect the unexpected!
Culture exists by its non-existence.
No matter how rich we are, we never make enough money.
One purchases what one doesn't purchase.
To work when we are not working.
To die might mean to live for ever [= for an artist].
One wants because one doesn't want [sometimes one wants something
only because someone else likes it].


     Look at this Funny Law example:
A Paradoxist Government:
  Suppose you have two cows.  Then the government kills them and
milks you!


     The list of such invented linguistic paradoxes can be
indefinitely extended.  It is specific to each language, and it
is based on language expressions and types of sentence and phrase
constructions and structures. 
One can also play with antonymic adverbs, prepositions, etc.
to construct other categories of linguistic paradoxes.


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 Transilvania University of Bražov>, 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 (Mathematics & 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, Bucharest, 26, 27-28, 1995.
     [12]  Rotaru, Ion, "Din nou despre Florentin Smarandache",
<Vatra>, Tg. Murež, Romania, Nr. 2 (299), 93-94, 1996.
     [13]  Seagull, Larry,  "Clasa de Paradoxuri Semantice
Smarandache" (in translation), <Abracadabra>, Salinas, CA, USA, 
Anul 2, Nr. 20, 2, iunie 1994.
     [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.
     [15]  Vasiliu, Florin,  "Paradoxism's main roots",
Translated from Romanian by žtefan Benea, Xiquan Publishing
House, Phoenix, USA, 64 p., 1994;  reviewed in <Zentralblatt fr
Mathematik>, Berlin, No. 5, 830 - 17, 03001, 1996.
     [16]  Tilton, Homer B., "Smarandache's Paradoxes", <Math
Power>, Tucson, AZ, USA, Vol. 2, No. 9, 1-2, September 1996.
     [17]  Weisstein, Eric W, "CRC Concise Encyclopedia of
Mathematics", <Smarandache Paradox>, CRC Press, USA, 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.
     [20]  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.