Paradox, in logic and mathematics, means an apparently contradictory 
conclusion derived from apparently valid premises. Many paradoxes prove to be based on false premises or arguments, or on incomplete presuppositions. Other paradoxes are more difficult to resolve, and their study has contributed to the development of modern mathematics. Semantic paradoxes depend on language structure, and the paradox is often used as a rhetorical device in epigrams and poetry.

1. "I must be cruel to be kind". Shakespeare in Hamlet

2. Million's description of God; "Dark with excessive bright thy skirts appear".

3. "The sun itself is dark simulacrum and light is shadow of God" Sir Thomas Browne

4. "Careless she is with artful care, 
Affecting to seem unaffected." _Congreve

The second kind is more complex both in prose and poetry For instance there is paradox at the heart of Christian Faith that the world would be saved by failure. Notable example of structural form of paradoxical poetry  are found in The Will, Good Friday, Riding Westward and the sonnet. For instance;

Death be not proud, though some have called thee,
Mighty and dreadful, for, thou art not so....

Alexander Pope in his Essay On Man combines a general statement about the paradoxical condition of man and nature with a series of particular paradoxes.

In doubt his Mind or Body to prefer 
Born but to die and reasoning but to err . . .
Created half to rise and half to fall;
Great lord of all things, yet a prey to all,
Sole judge of Truth, in endless Error hurl'd:
The glory, jest, and riddle of the world,

In modern times Goerg Bernard Shaw, Bertrand Russell and few others including G. K. Chesterton are regarded the great spinners of paradoxes. Here are some pieces of with from Bertrand Russell (1872-1970), British philosopher

1. In America everybody is of opinion that he has no social superiors, since all men are equal, but he does not admit that he has no social inferiors.

2. Ethics is in origin the art of recommending to others the sacrifices required for cooperation with oneself.
 

George Bernard Shaw (1856-1950), Anglo-Irish playwright, critic was one of the great master o paradox. 

1. I'm only a beer teetotaller, not a champagne teetotaller.

2. Dying is a troublesome business: there is pain to be suffered, and it wrings one's heart; but death is a splendid thing-a warfare accomplished, a beginning all over again, a triumph. You can always see that in their faces.
 

G. K. Chesterton (1874–1936) was also a gifted author often using paradoxical language.

1. An adventure is only an inconvenience rightly considered. An inconvenience is only an adventure wrongly considered.

2, A stiff apology is a second insult. … The injured party does not want to be compensated because he has been wronged; he wants to be healed because he has been hurt.

3, One may understand the cosmos, but never the ego; the self is more distant than any star.
 

Bruce Webber succinctly describes the paradoxical nature of politics. "The paradox of political speech - that it is demonstrably misleading, and that people believe it anyway."

While politicians may not be able to solve many of the problems they create, they have proven they are still adept at creating problems and causing crises and then blaming others for the results or taking credit for solution of problems created by themselves.

Finality is not the language of politics as explained by L. B. Johnson US Democratic politician and president.

"Son, in politics you've got to learn that overnight chicken shit can turn to chicken salad."
 

Some critical theorists go on so far as to suggest that the language of poetry is the language of paradox. In his book 'the Well Wrought Urn. the author Cleanth Brooks has elaborated this idea persuasively beside some other writers. 

As far as Urdu is concerned Mirza Asad ullah Khan Ghalib appears to be the greatest exponent of paradoxical language. Some of his gems are given below. Only first part of the verse is given in the interest of brevity.

1. Mushkilain itni parein kay asaan ho gaien.
    So many troubles I got that they become my comfort! 
2. Aadmi ko bhe mayyassar nahin Insan hona
    Even a man is not able to become human!
3. Tangiay dil ka gila kiya yeh woh kafir dil hai
   Why complain about heartlessness, the heart is heathen 
4. Jatay hoiy kehto ho qiamat ko mialaingay
    kiya khoob qiamat ka hai goya koi din aur
   To part saying that will meet again on dooms day,
    Well that is enough to make it a dooms day,
6. Qata keejiay na tallauq hum say
    kuch nahin to adawat hee sahee 
    Do not sever all relationship with us
    If nothing else let there be acrimony 
 

Oxymoron is a rhetorical figure in which incongruous or contradictory terms are combined, as in a deafening silence and a mournful optimist.

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