Oxymoron
An oxymoron is a figure of speech in which seemingly contradictory words appear side by side but still involving a point. That is, two opposite words are placed side by side to bring out a point. Examples are act naturally, original copy, conspicuous absence, found missing, alone together, criminal justice, old news, peace force, even odds, awful good, student teacher, deafening silence, definite possibility, definite maybe, terribly pleased, ill health, turn up missing, loose tights, pretty bad, small crowd, and clearly misunderstood.
Examples
Ade, if you’re going to be a phony, you might as well be a real phony
O brawling love! O loving hate! . . .
O heavy lightness! serious vanity!
Misshapen chaos of well-seeming forms!
Feather of lead, bright smoke, cold fire, sick health!
Still-waking sleep, that is not what it is!
This love feel I, that feel no love in this.
A yawn may be defined as a silent yell.
There goes another wise fool.
Paradox
A figure of speech in which a statement appears to contradict itself.
Examples of paradoxical statements
War is peace.
Freedom is slavery.
Ignorance is strength.
We are fixed and certain only when we are in movement. How can one be fixed and mobile at the same time?
The difference between Oxymoron and Paradox
While Paradox is a statement or a group of statements, oxymoron is a combination of two contradictory terms.
Paradox consists of a whole sentence. Oxymoron on the other hand comes with only two words that contradicts itself. In simple words, Paradox is considered to be an action that is contradictory (e.g I have found the paradox, that if you love until it hurts, there can be no more hurt, only more love) and oxymoron is a description of a phrase, which is contradictory(e.g the present situation is pretty bad).
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While paradox can be seen as a phrase like ‘freedom is slavery’, oxymoron is only a combination of two contradictory words like ‘cold fire’.
The best way to understand if a figure of speech is oxymoron is to look if they come in two words. The first word and the second word used in oxymoron will have completely different meanings. The two words stand opposite to each other. Military intelligence, icy hot and hottie-coldy are some of the examples of oxymoron. The dictionary defines oxymoron as a paradox reduced to two words (adjective-noun or adverb-adjective), which is used for giving more effect and emphasising contrasts. Unlike paradox, oxymoron is a descriptive phrase containing two terms, which do not seem fit. Though the two words used in oxymoron seem to be contradictory, it gives a dramatic effect to the words.
Unlike oxymoron, paradox uses many words, even a whole paragraph, to explain a thing. Paradox is a typically a true statement or a group of statements, which seems to lead to some contradiction. While the two words used in oxymoron is used for some dramatic effect and may not make any sense, a paradox statement that contains opposing elements when read together makes some sense. Read this:
I dare say that one of the strangest contradictions to beset contradiction fanciers recently was the situation confronting anybody who was seeking shelter in New York City. Not only were hotel rooms scarcer than the heath hen–after all, you could pick up an occasional heath hen before Christmas if you didn’t mind going into the black market for it–but the reason for their scarcity was that most of them were occupied by people who had flocked to the National Hotel Exposition to discuss the scarcity of hotel rooms. Sounds paradoxical, doesn’t it?
Reference: About.com and Difference Between.net