# Dictionary Definition

1 of words or propositions so related that both cannot be true and both cannot be false; "perfect' and imperfect' are contradictory terms"
2 that confounds or contradicts or confuses [syn: confounding]
3 in disagreement; "the figures are at odds with our findings"; "contradictory attributes of unjust justice and loving vindictiveness"- John Morley [syn: at odds(p), conflicting, self-contradictory]
4 unable to be both true at the same time [syn: mutually exclusive] n : two propositions are contradictories if both cannot be true (or both cannot be false) at the same time

# User Contributed Dictionary

## English

### Pronunciation

1. That contradicts something, such as an argument.
2. That is itself a contradiction.
3. That is diametrically opposed to something.
4. Mutually exclusive.

### Noun

1. Any of a pair of propositions, that cannot both be true or both be false.

# Extensive Definition

In logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical inversions of each other. Illustrating a general tendency in applied logic, Aristotle’s law of noncontradiction states that “One cannot say of something that it is and that it is not in the same respect and at the same time.”
By extension, outside of formal logic, one can speak of contradictions between actions when one presumes that their motives contradict each other.

In formal logic, particularly in propositional and first-order logic, a proposition \varphi is a contradiction if and only if \varphi\vdash\bot. Since for contradictory \varphi it is true that \vdash\varphi\rightarrow\psi for all \psi (because \varphi\rightarrow\bot\rightarrow\psi), one may prove any proposition from a set of axioms which contains contradictions.

Adherents of the epistemological theory of coherentism typically claim that as a necessary condition of the justification of a belief, that belief must form a part of a logically non-contradictory (consistent) system of beliefs. Some dialetheists, including Graham Priest, have argued that coherence may not require consistency.

Pragmatic contradictions often occur in philosophy that the very presence of the argument contradicts the claims of the argument. An inconsistency arising because of the normal implications of saying something, rather than because of the content of what is said. For examples, Heraclitus’s proposition that knowledge is impossible; or, arguably, Nietzsche’s statement that one should not obey others, or moore's paradox. These are self-refuting statements and performative contradictions.

Colloquial usage can label actions or statements (or both) as contradicting each other when due (or perceived as due) to presuppositions which are contradictory in the logical sense.
In dialectical materialism, contradiction, as derived by Karl Marx from Hegelianism, usually refers to an opposition of social forces. Most prominently (according to Marx), capitalism entails a social system that has contradictions because the social classes have conflicting collective goals. These contradictions stem from the social structure of society and inherently lead to class conflict, economic crisis, and eventually revolution, the existing order’s overthrow and the formerly oppressed classes’ ascension to political power.
Mao Zedong's philosophical essay furthered Marx and Lenin's thesis and suggested that all existence is the result of contradiction.