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In classical logic
Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties; non-classical logics are those that lack one or more of these properties, which are:...
, a contradiction consists of a logical incompatibility between two or more proposition
Proposition

This article is about the term proposition in logic and philosophy; for other uses see PropositionIn logic and philosophy, proposition refers to either the "content" or Meaning of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence....
s. It occurs when the propositions, taken together, yield two conclusion
Logical consequence

Logical consequence is a fundamental concept in logic. It is the Relation that holds between a Set of Sentence and a sentence when the former Entailment the latter....
s which form the logical inversions of each other. Illustrating a general tendency in applied logic, Aristotle’s
Aristotle

Aristotle was a Greeks philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, Poetics , theater, music, logic, rhetoric, politics, government, ethics, biology and zoology....
 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 classical logic
Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties; non-classical logics are those that lack one or more of these properties, which are:...
, one can speak of contradictions between actions when one presumes that their motives contradict each other.

a class="link1" onMouseover='showByLink("m276086",this)' onMouseout='hide("m276086")'href="http://www.absoluteastronomy.com/topics/Classical_logic">classical logic
Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties; non-classical logics are those that lack one or more of these properties, which are:...
, particularly in propositional and first-order logic
First-order logic

First-order logic is a formal deductive system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus , the lower predicate calculus, the language of first-order logic or predicate logic....
, a proposition is a contradiction if and only if
If and only if

If and only if, in logic and fields that rely on it such as mathematics and philosophy, is a biconditional logical connective between statements....
 .






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In classical logic
Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties; non-classical logics are those that lack one or more of these properties, which are:...
, a contradiction consists of a logical incompatibility between two or more proposition
Proposition

This article is about the term proposition in logic and philosophy; for other uses see PropositionIn logic and philosophy, proposition refers to either the "content" or Meaning of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence....
s. It occurs when the propositions, taken together, yield two conclusion
Logical consequence

Logical consequence is a fundamental concept in logic. It is the Relation that holds between a Set of Sentence and a sentence when the former Entailment the latter....
s which form the logical inversions of each other. Illustrating a general tendency in applied logic, Aristotle’s
Aristotle

Aristotle was a Greeks philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, Poetics , theater, music, logic, rhetoric, politics, government, ethics, biology and zoology....
 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 classical logic
Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties; non-classical logics are those that lack one or more of these properties, which are:...
, one can speak of contradictions between actions when one presumes that their motives contradict each other.

Contradiction in formal logic

In classical logic
Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties; non-classical logics are those that lack one or more of these properties, which are:...
, particularly in propositional and first-order logic
First-order logic

First-order logic is a formal deductive system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus , the lower predicate calculus, the language of first-order logic or predicate logic....
, a proposition is a contradiction if and only if
If and only if

If and only if, in logic and fields that rely on it such as mathematics and philosophy, is a biconditional logical connective between statements....
 . Since for contradictory it is true that for all (because ), one may prove any proposition from a set of axioms which contains contradictions.

Contradictions and philosophy

Adherents of the epistemological
Epistemology

Epistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope of knowledge. It addresses the questions:...
 theory of coherentism
Coherentism

There are two distinct types of coherentism. One refers to the coherence theory of truth. The otheris belief in the coherence theory of justification — an Epistemology theory opposing foundationalism and offering a solution to the regress argument....
 typically claim that as a necessary condition of the justification of a belief
Belief

Belief is the psychological state in which an individual holds a proposition or premise to be true....
, that belief must form a part of a logically non-contradictory (consistent) system
System

System is a set of interacting or interdependent entities, real or abstract, forming an integrated whole.The concept of an "integrated whole" can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the se...
 of beliefs. Some dialetheists
Dialetheism

Dialetheism is the view that there are true contradictions, or dialetheia. More specifically, dialetheists believe that for some sentence or proposition P, both P and its negation, not-P , are true....
, including Graham Priest
Graham Priest

Graham Priest is Boyce Gibson Professor of Philosophy at the University of Melbourne and a distinguished professor of philosophy at the CUNY Graduate Center, as well as a regular visitor at St....
, have argued that coherence may not require consistency.

Pragmatic contradictions

A pragmatic contradiction occurs when the very statement of the argument contradicts the claims it purports. An inconsistency arises, in this case, because the act of utterance, rather than the content of what is said, undermines its conclusion. For examples, Heraclitus
Heraclitus

Heraclitus of Ephesus was a Pre-Socratic philosophy Greeks philosopher, a native of Ephesus, Ionia, on the coast of Asia Minor.Heraclitus is known for his doctrine of change being central to the universe, and that the Logos is the fundamental order of all....
’s proposition that knowledge is impossible; or, arguably, Nietzsche’s statement that one should not obey others, or Moore's paradox
Moore's paradox

G. E. Moore remarked once in a lecture on the absurdity involved in saying something like "It's raining outside but I don't believe that it is." This paradox, sometimes known as Moore's paradox, might well have been forgotten if not for the fact that Ludwig Wittgenstein reportedly considered it Moore's most important contribution to philosoph...
. These are self-refuting statements and performative contradiction
Performative contradiction

A performative contradiction arises when the propositional content of a statement contradicts the noncontingent presuppositions that make possible the performance of the speech act, such as occurs with "all statements must be false."...
s.

Contradiction outside formal logic

Colloquial usage
Colloquialism

A colloquialism is an expression not used in formal Speech communication, writing or paralinguistics. Colloquialisms are also sometimes referred to collectively as "colloquial language"....
 can label actions or statements (or both) as contradicting each other when due (or perceived as due) to presupposition
Presupposition

In the linguistic branch of pragmatics, a presupposition is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse....
s which are contradictory in the logical sense.

In dialectical materialism
Dialectical materialism

Dialectical materialism is the philosophy of Karl Marx, which he formulated by taking the dialectic of Hegel and joining it to the Materialism of Feuerbach....
, contradiction, as derived by Karl Marx
Karl Marx

Karl Heinrich Marx was a Germanphilosophy, political economy, historian, sociologist, humanism, political theorist and revolutionary credited as the founder of communism....
 from Hegelianism
Hegelianism

Hegelianism is a philosophy developed by Georg Wilhelm Friedrich Hegel which can be summed up by Hegel's "the rational alone is real," which means that all reality is capable of being expressed in rational categories....
, usually refers to an opposition of social forces. Most prominently (according to Marx), capitalism
Capitalism

Capitalism is an economic system in which wealth, and the means of producing wealth, are private property and controlled rather than commonly, publicly, or state-owned and controlled....
 entails a social system that has contradictions because the social class
Social class

Social class refers to the hierarchy distinctions between individuals or groups in societies or cultures. Usually most societies have some notion of social class , but concretely defined social classes are not found in every known type of human societies....
es have conflicting collective goals. These contradictions stem from the social structure of society and inherently lead to class conflict
Class conflict

Class conflict refers to the underlying tensions or antagonisms which exist in society due to conflicting interests that arise from different social positions....
, economic crisis
Crisis (economic)

In economics, crisis is a term in Marxian theory, referring to the sharp transition to a recession. See for example 1994 economic crisis in Mexico, Argentine economic crisis , South American economic crisis of 2002, Economic crisis of Cameroon....
, and eventually revolution
Revolution

A revolution is a fundamental social change in power or organizational structures that takes place in a relatively short period of time....
, the existing order’s overthrow and the formerly oppressed classes’ ascension to political power.

Mao Zedong's philosophical essay
On Contradiction (Mao Zedong)

Mao Zedong's On Contradiction is considered his most important philosophical essay. Along with On Practice it forms the philosophical underpinnings of the political ideology that would later become Maoism....
 furthered Marx and Lenin's thesis and suggested that all existence is the result of contradiction.

Proof by contradiction is used in mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 to construct proofs
Mathematical proof

In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive reasoning or empirical arguments....
.

See also

  • Dialectical materialism
    Dialectical materialism

    Dialectical materialism is the philosophy of Karl Marx, which he formulated by taking the dialectic of Hegel and joining it to the Materialism of Feuerbach....
  • Doublethink
    Doublethink

    Doublethink is the act of simultaneously accepting as correct two mutually contradictory beliefs. It is related to, but distinct from, hypocrisy and Neutrality ....
  • Oxymoron
    Oxymoron

    An oxymoron is a figure of speech that combines two normally contradiction terms. Oxymoron is a loanword from Greek language oxy and moros ....
  • Paraconsistent logic
    Paraconsistent logic

    A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent systems of logic....
  • Paradox
    Paradox

    A paradox is a Proposition or group of statements that leads to a contradiction or a situation which defies intuition ; or, it can be an apparent contradiction that actually expresses a non-dual truth ....
  • Square of opposition
    Square of opposition

    In the system of Term Logic , the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related to each of the others....


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