Contradiction

In logic, a contradiction consists of a logical incompatibility between two or more propositions. Logic is the study of the principles of valid demonstration and Inference. In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence It occurs when the propositions, taken together, yield two conclusions which form the logical inversions of each other. A conclusion is a Proposition, which is arrived at after the consideration of Evidence, Arguments or Premises Logic 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. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. ”

By extension, outside of formal logic, one can speak of contradictions between actions when one presumes that their motives contradict each other.

1 Contradiction in formal logic
2 Contradictions and philosophy
- 2.1 Pragmatic contradictions
3 Contradiction outside formal logic
4 See also
5 References
6 External links

Contradiction in formal logic

In formal logic, particularly in propositional and first-order logic, a proposition $\varphi$ is a contradiction if and only if $\varphi\vdash\bot$ . This is a technical mathematical article about the area of mathematical logic variously known as "propositional calculus" or "propositional logic" First-order logic (FOL is a formal Deductive system used in mathematics philosophy linguistics and computer science ↔ Since for contradictory $\varphi$ it is true that $\vdash\varphi\rightarrow\psi$ for all $ψ$ (because $\varphi\rightarrow\bot\rightarrow\psi$ ), one may prove any proposition from a set of axioms which contains contradictions.

Contradictions and philosophy

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. Epistemology (from Greek επιστήμη - episteme, "knowledge" + λόγος, " Logos " or theory of knowledge There are two distinct types of coherentism. One refers to the Coherence theory of truth. Belief is the psychological state in which an individual holds a Proposition or Premise to be true System (from Latin systēma, in turn from Greek systēma is a set of interacting or interdependent Entities, real or abstract Some dialetheists, including Graham Priest, have argued that coherence may not require consistency. Dialetheism is the view that there are true contradictions or dialetheias Graham Priest (born 1948, London) is Boyce Gibson Professor of Philosophy at the University of Melbourne and a regular visitor at St

Pragmatic contradictions

A pragmatic contradiction occur 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. ^[1] For examples, Heraclitus’s proposition that knowledge is impossible; or, arguably, Nietzsche’s statement that one should not obey others, or Moore's paradox. Heraclitus of Ephesus ( Ancient Greek: &mdash grc-Latn ''Hērákleitos ho Ephésios'' English Heraclitus the Ephesian) (ca Friedrich Wilhelm Nietzsche (October 15 1844 August 25 1900 ( was a nineteenth-century German philosopher and classical philologist 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 These are self-refuting statements and performative contradictions. Self-refuting ideas are ideas or statements whose falsehood is a Logical consequence of the act or situation of holding them to be true 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

Contradiction outside formal logic

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. A colloquialism is an expression not used in formal speech, writing or Paralinguistics. 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

In dialectical materialism, contradiction, as derived by Karl Marx from Hegelianism, usually refers to an opposition of social forces. Dialectical materialism, according to many followers of Karl Marx 's thinking is the philosophical basis of Marxism. 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 Most prominently (according to Marx), capitalism entails a social system that has contradictions because the social classes have conflicting collective goals. Capitalism is the Economic system in which the Means of production are owned by private Persons and operated for Profit and where Social structure is a term frequently used in Sociology and Social theory — yet rarely defined or clearly conceptualised (Abercrombie et al Social class refers to the hierarchical distinctions (or stratification) between individuals or groups in Societies or Cultures. 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. Class conflict, also class war or class warfare, is both the friction that accompanies social relationships between members or groups of different A revolution (from the Latin revolutio, "a turnaround" is a fundamental change in power or organizational structures that takes place in a relatively

Mao Zedong's philosophical essay furthered Marx and Lenin's thesis and suggested that all existence is the result of contradiction. Mao Zedong 's On Contradiction ( is considered his most important philosophical essay

References

^ Stoljar, Daniel (2006). Dialectical materialism, according to many followers of Karl Marx 's thinking is the philosophical basis of Marxism. Doublethink is the act of simultaneously accepting as correct two mutually contradictory beliefs A paradox is a true statement or group of statements that leads to a Contradiction or a situation which defies intuition; or inversely In Mathematical logic and Automated theorem proving, resolution is a rule of Inference leading to a refutation Theorem-proving technique TRIZ (triːz is a romanized Acronym for Russian “ru Теория решения изобретательских задач” () meaning Ignorance and Imagination. Oxford University Press - U. S. , 87. ISBN 0195306589.

External links

Contradiction entry at the Stanford Encyclopedia of Philosophy by Laurence R. The Stanford Encyclopedia of Philosophy (SEP is a freely-accessible Online encyclopedia of Philosophy maintained by Stanford University. Horn

Dictionary

-noun

(uncountable) The act of contradicting.
(countable) A statement that contradicts itself.
(logic) (countable) A proposition that is false for all values of its variables.

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