Paradox

A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true (or, cannot all be true together). The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has often led to significant advances in science, philosophy and mathematics.

Related Topics:
True - Contradiction - Ambiguities - Equivocation - Science - Philosophy - Mathematics

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The word paradox is often used interchangeably with contradiction; but where a contradiction by definition cannot be true, many paradoxes do allow for resolution, though many remain unresolved or only contentiously resolved (such as Curry's paradox). Still more casually, the term is sometimes used for situations that are merely surprising (albeit in a distinctly "logical" manner) such as the Birthday Paradox. This is also the usage in economics, where a paradox is an unintuitive outcome of economic theory.

Related Topics:
Curry's paradox - Birthday Paradox - Economics

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The etymology of paradox can be traced back to the early Renaissance. Early forms of the word appeared in the late Latin paradoxum and the related Greek paradoxon. The word is composed of the preposition para which means "by way of", or "according to" conjoined to the noun stem doxa, meaning "what is received". Compare orthodox (literally, "straight teaching") and heterodox (literally, "different teaching"). The liar paradox and other paradoxes were studied in medieval times under the heading insolubilia.

Related Topics:
Etymology - Renaissance - Latin - Greek - Preposition - Orthodox - Heterodox - Insolubilia

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Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning. Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context (or language) to lose their paradox quality.

Related Topics:
Context - Language

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In moral philosophy, paradox plays a central role in ethics debates. For instance, an ethical admonition to "love thy neighbour" is not just in contrast with, but in contradiction to an armed neighbour actively trying to kill you: if he or she succeeds, you will not be able to love him or her. But to preemptively attack them or restrain them is not usually understood as loving. This might be termed an ethical dilemma. Another example is the conflict between an injunction not to steal and one to care for a family that you cannot afford to feed without stolen money.

Related Topics:
Moral philosophy - Ethics - Ethical dilemma - Steal

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