A paradox is a true statement or group of statements that leads to a contradiction or a situation which defies intuition; or, inversely, it can be an apparent contradiction that actually expresses a non-dual truth (cf. Koan). 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 word paradox is often used interchangeably with contradiction. Often, mistakenly, it is used to describe situations that are ironic. An example of this is hating cucumbers, hating yogurt, but loving tzatziki sauce.

The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has led to significant advances in science, philosophy and mathematics. But many paradoxes, such as Curry's paradox, do not yet have universally accepted resolutions.

Sometimes the term paradox is used for situations that are merely surprising. The birthday paradox, for instance, is unexpected but perfectly logical. The logician Willard V. O. Quine distinguishes falsidical paradoxes, which are seemingly valid, logical demonstrations of absurdities, from veridical paradoxes, such as the birthday paradox, which are seeming absurdities that are nevertheless true. Paradoxes in economics tend to be the veridical type, typically counterintuitive outcomes of economic theory. In literature a paradox can be any contradictory or obviously untrue statement, which resolves itself upon later inspection.

Logical paradox

Common themes in paradoxes include self-reference, the infinite, circular definitions, and confusion of levels of reasoning.

Patrick Hughes outlines three laws of the paradox:

• Self reference - so all Cretans are liars, said the Cretan, is self referential, because the Cretan describes all Cretans;
• Contradiction - so all Cretans are liars, said the Cretan, is a contradictory because the Cretan is saying that Cretans are liars
• Vicious circularity or infinite regress - so if all Cretans are liars, and the Cretan told us so, then it cannot be true, but if it is not true that Cretans are liars, then the statement stands, but then it is true that all Cretans are liars, so it must be a lie... and so on ad infinitum

Other paradoxes involve false statements or half-truths and the resulting biased assumptions.

For example, consider a situation in which a father and son are driving down the road. The car collides with a tree and the father is killed. The boy is rushed to the nearest hospital where he is prepared for emergency surgery. On entering the surgery suite, the surgeon says, "I can't operate on this boy. He's my son."