Definition
A paradox is an apparently valid argument that leads from apparently true premises to an unacceptable conclusion. Each ingredient seems fine on its own — the premises look true, the inference looks valid, the conclusion looks intolerable — yet they cannot all be fine together. Something must give.
A paradox is therefore not merely a surprising claim or a clever trick. It is a structured pressure point in our thinking: a place where a set of beliefs we each hold individually turns out to be jointly inconsistent. Resolving a paradox means locating which apparently safe assumption is the culprit.
Why it matters
How it works
Faced with a paradox, the logician has exactly three options. Reject one of the premises, showing it only seemed true. Reject the inference, showing the argument only seemed valid. Or accept the conclusion, showing it only seemed unacceptable. Each option carries a cost, and choosing the least costly response is the real philosophical work.
This is why paradoxes have been so productive. The liar paradox forced careful theories of truth; the sorites paradox forced careful theories of vagueness; Zeno's paradoxes sharpened the concept of infinity. A paradox marks a fault line, and following it leads to deeper structure.