nLab paradox

Idea

A paradox is an example of reasoning that seems perfectly valid on first sight, but which results in a contradiction or inconsistency. For example:

The following statement is false.

The previous statement is true.

Either sentence alone seems perfectly reasonable, and could meaningfully be said in another context; but together they form a paradox. It is not just that the sentences contradict each other (in which case one or both might simply be false); but the existence of the sentences contradicts the assumption that they are meaningful at all (at least using classical logic).

Examples

From logic and foundations

• Russell's paradox

• Curry's paradox

• Burali-Forti's paradox

• Cantor's paradox

• Banach-Tarski paradox

From natural science

In physics:

• Zeno's paradox of motion

• hole paradox

• Einstein-Podolsky-Rosen paradox

• ultraviolet catastrophe

• black hole information paradox

Related concepts

• axiom

• definition

  • inductive definition

  • coinductive definition

• theory

• lemma

• proposition/type (propositions as types)

• proof/program (proofs as programs)

• theorem

• example

• counterexample

• folklore

• conjecture

• analogy

• paradox

• exercise