nLab paradox

Paradoxes

Context

Foundations

foundations

The basis of it all

 Set theory

set theory

Foundational axioms

foundational axiom

Removing axioms

Paradoxes

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

From natural science

In physics:

Last revised on May 31, 2022 at 07:25:22. See the history of this page for a list of all contributions to it.