basic constructions:
strong axioms
further
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).
In physics:
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