A paradox of self-reference, where, supposing that every man either shaves himself or is shaved by the barber, and the barber shaves all and only the men who do not shave themselves, then it is impossible to determine who shaves the barber.

Hempel's paradox

A paradox arising from the question of what constitutes evidence for a statement. Observing objects that are neither black nor ravens may formally increase the likelihood that all ravens are black, even though, intuitively, these observations are unrelated.

(philosophy, logic) A paradox involving statements such as "this sentence is false", or "the following statement is true: the previous statement is false", which cannot be meaningfully regarded as either true or false.

The perceived failure of European countries to translate scientific advances into marketable innovations.

(medicine) An aggressive behaviour sometimes manifested by patients taking certain drugs, such as benzodiazepines.

plural of paradoxical rage reaction

(set theory) The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.

A paradox of deontic logic, whereby the plausible statements (i) if you murder, you ought to murder gently, (ii) you do commit murder, and (iii) to murder gently you must murder imply the less plausible statement (iv) you ought to murder.

A paradox about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. It is based on the idea that a prisoner, told that he will be hanged on a day unknown to him, concludes that "I cannot be hanged on Friday because if I haven't been hanged by the end of Thursday then it would no longer be a surprise", and so on backwards through the week.