Quick Turtle sounds like paradox and this webpage refers to well-known paradoxes.

 

A paradox ("aside belief") is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has led to significant advances in science, philosophy and mathematics.

 

The word paradox is often used interchangeably and wrongly with contradiction; but where a contradiction by definition asserts its own opposite, many paradoxes do allow for resolution of some kind, though many remain unresolved or only contentiously resolved, such as Curry's paradox. Still more casually, the term is sometimes used for situations that are merely surprising, albeit in a distinctly "logical" manner, such as the birthday paradox. This is also the usage in economics, where a paradox is a counterintuitive outcome of economic theory.

 

See also list of paradoxes – www.quickturtle.eu.