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Discovered by Bertrand Russell in 1901, this paradox is about the set of all sets that do not contain themselves. Does it contain itself? This paradox showed that naive set theory led to a contradiction and prompted the development of axiomatic set theory.

Cogito, ergo sum - a philosophical statement made by René Descartes, showcasing an attempt to establish a sure foundation for scientific knowledge starting from basic truths.

Part of a classical argument by the Greek philosopher Socrates. It exemplifies deductive reasoning through a syllogism: If all men are mortal, and Socrates is a man, then Socrates is mortal.

David Hilbert's program aimed to provide a solid foundation for all mathematics by proving all mathematical truths using a finite and complete set of axioms. It was later proven to be impossible by Gödel's incompleteness theorems.