Fermi paradox
The Fermi paradox, or Fermi's paradox, named after physicist Enrico Fermi, is the apparent contradiction between the lack of evidence and high probability estimates for the existence of extraterrestrial civilizations. The basic points of the argument, made by physicists Enrico Fermi (1901–1954) and Michael H. Hart (born 1932), are:
According to this line of reasoning, the Earth should have already been visited by extraterrestrial aliens. In an informal conversation, Fermi noted no convincing evidence of this, leading him to ask, "Where is everybody?" There have been many attempts to explain the Fermi paradox, primarily either suggesting that intelligent extraterrestrial life is extremely rare or proposing reasons that such civilizations have not contacted or visited Earth.
The Fermi paradox is a conflict between the argument that scale and probability seem to favor intelligent life being common in the universe, and a total lack of evidence of intelligent life having ever arisen anywhere other than on the Earth.
Naive set theory
Some believe that Georg Cantor's set theory was not actually implicated in the set-theoretic paradoxes (see Frápolli 1991). One difficulty in determining this with certainty is that Cantor did not provide an axiomatization of his system. By 1899, Cantor was aware of some of the paradoxes following from unrestricted interpretation of his theory, for instance Cantor's paradox and the Burali-Forti paradox, and did not believe that they discredited his theory. Cantor's paradox can actually be derived from the above (false) assumption using for is a cardinal number". Frege explicitly axiomatized a theory in which a formalized version of naïve set theory can be interpreted, and it is "this" formal theory which Bertrand Russell actually addressed when he presented his paradox, not necessarily a theory Cantor, who, as mentioned, was aware of several paradoxes, presumably had in mind.