The Fermi Paradox Is Our Business Model
"The Fermi Paradox Is Our Business Model" is a science fiction short story by Charlie Jane Anders. It was first published in the online magazine Tor.com August 11, 2010.
Burali-Forti paradox
If we use the von Neumann definition, under which each ordinal is identified as the set of all preceding ordinals, the paradox is unavoidable: the offending proposition that the order type of all ordinal numbers less than a fixed formula_25 is formula_25 itself must be true. The collection of von Neumann ordinals, like the collection in the Russell paradox, cannot be a set in any set theory with classical logic. But the collection of order types in New Foundations (defined as equivalence classes of well-orderings under similarity) is actually a set, and the paradox is avoided because the order type of the ordinals less than formula_1
turns out not to be formula_1.