Fermi paradox
Michael H. Hart published in 1975 a detailed examination of the paradox, which has since become a theoretical reference point for much of the research into what is now sometimes known as the Fermi–Hart paradox. Geoffrey A. Landis prefers that name on the grounds that "while Fermi is credited with first asking the question, Hart was the first to do a rigorous analysis showing that the problem is not trivial, and also the first to publish his results". Robert H. Gray argues that the term "Fermi paradox" is a misnomer, since in his view it is neither a paradox nor due to Fermi; he instead prefers the name Hart–Tipler argument, acknowledging Michael Hart as its originator, but also the substantial contribution of Frank J. Tipler in extending Hart's arguments.
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.