In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in which year, Kurt Gödel specifically cites Richard's antinomy as a semantical analogue to his syntactical incompleteness result?
Richard's paradox In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics. Kurt Gödel specifically cites Richard's antinomy as a semantical analogue to his syntactical incompleteness result in the introductory section of "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I". The paradox was also a motivation of the development of predicative mathematics.
Pocket set theory Pocket set theory (PST) is an alternative set theory in which there are only two infinite cardinal numbers, ℵ (aleph-naught, the cardinality of the set of all natural numbers) and "c" (the cardinality of the continuum). The theory was first suggested by Rudy Rucker in his "Infinity and the Mind". The details set out in this entry are due to the American mathematician Randall M. Holmes.