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.
Paradox of value The paradox of value (also known as the diamond–water paradox) is the apparent contradiction that, although water is on the whole more useful, in terms of survival, than diamonds, diamonds command a higher price in the market. The philosopher Adam Smith is often considered to be the classic presenter of this paradox, although it had already appeared as early as Plato's "Euthydemus". Nicolaus Copernicus, John Locke, John Law and others had previously tried to explain the disparity.