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?
Kurt Gödel Kurt Friedrich Gödel ( , ; ] ; April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered along with Aristotle, Alfred Tarski and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor.
Infinity (philosophy) In philosophy and theology, infinity is explored in articles under headings such as the Ultimate, the Absolute, God, and Zeno's paradoxes. In Greek philosophy, for example in Anaximander, 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass (ἄπειρον, "apeiron"). The Jain metaphysics and mathematics was the first to define and delineate different "types" of infinities. The work of the mathematician Georg Cantor first placed infinity into a coherent mathematical framework. Keenly aware of his departure from traditional wisdom, Cantor also presented a comprehensive historical and philosophical discussion of infinity. In Judeo-Christian theology, for example in the work of Duns Scotus, the infinite nature of God invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. In ethics infinity plays an important role designating that which cannot be defined or reduced to knowledge or power.