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In classical real analysis, one way to define a real number is as an equivalence class of Cauchy sequences of rational numbers.. In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ(n), together with a function g that takes a positive integer n and outputs a positive integer g(n) such that
Mathematics addresses only a part of human experience. Much of human experience does not fall under science or mathematics but under the philosophy of value, including ethics, aesthetics, and political philosophy. To assert that the world can be explained via mathematics amounts to an act of faith. 4. Evolution has primed humans to think ...
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship ...
Philosophy and the Mirror of Nature is a 1979 book by the American philosopher Richard Rorty, in which the author attempts to dissolve modern philosophical problems instead of solving them. Rorty does this by presenting them as pseudo-problems that only exist in the language-game of epistemological projects culminating in analytic philosophy .
Ludwig Wittgenstein considered his chief contribution to be in the philosophy of mathematics, a topic to which he devoted much of his work between 1929 and 1944. [1] As with his philosophy of language, Wittgenstein's views on mathematics evolved from the period of the Tractatus Logico-Philosophicus: with him changing from logicism (which was endorsed by his mentor Bertrand Russell) towards a ...
William Kingdon Clifford (4 May 1845 – 3 March 1879) was a British mathematician and philosopher.Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour.