Frege's theorem states that the axioms of second-order arithmetic can be derived in second-order logic from Hume's principle. It was first proven, informally, by Gottlob Frege in his Foundations of Arithmetic, published in 1884, and proven more formally in his Basic Laws of Arithmetic, published in two volumes, in 1893 and 1903. The theorem was re-discovered by Crispin Wright in the early 1980s and has since been the focus of significant work. It is at the core of the philosophy of mathematics known as neo-logicism. This article does not cite its references or sources. ... In mathematical logic, second order arithmetic is a stronger version of Peano arithmetic that allows quantification over subsets of the integers, rather than just over integers. ... In mathematical logic, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. ... Humes principle is a standard for comparing any two sets of objects as to size. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, Bad Kleinen, IPA: ) was a German mathematician who became a logician and philosopher. ... Crispin Wright (born 1942) is a British philosopher, who has written on neo-Fregean philosophy of mathematics, Wittgensteins later philosophy, and on issues related to truth, realism, cognitivism, skepticism, knowledge, and objectivity. ... Logicism is one of the schools of thought in the Philosophy of mathematics. ...