Russell’s Logicism
نویسندگان
چکیده
Logicism is typically de ned as the thesis that mathematics reduces to, or is an extension of, logic. Exactly what “reduces” means here is not always made entirely clear. (More de nite articulations of logicism are explored in section 5 below.) While something like this thesis had been articulated by others (e.g., Dedekind 1888 and arguably Leibniz 1666), logicism only became a widespread subject of intellectual study when serious attempts began to be made to provide complete deductions of the most important principles of mathematics from purely logical foundations. This became possible only with the development of modern quanti er logic, which went hand in hand with these attempts. Gottlob Frege announced such a project in his 1884 Grundlagen der Arithmetik (translated as Frege 1950), and attempted to carry it out in his 1893–1902 Grundgesetze der Arithmetik (translated as Frege 2013). Frege limited his logicism to arithmetic, however, and it turned out that his logical foundation was inconsistent. Working at rst in ignorance of Frege, Bertrand Russell’s interests in the fundamental principles of mathematics date back to the late 1890s. He published An Essay on the Foundations of Geometry in 1897 and soon thereafter began work on
منابع مشابه
The Cambridge companion to
Cambridge University Press, Cambridge, UK and New York, US, xvii + 550 pp.— therein: Ivor Grattan-Guinness. Mathematics in and behind Russell’s logicism, and its reception. Pp. 51–83. Richard Cartwright. Russell and Moore: 1895–1905. Pp. 108–127. Peter Hylton. The theory of descriptions. Pp. 202–240. Martin Godwyn and Andrew D. Irvine. Bertrand Russell’s logicism. Pp. 171–201. Michael Beaney. R...
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