Hume's principle

Hume's Principle is a principle of logic established by David Hume in A Treatise of Human Nature and called Hume's Principle or HP by George Boolos .

Hume's principle is: The number of Fs is equal to the number of Gs if and only if there is a bijection between the Fs and the Gs.

Gottlob Frege uses Hume's principle in his philosophy to derive the Peano axioms of arithmetic from it according to Frege's theorem , which is the basis of neo- logicism .

Frege's conception of numbers differs from that of Georg Cantor , since Frege defines cardinal and ordinal numbers independently of one another. Cantor's definition of cardinal numbers by means of ordinal numbers is part of the theories of transfinite numbers .

literature

• David J. Anderson, Edward N. Zalta : Frege, Boolos, and Logical Objects. In: Journal of Philosophical Logic. Vol. 33, No. 1, 2004, ISSN  0022-3611 , pp. 1-26.
• George Boolos : Logic, Logic, and Logic. Harvard University Press, Cambridge MA 1998, ISBN 0-674-53766-1 , Especially section II: Frege Studies.
• John P. Burgess: Fixing Frege. Princeton University Press, Princeton NJ et al. 2005, ISBN 0-691-12231-8 .
• G. Frege : Foundations of Arithmetic. A logico-mathematical inquiry into the concept of number. Blackwell, Oxford 1950.
• David Hume , A Treatise of Human Nature .

Web links

• Stanford Encyclopedia of Philosophy : " Frege's Logic, Theorem, and Foundations for Arithmetic " - by Edward Zalta .
• University of St. Andrews - Arche: The Logical and Metaphysical Foundations of Classical Mathematics
• University of St. Andrews - Arche: The Center for Philosophy of Logic, Language, Mathematics and Mind at St. Andrew's University.