Blackwell Reference Online

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Set theory is the branch of mathematics concerned with the general properties of aggregates of points, numbers, or arbitrary elements. It was created in the late nineteenth century, mainly by Georg Cantor. After the discovery of certain contradictions euphemistically called paradoxes, it was reduced to axiomatic form in the early twentieth century, mainly by Ernst Zermelo and Abraham Fraenkel. Thereafter it became widely accepted as a framework - or ‘foundation’ - for the development of the other branches of modern, abstract mathematics. Today, its basic notions and notations are widely used even outside mathematics proper. Set theory impinges on philosophy in several ways. First, the more formal areas of philosophy are among the areas outside mathematics proper where set-theoretic notions and notations are used. Further, the main topic of set theory (considered as a branch of mathematics in its own right rather than a framework for developing other branches of mathematics) is infinity, traditionally a topic of philosophical speculation. Finally, the fact that mathematics is in some sense reducible to set theory - though the specification of just what sense this is remains itself a philosophical problem - means that many problems of philosophy of mathematics reduce to problems of philosophy of set theory. A set is one thing composed of many things, its elements , the relation ... log in or subscribe to read full text