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Virtual Logic: The One and the Many

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Georg Cantor, the mathematician who discovered transfinite set theory, said: 'A set is a unity that can be seen as a multiplicity.' More speci.cally, he said (Cantor, 1941, p. 85): 'By an 'aggregate' (Menge) we are to understand any collection into a whole (Zusammenfassung zu einem Ganzen) M of definite and separate objects m of our intuition or our thought.' This definition lives next door to a deep philosophical problem: If one begins with a unity, how can multiplicity arise? How can many come from one? If one begins with multiplicity, how can unity arise? How can one come from many? It would seem that we must begin in multiplicity. Any explanation of unity must begin in multiplicity. It is possible to structure such an explanation so that it points beyond itself to a unity that it can never reach.
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Document Type: Research Article

Publication date: 01 January 2005

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