Conceptual Foundations of Operational Set Theory

Hansen, Kaj Börge, 1946- (författare): Uppsala universitet,Filosofiska institutionen

(creator_code:org_t)

Copenhagen : Museum Tusculanum Press, 2010
2010
Engelska.
Ingår i: Danish Yearbook of Philosophy. - Copenhagen : Museum Tusculanum Press. - 0070-2749 .- 2468-9300. ; 45:1, s. 29-50

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Abstract Ämnesord

Stäng

I formulate the Zermelo-Russell paradox for naive set theory. A sketch is given of Zermelo’s solution to the paradox: the cumulative type structure. A careful analysis of the set formation process shows a missing component in this solution: the necessity of an assumed imaginary jump out of an infinite universe. Thus a set is formed by a suitable combination of concrete and imaginary operations all of which can be made or assumed by a Turing machine. Some consequences are drawn from this improved analysis of the concept of set, for the theory of sets and for the philosophy and foundations of mathematics.

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