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The Many Worlds Interpretation of Set Theory

Published online by Cambridge University Press:  28 February 2022

Geoffrey Hellman
Geoffrey Hellman*
Affiliation:
University of Minnesota
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Extract

As standardly presented in axiomatic form, set theory exhibits two fundamental features which together give rise to a number of foundational and philosophical problems. These features are so basic that they are seldom even isolated. The first is that the axioms are taken as categorical assertions (e.g. “There exists an empty set”, “There exists an infinite set”, “The power set of any set exists”, etc.). The second is that actualist quantifiers are employed in these axioms, so that they appear to be about actual objects; the domain of these quantifiers forms the fixed universe of sets (up to a choice of urelement basis), relata of a unique, fixed membership relation entering into the statement of the axioms.

Such presentations are associated with the philosophical positions of platonism and set-theoretic foundationalism.

Type
Part XIV. Set Theory
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1988 , Issue 2: Volume Two: Symposia and Invited Papers 1988 , 1988 , pp. 445 - 455
Copyright
Copyright © 1989 by the Philosophy of Science Association

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