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Randomness and Reality

Published online by Cambridge University Press:  31 January 2023

Geoffrey Hellman
Geoffrey Hellman*
Affiliation:
Indiana University
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Extract

In previous technical work ([1] and [2]) on which his present paper [3] draws, Benioff has presented results conforming with the following argument-scheme:

First, if we construe Quantum Mechanics as making claims to the effect that infinite outcome sequences (generated by repeated measurements on a system for a given observable in a given state) be random; and second, if a strong definition of “random” is adopted in this construal, then certain models of Zermelo-Fraenkel set theory (ZF) cannot be “carriers for the mathematics of physics”.

How interesting is this? One can approach the matter on two levels, the level of the specific technical results, and the level of more general implications of this pattern of argument for understanding connections between mathematics and physics. The second more general level should be our primary focus, but it will pay at the outset to look briefly at the technical level.

Type
Part III. Physical Randomness
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 2: Volume Two: Symposia and Invited Papers 1978 , 1978 , pp. 79 - 97
Copyright
Copyright © 1981 Philosophy of Science Association

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References

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