The probabilistic argument for a non-classical logic of quantum mechanics

Philosophy of Science 33 (1/2):14-21 (1966)
Abstract
The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, to the conjunction of two events. The conclusion is that the working logic of quantum mechanics is not classical. The nature of the logic that is appropriate for quantum mechanics is examined
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DOI 10.1086/288067
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The Quantum Probability Calculus.J. M. Jauch - 1974 - Synthese 29 (1-4):131 - 154.
Dutch Books and Nonclassical Probability Spaces.Leszek Wroński & Michał Tomasz Godziszewski - 2017 - European Journal for Philosophy of Science 7 (2):267-284.

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