Does Science Influence the Logic we Ought to Use: A Reflection on the Quantum Logic Controversy

Studia Logica 95 (1/2):183 - 206 (2010)
Abstract
In this article I argue that there is a sense in which logic is empirical, and hence open to influence from science. One of the roles of logic is the modelling and extending of natural language reasoning. It does so by providing a formal system which succeeds in modelling the structure of a paradigmatic set of our natural language inferences and which then permits us to extend this structure to novel cases with relative ease. In choosing the best system of those that succeed in this, we seek certain virtues of such structures such as simplicity and naturalness (which will be explained). Science can influence logic by bringing us, as in the case of quantum mechanics, to make natural language inferences about new kinds of systems and thereby extend the set of paradigmatic cases that our formal logic ought to model as simply and naturally as possible. This can alter which structures ought to be used to provide semantics for such models. I show why such a revolution could have led us to reject one logic for another through explaining why complex claims about quantum mechanical systems failed to lead us to reject classical logic for quantum logic
Keywords Quantum mechanics  quantum logic  Boolean lattices  Hilbert lattices  semantics  science
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References found in this work BETA
Michael Dickson (2001). Quantum Logic is Alive ∧ (It is True ∨ It is False). Proceedings of the Philosophy of Science Association 2001 (3):S274 - S287.
Hilary Putnam (1968). Is Logic Empirical? Boston Studies in the Philosophy of Science 5.

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Michael R. Gardner (1971). Is Quantum Logic Really Logic? Philosophy of Science 38 (4):508-529.
Michael Dickson (2001). Quantum Logic is Alive ∧ (It is True ∨ It is False). Proceedings of the Philosophy of Science Association 2001 (3):S274 - S287.
James H. McGrath (1978). Only If Quanta Had Logic. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:268 - 275.
J. L. Bell (1986). A New Approach to Quantum Logic. British Journal for the Philosophy of Science 37 (1):83-99.
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