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

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.

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

“…In epistemological movements such as coherentism and (partly) externalism it is argued that rulecircular justifications, in which the rule to be justified is employed in the justificatory argument, are a viable solution to this problem. 1 However, it can be demonstrated that rule-circular justifications are epistemically worthless, because with such a justification both a rule and the opposite rule can be proved. For example, both the rule of induction and the rule of counterinduction (that infers the opposite of what induction infers) can be rulecircularly 'justified' as follows ( [56], 46):…”