Second Article: Michael Dummett
In an article also titled "Is logic empirical?," Michael Dummett argues that Putnam's desire for realism mandates distributivity: the principle of distributivity is essential for the realist's understanding of how propositions are true of the world, in just the same way as he argues the principle of bivalence is. To grasp why: consider why truth tables work for classical logic: firstly, it must be the case that the variable parts of the proposition are either true or false: if they could be other values, or fail to have truth values at all, then the truth table analysis of logical connectives would not exhaust the possible ways these could be applied; for example intutionistic logic respects the classical truth tables, but not the laws of classical logic, because intuitionistic logic allows propositions to be other than true or false. Second, to be able to apply truth tables to describe a connective depends upon distributivity: a truth table is a disjunction of conjunctive possibilities, and the validity of the exercise depends upon the truth of the whole being a consequence of the bivalence of the propositions, which is true only if the principle of distributivity applies.
Hence Putnam cannot embrace realism without embracing classical logic, and hence his argument to endorse quantum logic because of realism about quanta is a hopeless case.
Dummett's argument is all the more interesting because he is not a proponent of classical logic. His argument for the connection between realism and classical logic is part of a wider argument to suggest that, just as the existence of particular class of entities may be a matter of dispute, so a disputation about the objective existence of such entities is also a matter of dispute. Consequently intuitionistic logic is privileged over classical logic, when it comes to disputation concerning phenomena whose objective existence is a matter of controversy.
Read more about this topic: Is Logic Empirical?
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