Logical Pluralism

A widespread assumption in contemporary philosophy of logic is that there is one true logic, that there is one and only one correct answer as to whether a given argument is deductively valid. In this paper we propose an alternative view, logical pluralism. According to logical pluralism there is not one true logic; there are many. There is not always a single answer to the question “is this argument valid?” 1 Logic, Logics and Consequence Anyone acquainted with contemporary Logic knows that there are many so-called logics.1 But are these logics rightly so-called? Are any of the menagerie of non-classical logics, such as relevant logics, intuitionistic logic, paraconsistent logics or quantum logics, as deserving of the title ‘logic’ as classical logic? On the other hand, is classical logic really as deserving of the title ‘logic’ as relevant logic (or any of the other non-classical logics)? If so, why so? If not, why not? Logic has a chief subject matter: Logical Consequence. The chief aim of logic is to account for consequence — to say, accurately and systematically, what consequence amounts to, which is normally done by specifying which arguments (in a given language) are valid. All of this, at least today, is common ground. Logic has not always been seen in this light. Years ago, Logic was dominated by the Frege–Russell picture which treats logical truth as the lead character and consequence as secondary. The contemporary picture reverses the cast: consequence is the lead character. For example, Etchemendy writes: Throughout much of this century, the predominant conception of logic was one inherited from Frege and Russell, a conception according to which the primary subject of logic, like the primary subject of arithmetic or geometry, was a particular body of truths: logical truths in the former case, arithmetical or geometric in the latter . . . This conception of logic now strikes us as rather odd, indeed as something of an anomaly in the history of logic. We no longer view logic as having a body of truths, the logical truths, as its principal concern; we do not, in this respect, think of it as parallel to other mathematical disciplines. If anything, we think of the consequence relation itself as the primary subject of logic, and view logical truth as simply the degenerate instance of this relation: logical truths are those that follow from any set of assumptions whatsoever, or alternatively, from no assumptions at all. [16, page 74]2 1Except where grammar dictates otherwise, ‘Logic’ names the discipline, and ‘logic’ names a logical system. 2For a more detailed discussion of the centrality of consequence in logic, see Chapter 2 of Stephen Read’s Thinking About Logic [39].