Introduction

The central concept of logic is that of logical consequence: whether, in an argument, a given statement (the conclusion) logically follows from certain other statements (the premises).

The first issue is concerned with conceptual analysis. Can the concept of logical consequence be analyzed ? And if so, how? That is, are there neces­sary and sufficient conditions that specify the extension of this concept; that determine the conditions under which a statement is a logical consequence of another (or of a group of others)? Given that, in natural language, we do have an intuitive, informal notion of what follows from what, at stake here is a process of uncovering the conditions that characterize the concept of logical consequence. (This is the issue of the conceptual analysis of logical consequence.)

Second, after this concept is analyzed, the issue arises as to whether there is only one correct specification of the concept, or whether the latter admits multiple specifications. The logical monist insists that there is only one such specification; the logical pluralist, in turn, argues that there are several correct specifications of logical consequence. (This is the logical pluralism issue.)

Third, once the plurality of logic is resolved, the issue arises as to how the application of logic can be accommodated. Is the application of logic similar to the way in which mathematical theories are applied? Or is logic applied in some other way? (This is the issue of the applications of logic.)

The articulation of a philosophy of logic involves careful reflection about these issues. All of them emerge, in one way or another, from the conceptual analysis of logical consequence. In this essay, I will examine each of these issues in turn, exploring, along the way, the interconnections among them.

2.