Using a Formal Theory of Logic Metaphorically

Abstract

At the end of the last chapter I invoked the idea that a formal system of logic, such as LP, is used metaphorically by the pluralist. It is essential to the pluralist position, and possibly to many other positions, that we should be able to make sense of this, and say something quite definite about it. Otherwise, our claims about appealing to formal systems of logic are empty. I look at three ways in which the pluralist makes use of a formal logical system. The first is in direct appeal to a rule or axiom to justify a move in an argument. The second is when the pluralist uses a formal theory in order to reconstruct another theory. This is done to understand the theory from another perspective. The third use is dialectical. In invoking or developing a formal theory to represent a form of reasoning, we bring some features of that reasoning into relief, and we obscure other features. We can evaluate the fit between the formal theory and the informal one. In the evaluation, we might well consider alternative formal representations. Thus, we enter a dialectic. Lastly, in order to remind us that pluralists are not the only ones who use formal logic informally, I look at how it is that mathematicians use formal logical theories.