The Applications of Bivalent Logic, and the Misapplication of Multivalent Logic to Law

Abstract

The argument of this chapter proceeds, after a general introduction in Section 1, in the following way. In Section 2, I set out my understanding of the relationship between bivalent logic and multivalent logic. The key suggestion made here is that the generally accepted limitations of bivalent logic, which proved a spur for the move into multivalent logic, can be overcome by recognizing the need in some circumstances for a dual application of bivalent logic (the plural applications in the title of this chapter). I show how this dual application leaves open, within a bivalent framework, the uncertainties and possibilities that multivalent logic seeks to address. This has implications for the relationship between the two. More importantly for our present concerns, it provides within the expanded bivalent framework the possibility of recognizing resolved and unresolved states of the primary entity that is subject to the initial bivalent analysis. It is then a simple matter to extend this framework to cover a number of entities, whose ultimate manifestations are mutually exclusive, thus recognizing at one (unresolved) stage the presence of contradictory possibilities, while at the other (resolved) stage the emergence of one entity at the expense of the other(s). And all this within a bivalent framework. Section 2 emphasizes the advantages of this bivalent approach over a multivalent approach, raising the concern that a multivalent approach may distort our analysis of certain phenomena by disregarding the underlying bivalent possibilities, or choices, that confront us (the misapplication of the title). Section 3 then surveys the different legal practices and phenomena discussed by Glenn in his “Cosmopolitan Thought”, as evidence of the application of multivalent logic, or of the inadequacies of bivalent logic, within law in general and the law of a cosmopolitan state in particular. These are divided into a number of topics, and for each topic I mount the argument that the multivalent (or new logics) perspective provides a distorted analysis, which the expanded bivalent framework can be used to correct. Within the introductory part of Section 3 a further technical matter is discussed, in establishing a distinction that is often elided between binary (bivalent) logic and a binary division (divisio). The significance of this distinction for the application of the bivalent framework flows into the subsequent discussion. The final Section 4 offers some concluding reflections on logic, law, and the cosmopolitan state as envisaged by Glenn; and, more speculatively, on how the present case study might be relevant to wider discussions of the new logics.

Keywords: law and logic, legal reasoning, bivalent logic, multivalent logic, cosmopolitan thought