17 - Contingent Identity in Modal Logic

Summary

Introduction

17.1.1 In this chapter we will look at the behaviour of contingent identity in modal logic. We assume that the logic to which identity is being added is any quantified normal modal logic, constant or variable domain, without the Negativity Constraint. Recall that if L is any logic L(CI) is L augmented by contingent identity.

17.1.2 First, we will take all constants to be rigid designators. We then look at the addition of descriptors.

17.1.3 Finally, we will take up briefly two important philosophical issues concerning identity, tense and modality.

Contingent Identity

17.2.1 In 16.4.1 we looked at a problem concerning SI. Later in 16.4 we saw how the distinction between rigid and non-rigid designators solves the problem. But there would appear to be a more virulent form of it. The Morning Star is the planet Venus, as is the Evening Star, m = v = e. But arguably, these noun phrases are rigid. So it follows by NI that □m = e; and this would seem not to be true. It would seem to be a contingent matter that the heavenly object that appears in the sky around dawn, and christened by the Ancients ‘the Morning Star’, turned out to be identical with the heavenly body that appears in the sky around dusk, and christened by the Ancients ‘the Evening Star’. The latter, for example, could have turned out to be Mercury.