Wouter Cohen
(ILLC)
### The Logic of Relative Modality

December 7th at 18:00, in F1.15

Most modalities seem to be relative. For instance, it is physically impossible to accelerate beyond the speed of light because it is impossible relative to the laws of physics to accelerate beyond the speed of light. Similarly, in an ordinary context `it is impossible to travel between London and Amsterdam in under 15 minutes' is true because it is impossible relative to ordinary facts about modes of transportation to travel between London and Amsterdam in under 15 minutes. But what does impossibility relative to ... amount to? To answer this question, I will simply take it for granted that there is an absolute modality underlying all relative modalities. So we might characterize, say, physical necessity more specifically as absolute necessity relative to the laws of physics. The main question I address, then, is this: given absolute modality, how can we satisfactorily define the various relative modalities in terms of it? In the first part of my talk, I get you up to speed on the little literature there is on defining relative modality in terms of absolute modality. In particular, I discuss the standard account, which analyzes relative modalities as strict conditionals, look at some its problematic formal properties and argue for an underlying problem in terms of a new distinction between rigid and non-rigid relative modalities. In the second part, I introduce the recently developed HLSY account, argue that it has no straightforward translation into first-order modal logic and propose my own semantic account which is equivalent to the HLSY account w.r.t. propositional modal logic but is naturally generalized to first-order modal logic.