Abstract
In the last twenty years, Chalmers has argued for a two-dimensional seman- tics, according to which every expression (of the sort that is a candidate to have an extension) is associated with a primary intension and a secondary intension. A primary intension is a function from scenarios (epistemically possible worlds) to extensions. A secondary intension is a function from (metaphysically) possible worlds to extensions. Starting from this, Chalmers maintains that a sentence S is metaphysically necessary iff the secondary intension of S is true at all worlds, and a sentence S is epistemically necessary iff the primary intension of S is true at all scenarios. I will call this 'Chalmers' Two-Dimensional Semantics'.
In this talk, I will present an argument against Chalmers' Two-Dimensional Semantics. First, I will argue with Chalmers that in connection with indexicals his two-dimensional semantics leads to the problem of how scenarios could best represent the information who I (the speaker) am, where I am, and what time it is now. I will call this 'the problem of indexicality'. For Chalmers, the natural solution to the problem of indexicality is to identify scenarios with centered worlds: ordered tuples of worlds, individuals, places, and times, with the individual, the place, and the time being the center of the world. According to such a solution, two arbitrary tokens of 'now' and 'here' (respectively) have the same primary intension, picking out the time/place marked at the center of any given scenario. Against this, I will object that there are a posteriori true, i.e. epistemically contingent, utterances of both 'Now = now' and 'Here = here'. I will call this 'the problem of a posteriori truths'. I will argue that as long as Chalmers' Two-Dimensional Semantics entails a compositionality principle for primary intensions the centered worlds account does not provide a solution to the problem of a posteriori truths. It will follow that an advocate of Chalmers' Two-Dimensional Semantics has to come up with an alternative candidate for scenarios which provides both a solution to the problem of indexicality and a solution to the problem of a posteriori truths. Since identifying scenarios with centered worlds seems to be the natural solution to the problem of indexicality, this will undermine Chalmers' Two-Dimensional Semantics. Concluding, I will discuss possible alternatives to a two-dimensional account of indexicals, starting from the theory of direct reference.
