Ulrich Meyer

This paper argues that modal realism has a problem with mathematical impossibilities. Due to the peculiar way it treats both propositions and mathematical objects, modal realism cannot distinguish the content of different mathematically impossible beliefs. While one might be happy to identify all logically impossible beliefs, there are many different mathematically impossible beliefs, none of which is a belief in a logical contradiction. The fact that it cannot distinguish these beliefs speaks against adopting modal realism.

Many philosophers believe there to be a fundamental difference between the present and past and future times, but they tend to disagree amongst themselves about what this difference is. Some think that the present is singled out by consciousness, while others believe that it marks the position to which the flow of time has advanced. According to presentism, the current moment is ontologically privileged: nothing exists that is not present. My aim in this chapter is to argue that this particular attempt at distinguishing the present from other times is unsuccessful.

A perennial question in the philosophy of time concerns the relation between the objective “physical time” that features in empirical theories of motion and the subjective “human time” in which our own experiences unfold. This article is about one facet of this broader question: whether the phenomenon of consciousness allows us to make a principled distinction between the present and other times. A number of authors have argued that, without conscious observers, there would be no distinctions of past, present, and future. This paper defends the opposing thesis that there is no interesting connection between consciousness and presentness.

With the rigorous development of modal logic in the first half of the twentieth century, it became custom amongst philosophers to characterize different views about necessity and possibility in terms of rival axiomatic systems for the modal operators ‘ ’ (‘possibly’) and ‘ ’ (‘necessarily’). From the late 1950s onwards, Arthur Prior began to argue that temporal distinctions ought to be given a similar treatment, in terms of axiomatic systems for sentential tense operators, such as ‘P’ (‘it was the case that’) and ‘F’ (‘it will be the case that’).1 My aim here is to give a brief survey of the extent to which time can be treated on the model of modality. I shall not try to address the further question of whether such ‘modal’ accounts of time are to be preferred over ‘spatial’ accounts that treat times more like places.

This paper explains how to obtain quantification over times in a tense logic in which all temporal distinctions are ultimately spelled out in terms of the two simple tense operators “it was the case that” and “it will be the case that.” The account of times defended here is similar to what is known as “linguistic ersatzism” about possible worlds, but there are noteworthy differences between these two cases. For example, while linguistic ersatzism would support actualism, the view of times defended here does not support presentism.