Thomas Sattig

This chapter presents a new account of temporal predication — the representational account — combined with four-dimensionalism to yield the temporal-parts account of temporal supervenience. This elegant account asserts and explains the theses that the facts of persistence logically supervene on facts about the spatiotemporal location of temporal parts of objects, and that the facts of temporal instantiation logically supervene on facts about the atemporal instantiation of properties by temporal parts of objects. It is further shown that the questions of temporal supervenience as well as the four-dimensionalist answers to these questions have interesting spatial and modal analogues. Despite its success in explaining the supervenience of facts of persistence and change, the temporal-parts account has objectionable consequences. Three problems are raised, the most serious of which is the problem of predicational overkill. Each of these problems concerns the account’s failure to capture certain ordinary temporal facts.

Can our ordinary conception of macroscopic objects be transposed to the framework of relativity theory? According to common sense, ordinary objects cannot undergo radical variation in shape, whereas according to a compelling and widely accepted metaphysical picture of ordinary objects’ shapes in Minkowski spacetime, they do undergo such radical variation. This problem raises doubts about the compatibility of the ordinary conception and the relativistic conception of the world. I shall propose to reconcile common sense with relativistic metaphysics by viewing ordinary objects as doublelayered compounds of matter and form. The different layers permit different perspectives on the objects, the one perspective focusing on form and the other focusing on matter. This ontology allows the conception of common sense and the conception of relativistic metaphysics to manifest different and compatible perspectives on the same objects

Four-dimensionalists offer a unified picture of various puzzles about identity over time, including the puzzle of fission, the puzzle of constitution and the puzzle of undetached parts. What unifies the four-dimensionalist approaches to these puzzles is the possibility of temporal overlap—the possibility for distinct continuants to share a common temporal part, or stage. I claim that the unified picture is inconsistent, if there are informative criteria of identity over time. I will show that while temporal overlap is compatible with four-dimensionalist criteria of diachronic composition, temporal overlap is incompatible with any four-dimensionalist criteria of diachronic identity.