Ought a Four-Dimensionalist To Believe in Temporal Parts?

I Introduction

I borrow the title of this paper, slightly amended, from Parsons’ recent ‘Must a Four-Dimensionalist Believe in Temporal Parts?’¹ Four-dimensionalism, as I use the term, is the view that persisting objects have four dimensions: they are four-dimensional ‘worms’ in space-time. This view is contrasted with three-dimensionalism, the view that persisting objects have three-dimensions and are wholly present at each moment at which they exist. The most common version of four-dimensionalism is perdurantism, according to which these four-dimensional objects are segmented into temporal parts — shorter lived objects that compose the four-dimensional whole in just the same way that the segments of real earth worms compose the whole worm.

According to Parsons, a four-dimensionalist need not believe in temporal parts. But ought a four-dimensionalist to believe in temporal parts? This question might be thought uninteresting, insofar as it has largely been answered by force of numbers. But asking it is instructive. For there are reasons to suppose that a non-perdurantist four-dimensionalism might provide an attractive middle position between perdurantism and endurantism:² a position that avoids many of the different counterintuitive costs associated with each of these views. So it is worth determining whether non-perdurantist four-dimensionalism is a viable theory of persistence. To that end I develop the most plausible non-perdurantist version of four-dimensionalism.

Ultimately, however, I argue that non-perdurantist four-dimensionalism does not offer a plausible middle ground position between perdurantism and endurantism. Further, in considering the reasons why non-perdurantism is unappealing, a number of problems are revealed for endurantism. Much of what is problematic about non-perdurantism is equally problematic for endurantism. What is illuminating is that the analogous problems we discover for endurantism are not those that typically constitute objections to the view. This is because evaluating non-perdurantism allows us to abstract away from two issues that cloud the debate between three- and four-dimensionalists: first, the idea that three-dimensional objects are wholly present whenever they exist, and the associated problems with cashing out this notion; and second, the idea that three-dimensional objects are strictly identical to themselves at every time at which they exist, and the attendant problems with that notion in the light of change across time. Abstracting away from these issues is fruitful, because frequently with respect to these issues, debate on either side reduces to an appeal to brute intuition leaving the debate stagnant.

That endurantism faces the same problems as non-perdurantist four-dimensionalism tells us that the debate between perdurantists and endurantists has been misplaced. We discover that perdurantism is in some sense resilient: as soon as we move away from a perdurantist to a non-perdurantist four-dimensionalism, the account exhibits fundamental problems. What is wrong with endurantism is not that it embraces identity across time, rather, what is problematic is that it is non-perdurantist. Non-perdurantist theories of persistence fail because ultimately, temporal parts are resilient: we need them in any account of persistence.

I begin by outlining some reasons to find non-perdurantist four-dimensionalism an attractive view. Then in sections three, four and five I set out a more detailed account of a non-perdurantist four-dimensionalism. This allows us, in section six, to see the shortcomings of such a position. In this section I outline a number of key objections to non-perdurantism, before in section seven arguing that analogous problems arise for endurantism.

II A Middle-ground Position

This section aims to motivate the idea that a non-perdurantist four-dimensionalism — non-perdurantism as I call the view — might be attractive. To do so I will make two assumptions. First, that the key objections to endurantism and perdurantism are widely known and do not require explication here. Second, that although the details of non-perdurantism are left to section three, we have a sufficient grasp of the general idea of non-perdurantism to see, at least prima facie, why it might be thought appealing.

The general idea then, is that persisting objects are...