In the course of refereeing a paper whose title I won’t disclose, for a journal I won’t name, I was reminded of Kristie Miller‘s notion of terdurance. Here’s how she defines the notion (in ‘Ought a Four-Dimensionalist To Believe in Temporal Parts?‘):

A complex object O, terdures iff: (i) O persists through some temporal interval T which contains temporal instants t and t* and (ii) the three-dimensional slice of O at t is not strictly identical to the three-dimensional slice of O at t* and (iii) it is not the case that for every instant t in T and sub-interval I in T, that there is some object O* that exists at exactly that instant or sub-interval, and which overlaps every part of O at that instant or during that sub-interval. (p. 631)

What’s going on here? Miller is arguing that there is a third kind of persistence, a kind of non-perdurantist four-dimensionalism, which she calls terdurance. Clause (i) of the definition is supposed to secure that terduing objects persist; clause (ii) secures that the object doesn’t persist by enduring (since in that case O would be wholly present at each moment at which it exists, and would be strictly identical to itself at each such moment). Clause (iii) is supposed to secure the difference of terdurance from perdurance, by denying the existence of temporal parts of O that exist at arbitrary sub-intervals of the time during which O persists.

As a definition, this is of course fine. There fact that there may be no objects which satisfy these clauses hardly undermines the cogency of definition, though it would be rather useless. But one might very well wonder what kind of world ours would be if it could contain terduring objects. The notion of terdurance initially seemed very puzzling to me, and very difficult to make sense of. I suspect that others too find it puzzling. So here’s my attempt to make sense of it.

We are told that terduring objects persist across an extended interval, without having (proper) temporal parts, and without being wholly present at each moment during the interval. This almost entirely negative definition is difficult to understand, particularly if one doesn’t have a particularly firm grasp on ‘wholly present’ to begin with. So let me offer an account of terdurance that is easier to understand. Let’s start with ‘wholly present’, the characteristic endurantist notion that clause (ii) is supposed to deny holds of terduring objects.

Following Josh Parsons (in ‘Theories of Location‘), we can define endurance through a region to involve an object’s being wholly located in each time in that region (which is to say, each part of the object is located in each time). Endurance, on this view, involves multiple temporal location. So a terduring object would be one that is temporally simple, but doesn’t occupy an extended region in virtue of being multiply located throughout it (as an enduring object would). The natural candidate is what Kris McDaniel (in ‘Extended Simples‘) calls a spanner: an extended simple which ‘bears the occupation relation to exactly one extended spatiotemporal region, without bearing the location relation to any proper part of that extended region.’ (p. 134). I myself share worries Parsons raises (in ‘Hudson on Location‘) about the notion: it makes use of a conception of location that cannot be understood in mereological and spatiotemporal terms. The natural conception of an exact location that Parsons’ framework allows us to define—as being a region pervaded by an object and in which the object is entirely contained—ensures that spanners are not possible in a way that makes them distinct from entended objects (the spatial analogue of endurance). For suppose there was a simple spanner S, that was located in some extended region R. Because R is a location of S, then S pervades R, and also S is wholly contained in R. Consider now two subregions of R, R1 and R2. S also pervades R1 and R2; moreover, since S is simple, S is entirely in R1 and R2 (every part of S is inside each of those regions, which is clearly not to say that their complement is entirely free of S). So S is wholly located in R1, and wholly located in R2. But then S is wholly present at both of those regions. But we were supposed to be thinking that spanning objects were a different way of being extended and simple than endurance. Saying that spanners have only one (exact) location certainly captures what their defenders wish to endorse, but saying that they are moreover not wholly located in multiple regions is not consistent with these Parsonian conceptions of location.

But this might be alright, if location is itself fundamental. In that case, we needn’t endorse these conceptual truths connecting location with mereology and the subregion relation. For we might accept the broadly Humean principle that recombination of fundamental relations is permissible, and this recombination will permit cases where the location relation holds between O and R, but where—because that relation is fundamental—we needn’t say that leads ineluctably to any claims at all about the relation between O and any subregions of R. For example, it could be that O is simple, and is located at R, but also is located at every proper subregion of R. Or we could have O being simple, and located at R, but located at no proper subregion of R. These will be distinct scenarios for the location fundamentalist, but none of Parsons’ location relations will yield these verdicts (his ‘exact location’ says that only the second scenario is possible; his ‘entire location’ says that only the first is possible). McDaniel uses this kind of recombination argument to argue for the existence of spanners, but as Raúl Saucedo has recently noted (in ‘Parthood and Location‘), the argument generalises, to such an extent that it permits the existence of crowded simples, which

are mereologically simple but spatiotemporally complex material objects, i.e. material objects that have proper contractions but no proper parts. Crowded simples may then be arbitrarily large, since they may have arbitrarily large proper contractions. They may also have arbitrary spatiotemporal complexity, since they may have arbitrarily many proper contractions. Moreover, they may have contractions all the way down, i.e. each of their contractions may have proper contractions. Their location may even be scattered. Nonetheless, they would be mereologically simple—they would have no proper parts. (§6)

If we are willing to follow McDaniel, Sider, and Saucedo, among others, down this path, we have a fairly direct argument for the existence of spanners. And we can parlay such an argument into an account of temporal spanners—or, as Miller terms them, terduring objects. That is, O terdures iff O is a temporally simple object that bears the fundamental location relation to one and only one temporally extended region.

As to the prospects for terdurantism as a general account of the persistence of ordinary continuants, I’m not confident. But it seems to me a view worth exploring, especially given how it can be naturally motivated from within frameworks for fundamentality of location that are currently the subject of a lot of really interesting discussion.


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