‘Terdurance’

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.