Only Fourdimensionalists Can Have 3D/4D Equivalence
When first introduced to the distinction between three- and fourdimensionalism and between perduranitsm and endurantism, many, myself included, have the feeling that both are valid ways of looking at the same reality and hence that at bottom they must be somehow equivalent or inter-translatable.
I still believe some of this. Consider for example the question of interpreting temporal predications. Endurantists say that "x is F at t" is true iff (the whole of) x stands in the F-relation to t, or iff x instantiates-at-t F, or something like that. As a perdurantist, I need not deny that. Rather, I have a further analysis of what it means to stand in the F-relation to t, or to instantiate-at-t F: it means to have a temporal part located at t which is F. Similarly, I needn't deny that I am wholly present right now. Applying the perdurantist analysis, what this claim says is that I -- the entire worm, with all his spatial and temporal parts -- have a temporal part which is present right now. Perhaps I could even try to make sense of claims like "people don't have temporal parts" by appealing to restricted quantification. But somewhere around this point the translatability comes to an end. Endurantists usually build the rejection of perdurantism into the very heart of their account, and it is certainly uncharitable to re-interpret this rejection so that it is after all compatible with what it rejects. (Here is something odd, by the way: how can it be uncharitable to interpret someone's utterances in such a way that they come out true rather than in a way in which they are false?)
So the inter-translatability must be restricted to claims of the relevant theories that are not just rejections of the respective opponent theory.
Inter-translatability? So far I've only argued that as a perdurantist I can make sense of most endurantist claims. How about the other way round? Well, where a perdurantist says that a temporal part of x, existing at t, is F, the endurantist can of course understand this as meaning that x instantiates-at-t F (or whatever his preferred account of temporal predication says). But the translatability comes to an end long before we reach perdurantist claims aimed at rejecting endurantism. For instance, what is the endurantist to make of my claim that I consist of my temporal parts; that some part of me came into existence at noon today and ceased to exist at 13:00; that I am the fusion of temporal parts of microphysical fields and particles; that a person's temporal parts are related to each other by a chain of causal dependence; that a thing's instantaneous temporal parts are 'events' in the Minkowski spacetime of relativity theory; that our linguistic conventions often fail to settle exactly which fusion of temporal parts our terms denote; etc.?
The asymmetry has an obvious explanation. Perdurantists have a richer ontology in which they can easily find objects that can do as ersatz enduring objects, viz. worms. But the endurantist ontology doesn't contain things that could do as ersatz temporal parts. At best it contains things like ordered pairs of enduring things and times, but these hardly fit much of what the perdurantist says.
Thus I believe that both endurantism and perdurantism (modula their rejection of the opponent) can be regarded as acceptable accounts of ordinary objects. But I can only believe that because I am a perdurantist.
If that's right, E.J.Lowe, once at the forefront of endurantism, should perhaps be regarded as a perdurantist now that he holds that three-dimensionalism and four-dimensionalism are equivalent (Analysis 63/2, 2003: 114--23).