I’ve been reading Schaffer on supersubstantivalism today (although he calls the position monistic substantivalism, which is probably a better name). He gives a typically eloquent characterization of the view, presents it as parts of a ‘package deal’ with other four-dimensionalist-style positions, and then defends it. The presentation makes it look like there are lots of arguments, but really they reduce to two main lines of thought:

1) (parsimony/harmony) There’s no explanatory gain to positing material objects over and above four-dimensional regions of spacetime; rather, doing so generates some demands for explanation which the non-supersubstantivalist cannot easily meet

2) (parsimony/field theory) Best physical theory involves ubiquitous and indispensable reference to fields as ontologically fundamental, and these fields play the material-object role so well that it is otiose to add objects over-and-above the fields.

I think both these motivations are good ones (although 2 seems more compelling than 1) and I’m antecedently inclined to buy the package deal which Schaffer recommends. So I agree with his main conclusions.

Something that occurred to me while reading the paper was how this debate interlocks with the debate in philosophy of physics over how to respond to the ‘Hole argument’. Briefly, there are three alternative versions of substantivalism which survive the hole argument:

a) Haecceitistic indeterminism, which embraces indeterminism about the haecceitistic properties of spacetime points (models related by hole diffeomorphisms represent different possible worlds);

b) Sophisticated substantivalism, which embraces anti-haecceitism about spacetime points (models related by hole diffeomorphisms represent the same possible worlds);

c) Metrical essentialism, which makes the metrical properties of points essential to them (only one of a class of models related by hole diffeomorphisms represents a genuine possible world).

From what he says in the paper, it looks like Schaffer leans towards response c). I, and a lot of people at Oxford, find b) (or some structuralist variant on it) much more plausible. But supersubstantivalism plus b) leads to anti-haecceitism about material objects. Worlds differing only by a permutation of me and you, keeping all the qualitative features fixed, are not really two distinct worlds at all – this follows directly from anti-haecceitism about spacetime points and the conception of material objects as spacetime regions. Anti-haecceitism about material objects isn’t obviously part of Schaffer’s ‘package deal’, and a lot of metaphysicians are paid-up haecceitists about material objects – so it’s a potential cost for his position that combined with b), it entails anti-haecceitism about material objects. A dualistic substantivalist, who thinks of spacetime as a container for matter, could combine anti-haecceitism about spacetime points with haecceitism about material objects located at those points. Supersubstantivalism rules out this combination.

Some non-substantivalist responses to the whole argument can also, surprisingly, be combined with ‘supersubstantivalism’. If we buy ontic structural realism about space-time points, identifying points with loci of the genuinely real relational descriptions, then we are driven to ontic structural realism about material objects also.

I expect lots of people have had these thoughts already, but I want to put something or other on this blog, so here goes..


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