Holes in Spacetime: Some Neglected Essentials

Abstract

The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including General Relativity. The argument has sparked an industry of searching for a metaphysics of spacetime with the right modal implications to rescue determinism. In this paper, I first argue that certain prominent replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. My argument involves showing that threats to determinism like the hole argument are more general than has heretofore been recognized. I then propose a novel essentialist doctrine about spacetime that successfully rescues determinism, what I call sufficiency metric essentialism. However, I ultimately argue that this doctrine is independently problematic, and teaches us that no essentialist doctrine about spacetime can succeed. I close by suggesting some lessons for future work on spacetime and the metaphysics of physics more broadly, and also drawing some morals for contemporary metaphysics, in particular about whether essence can be used to articulate a precise structuralist doctrine, and the relationship between essence and modality.

How to Be a Spacetime Substantivalist

“…Mutatis mutandis for the property containing spacetime point o, for all spacetime points o, given demanding-modal-essences. Yet I don't take these facts to cast doubt on the strong judgment that the properties containing quasi-point o or containing spacetime point o are intrinsic to times that instantiate them all the same, even granting the truth of the relevant doctrines 54 This is the status I called 'full determinism' in Teitel (2019b). A few qualifications.…”

“…14 Again, Pooley (2006, 101) describes the doctrines as "close to a consensus" in the literature. For just a sampling of proponents of anti-haecceitism or no-shifts (which nevertheless sometimes hold views that are altogether different in other respects), see Field (1984), Butterfield (1989), Maidens (1992), Brighouse (1994), Hoefer (1996), Pooley (2006), Dasgupta (2011), andTeitel (2019b). Maudlin (1988Maudlin ( , 1990) defends an essentialist doctrine, also with the aim of securing no-shifts, though its modal implications are in fact somewhat weaker, and don't rule out all shift-related possibilities (see Teitel (2019b, 369-73)).…”

“…For an overview of the hole argument and the sea of replies it has provoked, see Norton (2015). 18 It is worth flagging that no-shifts (and hence anti-haecceitism) is strictly stronger than what's required for those concerned only to rescue GR's determinism: only shifts that leave everything unchanged at some time need be eliminated to rescue determinism (see footnote 33 of Teitel (2019b)).…”

“…Again, similar remarks abound throughout the philosophical literature (including most of the works cited in footnote 14), and various other textbooks on GR (see, for example, Sachs & Wu (1977, 27)). 22 See Teitel (2019b) for a more careful definition, which I'll present in section 7 below. Modal definitions of determinism of this sort have been the standard in the literature at least since Lewis (1983) and Earman (1986a).…”

“…Thus even views according to which modal doctrines like anti-haecceitism are highly non-fundamental facts face exactly the same challenge: if there are facts about the modal profiles of particular objects, and those objects do not have super demanding modal essences, then given anti-haecceitism or noshifts such facts would seem to be inevitably arbitrary. The challenge thus arises for views that follow Fine (1994) in holding that modal doctrines like anti-haecceitism obtain in virtue of underlying essentialist doctrines (in this case the doctrine of sufficiency metric essentialism that I developed in Teitel (2019b)). Similarly, the challenge arises for views where all haecceitistic facts obtain wholly in virtue of qualitative facts (sometimes called grounding qualitativism or generalism), which nevertheless maintain that there are the relevant non-fundamental haecceitistic facts, and moreover are meant to imply antihaecceitism.…”