Armstrong on thespatio-temporality of universals 1

¹My thanks to Evan Fales, Richard Fumerton, and Franz-Peter Griesmaier for their helpful comments on the issues discussed in this paper.

Abstract

Provocatively, David Armstrong's properties are supposed to be both universals and spatio-temporal. What does this amount to? I consider four of Armstrong's views, in order of ascending plausibility: (1) the exemplification account, on which universals are exemplified by space-times; (2) the location account, on which universals are located at space-times; (3) the first constituent account, on which spatio-temporal relations are elements of what I call the form of time; and, the true view, (4) the second constituent account, on which universals are spatio-temporal only ‘derivatively’ by being constituents of states of affairs which are so ‘primarily’. The first two accounts are rejected because they entail that space-times must be substantival. In making plausible the second constituent account, I distinguish primitive and derivative spatio-temporality. Something is primitively spatio-temporal when it is at a space-time, or stands in spatio-temporal relations. Something is derivatively spatio-temporal when it is a constituent of something primitively spatio-temporal.

Notes

²It is common to understand immanent realism as requiring the thesis that universals are spatio-temporally located; see O'Leary-Hawthorne and Cover 1998: 205], for example. In part because this is the very thesis to be investigated, I do not include it in the definition of the view.

¹My thanks to Evan Fales, Richard Fumerton, and Franz-Peter Griesmaier for their helpful comments on the issues discussed in this paper.

³Not necessarily a thin particular: since he accepts second-order universals, Armstrong also thinks there are states of affairs that only involve universals 1978a: 115n.].

⁴In accordance with his four-dimensionalism, Armstrong thinks of p₁t₁ as the aggregate of all the spatio-temporal locations of each of the persisting entity's stages 1978a: 118]. To simplify, suppose p₁t₁ is the spatial cum temporal position of just one stage.

⁵Armstrong tentatively accepts the principle of order invariance, according to which if a universal is exemplified by something of order n, it is only exemplified by things of order n 1978b: 142]. Since he also accepts second-order universals, he cannot hold that all universals are spatio-temporal by being exemplified by space-times. This is because the entities that exemplify those second-order universals are not held to be thin particulars. This is a limitation on naturalism, but not one I will dwell on.

⁶Compare Aune 1984: 165 – 6]. Note that Armstrong later rejects this reduction of thin particulars to space-time positions 1997: 109]. His reasons are different from mine: he worries that some particulars might not be spatio-temporal, that diverse particulars might interpenetrate, and that a single particular might be at more than one space-time.

⁷Tweedale has a similar complaint, although he does not stress the connection to substantivalism 1984: 179 – 82]. I assume also that substantivalism and relationism are exhaustive and mutually exclusive options. My arguments are directed toward the possibility of combining Armstrong's view with relationism.

⁸Accordingly, in what follows ‘space-times’ means the same as ‘space-time locations’.

⁹The context implies that this is the spatio-temporal ‘wherever’.

¹⁰Armstrong has also changed his mind on this account 1997: 138], although in a nuanced way. Maybe even if universals ‘cannot be located’, he claims, still the ‘truths of location in space and time’ could be provided by a world of particulars with universal properties [ibid.]. Somehow, that universals lack location and yet that universals are not apart from space-time are supposed to be different vocabularies to describe a single reality [ibid.: 137].

¹¹The location and exemplification accounts would be equivalent if to be located at a space-time just is to be exemplified by it. Dainton 2001: 140] explores such a version of substantivalism about space. Thanks to Evan Fales for bringing this possibility to my attention.

¹²Chisholm's distinction concerns states of affairs rather than universals. Also, this is somewhat misleading as an interpretation of Chisholm: On his view, ‘the first occurrence of X’ is no more a designating expression than ‘the average baseball fan’. The former expression is contextually defined by sentences that correspond to situations in which X has relations to unique entities. Pursuing Chisholm's proposal more strictly would avoid the problem I mention, though it would raise different ones.

¹³Again, I take this to be the spatio-temporal ‘where’.

¹⁴In the following I consider mainly temporal rather than spatio-temporal features. This is in part because I do not accept the framework of inseparable spatial cum temporal relations.

¹⁵Suppose a state of affairs A is a constituent of a primitively spatio-temporal state of affairs B. The first clause allows that A may also be primitively spatio-temporal.

¹⁶A relation R is divisible if it follows from x having R to y that the constituents of x have R to y.