Monism and heterogeneity: a plural grounding solution

ABSTRACT

Priority monism has been criticised on the grounds that monists cannot give an informative story about how the world is heterogeneous: how can there be qualitative variation in the world, given we cannot explain the world’s qualitative variation in terms of its proper parts? I will argue that none of the traditional solutions to this problem are plausible, and instead argue that we should hold that what accounts for the world’s heterogeneity is that the Cosmos is identical to the collective plurality of all the world’s tropes, and each individual trope, in the plurality, is non-distributively grounded in the plurality/bundle of all the world’s tropes. I go onto note that as well as providing a solution to the monistic problem of heterogeneity, this view – which I call (PUT) – could well be a promising trope bundle theory in its own right.

KEYWORDS:

• Priority monism
• heterogeneity
• plural grounding
• trope bundle theory

Acknowledgements

The author is sincerely grateful to Matthew Tugby and Giacomo Giannini for providing helpful feedback. The author is also grateful to the AHRC for providing me with a NBDTP scholarship which helped make this research possible during the author’s PhD.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Such pluralists, then, subscribe to what Schaffer (2010a, 44) denotes as ‘Atomism’: x is a fundamental object iff x is a mereological simple.

2 There is another version of monism, however, in which only one object exists: existence monism. Existence monism entails priority monism (i.e. as only one object is fundamental if only one exists), but not vice versa (Schaffer 2010a, 66). Much of what I have to say in this paper also applies to existence monism, but my intention in writing this paper is to formulate a solution to the problem of heterogeneity which serves as a solution for the priority monist.

3 Though to be precise, it is Sider’s (2007) statespace objection that McDaniel is concerned here with, in particular, as opposed to the more general problem of heterogeneity. I shall look at Sider’s statespace worry later on in the paper.

4 It should be mentioned that other problems raised against priority monism, such as the possibility of junk (Bohn 2012) and island universes (Baron and Tallant 2016), will be not considered in this paper. The task of this paper is to provide a novel solution to the problem of heterogeneity for monism, and not to argue against any possible objection to monism, in general. I do, however, recommend my paper in Analytic Philosophy (Taylor 2021) for anyone interested in how a monist could attempt to get round the problem of junk.

5 This is the same conception of ground had by Jonathan Schaffer (2016). Other authors, however, think that grounding is either a relation which holds between facts (i.e. Rosen 2010) or is a sentential operator (i.e. Fine 2012). If the reader is of the view that one of these other conceptions of ground is correct they are free to try and define my use of grounding in terms of their own.

6 A referee at another journal, however, claimed this isn’t necessarily the case if we think that (i) the Cosmos grounds its parts is a case of entity-grounding, and (ii) the Cosmos has a particular qualitative nature because its parts are such and such is a case of fact-grounding. Accepting (ii), then, would not entail the Cosmos is grounded in its parts. I am not convinced by this move, however, given that I think that grounding is needed to underwrite metaphysical explanation. If facts about the Cosmos’ qualitative nature can be explained by facts about its parts, then those parts must ground the Cosmos itself.

7 Sider also raises two other objection to monism: one from ‘haecceistic’ possibilities and the other from the monist’s inability to utilise Lewis’ (1986) account of intrinsic properties. Sider’s objection from haecceistic possibilities is similar to the statespace objection and can be dealt with by (PUT) in the same way it deals with the statespace objection, so I will not look at it in any detail in the main text. As for the objection from intrinsicality, Sider is right, but it should be noted that Lewis’ naturalness account of intrinsicality is controversial (see Marshall (2012)) and Kelly Trogdon (2009) has attempted to devise an account of intrinsicality which is compatible with both priority monism and priority pluralism. Indeed, it might turn out that we cannot give any plausible reductive account of what intrinsic property is; the notion of an intrinsic property might well be primitive (see Skiles (2014)).

8 See Johnston and Forbes (1987, 127–129), though Johnston utilizes adverbial properties to solve the problem of temporary as opposed to spatial intrinsics.

9 It might be thought my complaint here can be resisted by some adverbialists such as Haslanger (1989), who (unlike Johnston) deny that property instantiation for continuants is a three-place relation involving objects, properties, and times/spacetime regions. This is not so, as Haslanger still thinks that ‘x is red t₁-ly’ amounts to x having that property at time t, even though the relation between properties and their bearers does not involve a three-place relation. In which case, the Cosmos being ‘red R₁-ly’ means it will have that property relative to a proper subregion of the region it occupies.

10 Sider (2007, 3) presumes anti-haecceitism is false here, otherwise the statespace will have fewer members than this. If anti-haecceitism is true, though, this will make no real change to Sider’s objection here.

11 Sider claims the monist cannot explain the statespace’s structure, given they cannot appeal to the natural groupings amongst the pixels. However, following Cornell (2013), the monist – who utilizes distributional properties – could just hold that the global distributional properties the Cosmos could themselves instantiate higher-order properties. We could say, for instance, that in any world where only one pixel is lit, the Cosmos instantiates a distributional property which has a distribution ratio of 15:1 of off-ness to on-ness. It is that each of these distributional properties have this distribution ratio which accounts for why the statespace members – they correspond to – ‘go together’.

12 This is why I think, then, that Cornell’s (2013) reply to Sider is unsuccessful. Cornell holds that the pluralist explanation for the statespace size is just as brute as the monist’s, as ‘if one were to ask the pluralist why there are 16 pixels at the Screenworld  … there would be no informative answer forthcoming – that is just the way the world is’ (2013, 233). Both views have brute facts. What is important, Cornell claims, is that providing we know how many objects there are in a world and what properties they can instantiate, we can derive the statespace size. But there is a difference here between the monist and the pluralist. Suppose the monist argues that the Cosmos instantiates a single global distributional property in Screenworld which guarantees that only two pixels are on. Then, as mentioned above, how does the instantiation of such a property account for the other potential states the Cosmos could be in? We just, it seems, have to hold it’s a brute fact there are (2¹⁶–1) other states the Cosmos could be in. By contrast, the pluralist can explain that it could have been in other states than it was via a combinatorial account of the pixels and their intrinsic properties, which explains why there are 2¹⁶ statespace members. The pluralist can entirely account for the statespace size via the pixels and properties they actually instantiate, while the monist is forced to appeal to properties it could hypothetically instantiate, but which it does not. That the Cosmos could have instantiated those other distributional properties is not entailed by any distributional property it presently instantiates and is thus a brute fact. So, I do not think that Cornell’s suggestion can save the monist who utilises distributional properties. The monist’s explanation is clearly inferior.

13 Jacek Brzozowski (2016) has also argued, for similar reasons, that monists who appeal to GDPs may potentially have to rule out the possibility of gunk.

14 Again, a similar concern about monism and GDPs is also raised by Brzozowski (2016). Brzozowski is concerned that if the world’s qualitative facts are explained by some maximally specific GDP, the monist will have to take it is a brute fact that higher-level qualitative facts generally supervene on lower-level qualitative facts (i.e. why does something which has two proper parts which each have a mass of two grams, must have a mass of four grams?).

15 I, therefore, endorse trope bundle theory: that material objects are to be metaphysically identified with bundles of tropes. To be a material object is to be a bundle of tropes. It might be thought that accepting bundle theory goes against priority monism, as what would be fundamental would be the Cosmos’ tropes rather than the Cosmos itself. Once I have properly outlined (PUT), however, it will be clear that (PUT) is compatible with and is in the spirit of monism.

16 See Dasgupta (2013) for arguments in favour of comparativism about quantity. One notable reason that Dasgupta favours comparativism is that he thinks that if facts about quantity were fundamental, then they would be epistemically inaccessible.

17 To quote Dasgupta (2014, 17), ‘let K be the set of all kilogram facts and R be set of all fundamental facts about mass relations, and then say that the members of K are plurally grounded in the members of R even though no member of K is grounded in any subset of R. Call this a structuralist view of kilograms, since an explanation of any kilogram fact is … inevitably an explanation of them all’.

18 These include Dasgupta’s view that the world is fundamentally qualitative (2009; 2014, 5–15), as well as mathematical structuralism (Litland 2016, 536–537).

19 For instance, both Saucedo (MS) and myself (Taylor 2021) have elsewhere argued that every object in the world is collectively, though not distributively, fundamental.

20 As alluded to in the main text, this of course puts me in tension with many traditional trope bundle theorists, such as Campbell (1990), who take each of the fundamental tropes to be explanatorily basic. But so what? The plural universal theory is supposed to be different from traditional bundle theory, just as Peter Simons (1994) intended for his nuclear theory of tropes to be distinct from traditional bundle theory. If it was not different in some way, how could I claim it had any advantage over traditional bundle theory in respect to solving the monistic problem of heterogeneity and in explaining bundling?

21 Unlike Dasgupta, then, I do not deny ‘Distributive Grounded’ in proposing this solution: each trope is individually grounded, unlike quantities on Dasgupta’s comparativist view.

22 Crucially, this will also include whatever tropes account for whether we have an ‘on’ or an ‘off’ pixel trope, so the base of the statespace size will necessarily follow from what the identity of the universal trope plurality is.

23 Following up on footnote fifteen, this is why I believe (PUT) is perfectly compatible with monism: both in letter and in spirit. In accepting trope bundle theory, one accepts that material objects are bundles of tropes. Now as previously mentioned, traditional bundle theorists typically think that the tropes distributively are ontologically prior to the objects they are collectively identical to, but on (PUT) the order of dependence is the other way round: each trope in the world is grounded in the world bundle that is identical to the Cosmos. According to (PUT), there is only one fundamental object, the Cosmos; it’s just that this object is also a bundle of tropes as well as being a material object. Being a priority monist does not mean that one must think that material objects cannot be bundles of properties (as Schaffer himself would acknowledge (2010b, fn. 3)).

24 Why should one suppose the ‘world bundle’ fixes the location of each trope? Suppose some soldiers surround a castle. The soldiers collectively occupy a fusion of distinct space-time regions. If we know the regions the soldiers occupy collectively, then it obviously follows we know each region they occupy distributively. Their collective location determines their distributive location. Also consider Nikk Effingham’s (2015) view that properties are located at the fusion of every region its instances are located at. On such a view, the location of any property will determine where each of its instances are located. If someone, however, is still not convinced that the world bundle will fix the location of each trope, then we can either hold that the bundle is a plurality of spatiotemporally indexed tropes or that perdurantism is true, and thus the world bundle will consist of tropes of spatiotemporal stages. The world bundle being identical to the collective plurality of such tropes will then settle where every individual trope is.

25 For a discussion of trope bundle theories and Bradley’s regress, see Maurin (2010).

26 Not only would this be parsimonious, but it meets Benovsky’s (2008) challenge on how to differentiate trope bundle theory from substratum trope theory. Benovsky claims there is no reason to prefer one from the other, as both involve a primitive unifying device which binds tropes together to make objects. But according to (PUT), there is no need for any kind of unifying device at all. If the world bundle is prior to its individual tropes, the question of what binds the tropes together to make bundles never arises.