Abstract
This paper proposes an analysis of statements about universals according to which such statements assert nothing more than that the evidence we’d take to confirm them obtains, where this evidence is understood to consist solely of patterns in the behavior of particulars that cannot be explained by other regularities in the way things behave. On this analysis, to say that a universal exists is simply to say that there is such a pattern in the behavior of certain particulars, and for any predicate F that is presumed to correspond to a universal, to say that a particular is F is simply to say that its behavior exhibits a pattern of this sort. I argue that there is no theoretical work that we want postulations and ascriptions of universals to do that they’d be unfit for if analyzed in this way, and consequently that there is no reason to treat such statements as asserting anything more than what the proposed analysis suggests.
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Notes
The terms “pattern” and “regularity” are used interchangeably throughout. I’ll also speak interchangeably of the behavior of certain particulars as “exhibiting” or “manifesting” a regularity R, by which I mean merely that their behavior provides positive instances of R (or, alternatively, that if there were no particulars that behaved as the particulars whose behavior “exhibits” or “manifests” R do, we’d have no reason to believe that R exists).
A precedent for this view might be found in Alexander (1920, pp. 208–232), who similarly describes universals as “habits,” “laws,” “patterns,” or “plans of configuration” of space–time, and holds that “particulars are complexes of space–time and belong therefore to the same order or are of the same stuff as the universals which are plans of space–time.” Many thanks to an anonymous reviewer for bringing this to my attention.
Here I have in mind such examples as behaviorist and functionalist analyses of psychological statements in terms of stimuli and behavioral responses (Carnap 1932; Lewis 1972), analyses of statements about material objects in terms of sensory experiences or sense-data (Berkeley 1710/1982; Russell 1914; Ayer 1936, chap. 3), Hume’s (1748/2007) analysis of statements about causal relations in terms of constant conjunctions, and (more generally) empiricist analyses of statements containing theoretical terms in terms of the observational evidence on the basis of which such statements are made. While analyses of this sort have often been framed in terms of observational evidence, this is, I think, inessential to the general strategy at issue. I thus see no reason why non-observational knowledge couldn’t serve as evidence for certain types of statements which turn out to be analyzable in terms of that evidence. If my proposed analysis is sound, some of the patterns of behavior that statements about universals are to be analyzed in terms of may qualify as non-observational evidence of this sort.
This may sound like dispositional essentialism, but it’s not. I’ll explain why in Sect. 4.
Thanks to an anonymous reviewer for raising this issue.
The same may be true of jadeite and nephrite as well. If we can explain why all samples of jadeite share the distinguishing features of jadeite by means of more basic regularities in the behavior of their constituent particles that make no reference to jadeite, then we have no reason to postulate a universal of being jadeite either.
Note the implications this has for natural kinds like bosons, or mammals, whose membership includes such heterogenous entities as photons, gluons, and Higgs particles, or humans, whales, and bats. As with jade, I suggest that we treat such kinds as universals if and only if there is some basic regularity in the behavior of all and only their members. Otherwise we view them (like jade) merely as classes of particulars whose membership is defined by some cluster of features, each of which may or may not itself qualify as a universal, depending on whether there is a basic regularity in the behavior of all and only the things that possess that feature. Thanks to Donnchadh O'Conaill for raising this issue.
One might worry that statements about universals can’t be analyzed in terms of basic regularities in the behavior of particulars, because talk of ways of behaving is universals-talk, and as such is supposed to be subject to the proposed analysis. My “counter-worry” is that the same sort of objection might be raised against any analysis, for Paradox of Analysis-type reasons. For any analysis presents the kind of talk being analyzed as equivalent to the talk in terms of which it’s analyzed, so if the analysis is successful, then naturally the analysans-talk will be of the same sort as the analysandum-talk. Thus, since A + holds that statements about universals just are statements about basic ways that particulars behave, if A + is successful, then talk of basic ways of behaving is indeed universals-talk. To reject A + on these grounds would, however, seem to require that one reject the very possibility of analysis, for in any successful analysis, again, the talk being analyzed is shown by the analysis to be of the same sort as the talk in terms of which it’s analyzed. Thanks to an anonymous reviewer for raising this issue.
I’ll occasionally switch from the formal to the material mode like this, for ease of exposition. I stress, however, that A + is intended first and foremost as an analysis of statements about universals. It is a further question whether there are in fact universals whose nature corresponds to the content of our statements about them, as analyzed via A + . Advocates of A + thus have the option of holding that while A + explicates our concept of universals, there is nothing that answers to that concept (either because one thinks that there are no universals, or that universals exist but that our concept of them somehow misrepresents their nature). To this point, whenever I switch to the material mode and speak of A + as providing an analysis of universals, or as involving certain claims about the nature of universals, such talk should be understood as prefaced by the qualification “if universals exist and are such as our statements about them, analyzed according to A+, suggest…” Thanks to an anonymous reviewer for drawing my attention to this issue.
Classes here being understood as particulars that consist of (i.e. aren’t distinct from and are nothing over-and-above the sum of) their members.
A + might also give nominalists a way of distinguishing predicates that correspond to properties from predicates that don’t, or of distinguishing “perfectly natural” properties (or properties that play a role similar to that which Lewis (1983) assigns to such properties) from other properties. The first two conjuncts in the following translation could be put to this use, although nominalists who have no use for these distinctions could translate “x is F” simply as “x is one of the Fs”. More on this in Sect. 5.
This isn’t to say that nominalists can’t also view basic regularities as thick. Trope-theoretic forms of dispositional essentialism might thus be seen as combining trope nominalism with a thick conception of the regularities that tropes with dispositional essences give rise to (Molnar 2003; Heil 2003, pp. 111–125, 137–150; Whittle 2008). Insofar, however, as realist and trope-theoretic forms of dispositional essentialism distinguish the dispositional universals or tropes they posit from the regularities they give rise to, A + has the advantage of simplicity over them both. See footnote 18.
Realists (e.g. van Inwagen 2011) who are averse to such forms of realism might opt for a non-reductive, Platonic, relational (but still sparse) form of realism similar to the reductive form of realism described above by treating universals instead as abstract, non-spatiotemporal entities that are distinct from the basic regularities on the basis of which they’re postulated, but which are related to them in something like the way that Fregean propositions are related to the particular sentences that express them. In comparison with this non-reductive, Platonic, relational alternative, however, reductive realism has the advantage of greater simplicity and can I think avoid (or at least mitigate) the problems that van Inwagen (2011) raises for constituent realism, as mentioned below.
Thanks to an anonymous reviewer for pressing me on this point.
See Dretske (1977), Tooley (1977, pp. 668–671), Armstrong (1983, pp. 10–68), Carroll (1994, pp. 57–80), Bird (2007, pp. 81–90), Briggs (2009), Lange (2013), Demarest (2017, pp. 41–45), and Kimpton-Nye (2017, pp. 143–147). The topics of counterfactuals and nomological explanation are taken up in the following section. Regarding chances, since reductive realists distinguish thick regularities from the sum of their instances, if they treat a given thick regularity R as irreducibly probabilistic (so that, e.g., any particular that manifests R thereby has a 50% chance of being F), they can allow the frequencies found in the sum of R’s instances to deviate from the probabilities built into R itself (so it may turn out, e.g., that more or less than half of R’s instances are actually F). Nominalists of course have their own ways of allowing for such divergences between the chances and actual frequencies. Those dissatisfied with such stratagems may, however, find the reductive realist approach more appealing. The points mentioned in footnote 14 should be borne in mind here as well.
These considerations tell equally against the idea that we must postulate dispositional tropes in addition to the regularities in the behavior of the concrete particulars that possess or are constituted by them to explain why some regularities are manifested only by certain particulars. Rather than trying to explain this fact by postulating a class of perfectly resembling dispositional tropes that are only possessed by or constituents of those concrete particulars that exhibit a certain regularity (which simply raises the further question: why are these tropes only possessed by or constituents of these concrete particulars?), we can again simply take it as primitive that only these particulars behave in this way.
This isn’t compulsory; even those who view basic regularities as thick might deny that they’re laws. Mumford (2004) thus argues that while there are necessary connections in nature (and thus thick, non-Humean patterns in the behavior of particulars), there are nevertheless, strictly speaking, no laws of nature. Another option would be to treat laws as linguistic entities that describe certain regularities that have a special pragmatic status for us, e.g. as being particularly salient, or useful in making predictions and/or systematizing experience (Dorst 2019; Kimpton-Nye 2021). In this case, the basic regularities that reductive realists identify universals with would presumably qualify as more fundamental than the laws that (on this view) are descriptions of them, and reductive realism hence wouldn’t face the circularity worry raised above. While this may consequently be an easier route for reductive realists to take in their treatment of laws, I do want to consider how the position might be developed in tandem with a more realist conception of laws, according to which laws are language-independent regularities whose status as laws doesn’t depend on our pragmatic interests. Thanks to an anonymous reviewer for raising this issue.
Kimpton-Nye (2021) argues that a version of this circularity objection actually does arise for realist advocates of what he calls “Canonical Dispositional Essentialism” (e.g. Bird 2007), because they are committed to treating laws as constituting the essences of universals, while also using universals to explain laws. (See also Jaag (2014).) If so, then so much the better for reductive realism, as RDEists of this stripe then cannot claim any advantage over reductive realism on this score. Thanks to an anonymous reviewer for pointing this out.
I thus share Armstrong’s (1983, p. 162) view that “derived” laws are not genuine laws. (See footnote 26). Some may want to add further conditions that basic regularities must satisfy in order to qualify as laws (e.g. those associated with Best Systems accounts), in which case the following sentence should be modified accordingly.
Since these theorists speak in terms of properties instead of universals, I do the same in the next two paragraphs, to facilitate discussion of their views. This poses no problem, since A + is compatible with treating properties as either universals or classes of resembling particulars.
See also Demarest (2017, pp. 41–43).
Cohen and Callender (2009, pp. 6–8) would likely see this as an instance of what they call the “strategy of denial.” Their objections to this strategy, however, strike me as overestimating the likelihood of substantial underdetermination at the limit of inquiry, while also underrating the option of treating any packages remaining at that limit as notational variants.
What about the regularity that all emerires are grue? While this regularity can be explained by the fact that all emeralds are green and all sapphires blue, the latter regularities could in turn be explained by the fact that all emerires are grue and all sappheralds bleen. However, given again the broader network of laws that we know of (which imply, e.g., that organisms generally classify things with similar chemical compositions as being of the same type and things with very different chemical compositions as being of different types), the former regularities provide a better explanation of the latter, gruesome regularities than the other way around. One might construct gruesome parallels of these other laws as well, involving, e.g., different, appropriately gerrymandered criteria for what chemical compositions count as similar, and what counts as an organism’s classifying two things as being of the same type. At the point, however, where the resulting gruesome and non-gruesome packages of laws and universals each provides an equally good explanation of the other, it seems reasonable to treat the two packages as mere notational variants in the manner suggested above (Loewer 1996, p. 110).
We may also want to distinguish a class of regularities that are nomic but not laws; these would be regularities that can be explained in terms of basic regularities, but which could not fail to obtain in worlds with the same basic regularities as the actual world, regardless of what the initial conditions might be. The fact that all solid lumps of uranium are less than 1 mile3 in volume might be an example.
Reductive realism may seem better able to assign this kind of modal force to statements about laws than the nominalist version of A + , since (in contrast to the latter) it treats the basic regularities that statements about laws are based on as thick. Those who adopt the nominalist version of A + might hold, however, that to say that non-G Fs are impossible is merely to say that unlike a solid lump of gold greater than 1 mile3 in volume, there could be no non-G F unless some basic regularity were violated, which is compatible with claiming that all regularities are merely thin.
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Acknowledgements
Many thanks to two anonymous reviewers for their insightful comments, and to participants in the 2019 PHYSIS Conference on The Problem of Universals for their helpful feedback on an early version of this paper. Special thanks also to Jim Levine for a conversation that provided the initial impetus for this paper, and to Alison Fernandes for several conversations that were extremely helpful in clarifying my thoughts on these issues, and (for me, at least) highly enjoyable as well.
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White, B. A reductive analysis of statements about universals. Synthese 200, 22 (2022). https://doi.org/10.1007/s11229-022-03573-6
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DOI: https://doi.org/10.1007/s11229-022-03573-6