Metaphysics of States of Affairs: Truthmaking, Universals, and a Farewell to Bradley’s Regress

By Bo R. Meinertsen

This book addresses the metaphysics of Armstrongian states of affairs, i.e. instantiations of naturalist universals by particulars. The author argues that states of affairs are the best candidate for truthmakers and, in the spirit of logical atomism, that we need no molecular truthmakers for positive truths. In the book's context, this has the pleasing result that there are no molecular states of affairs. Following this account of truthmaking, the author first shows that the particulars in (first-order) states of affairs are bare particulars. He then argues that the properties in states of affairs are simple, non-relational and concrete universals. Next, he argues that (material) relations in states of affairs are external relations. Lastly, he argues that a state of affairs is unified by a distinctive formal relation without giving rise to Bradley’s regress. Written in a relatively non-technical style, the book offers a valuable resource for philosophers working on analytic metaphysics and ontology, as well as their graduate students.

• Language: English
• Publisher: Springer
• Release date: Apr 6, 2019
• ISBN: 9789811330681

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© Springer Nature Singapore Pte Ltd. 2018

Bo R. MeinertsenMetaphysics of States of AffairsPhilosophical Studies Series136https://doi.org/10.1007/978-981-13-3068-1_1

1. Introduction

Bo R. Meinertsen¹ 

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Department of Philosophy, Tongji University, Shanghai, China

1.1 A State of Affairs Ontology

States of affairs are unified complexes that are instantiations of properties or relations by particulars.¹, ² This raises the following questions. (1) Which ontological role(s) do states of affairs play? (2) What are the particulars in states of affairs? (3) What are the properties in states of affairs? (4) What are the relations in states of affairs? (5) How are particulars and properties (or relations) unified into the complexes that are states of affairs? (This is what I call the problem of unity). This work attempts to answer these questions, as follows: (i) states of affairs play the ontological role of being truthmakers (which, as I shall argue in Sect. 2.​1, subsumes other ontological roles they may play); (ii) the particulars in states of affairs are bare particulars; (iii) the properties in states of affairs are simple universals; (iv) the relations in states of affairs are external relations (polyadic universals, which, by implication, arguably are also simple); and (v) a state of affairs is unified by a constituent formal relation (or ‘relation’) that relates itself to the other constituents of the state of affairs. A full explanation of what this means, and what motivates it, can of course only be provided by this work as a whole. First, however, I shall describe my approach, and state my main assumptions and restrictions.³

1.2 Approach, Assumptions and Restrictions

1.2.1 Approach

The philosopher who has inspired me most for this work is David Armstrong in his middle-period (late 1970s to late 1990s), especially his A World of States of Affairs (1997). But whereas Armstrong in that book applies the notion of states of affairs to a whole range of other metaphysical topics, such as causation, laws, modality, number, classes, and ‘the world’ (‘the unity of the world’), he says comparatively little about states of affairs ‘in themselves’. My aim is largely, although not exclusively, the converse: to focus on states of affairs in themselves, rather than attempting to employ them in ‘external’ areas. This I do especially in Part II, where I look closer at the constituents of states of affairs, and next in Part III, where I examine how these constituents come together to form states affairs. There is already a vast literature on the questions of Part II, but it is more moderate for Part III. William Vallicella (e.g. 2000, 2002a, b) is a prominent exception and, as will be clear from the discussion, I am deeply indebted to him. Related to these goals, I have no intention of making grand claims about ‘the world'. In particular, I shall not make any pronouncement on whether or not ‘the world is a world of states of affairs', which Armstrong describes as ‘the hypothesis' of his 1997 book. This is an interesting hypothesis, but it is not one that I need to have a view on for my purposes here.

However, methodologically I share two important things with Armstrong, again especially his (1997): (i) I am not doing ontology in a logically or semantically oriented way, and (ii) I attempt to address many issues, even in a relatively limited space. As a natural consequence, my level of precision often is not higher than Armstrong’s. There are, however, several areas where I have had ambitions of being more precise than him. One of these is extraordinarily important, and, as I shall make clear below (Sect. 1.3), it is a central point where Armstrong is too loose.

1.2.2 Assumptions

Many of the assumptions and restrictions of this work are best stated along the way, in the relevant chapters. However, it will be useful to mention some of them here.

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The theory of universals

The problem of universals is the problem of accounting for the apparent commonality of repeatables or ‘features’ (as properties and relations in a pre-theoretical sense are often called). It is a both very common and natural view that states of affairs in my sense go hand in hand with realism (universal-realism, the theory of universals) as a solution to this problem, such that repeatables are the monadic and polyadic universals of realism (in some appropriate version). This is also my own view. However, I have not actually stipulated that this is the case. It seems logically possible that (some sort of) state of affairs ontology can be combined with another ontology of properties and relations than realism, although the result would be very odd and highly implausible. The two general ontologies I consider the main rivals of state of affairs ontology, trope theory (sometimes called ‘moderate nominalism’) and Donald Mertz’s rather kindred moderate realism, prima facie also provide ontologies of properties and relations, and could as such perhaps supply the properties and relations needed by (some sort of) state of affairs ontology. I shall not consider either theory in this respect, as the problem of universals does not belong to our purposes (see below). However, since, as I shall argue, both theories fail (in our context) independently of this problem, they ipso facto fail as ontologies of properties and relations. It is an assumption of this work that the only viable alternative for a solution to the problem of universals is realism. Consequently, given the mentioned failures, the properties and relations in states of affairs are universals.

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The Principle of Spatiotemporally Homogenous Composition

For want of a better term, this is what I call the principle that no complex (of the kind I shall in Sect. 1.3 below call ‘non-mereological’) can have both concrete and abstract constituents. Since states of affairs are such complexes and the particulars in (physical) states of affairs by definition are concrete, it immediately follows that no universal in a state of affairs is abstract. This is why I shall in Chap. 8 defend the view that universals in states of affairs are concrete. This is an important constraint on states of affairs, and I find it has support in spatiotemporal intuitions. It is perhaps also congenial to Simons’s strong opposition to ‘transcategorial wholes’ (2009), though that sentiment rules out far too much. In particular, it rules out states of affairs, since they are by definition made up of entities from different categories. But with regard to one respect (spacetime), I do share with Simons the intuition that there is something horrid about a whole with two entities that are categorially very different. Of course, we could have obtained the thesis that no universal in a state of affairs is abstract in at least two different ways. On the one hand, it would also follow from assuming naturalism, in the sense of an ontology that denies the existence of any abstract entities. I happen to be of a naturalist bent, but since assuming the Principle of Spatiotemporally Homogenous Composition is metaphysically ‘lighter’ than assuming naturalism, I prefer the former. On the other hand, it could also—trivially—be obtained by just assuming the thesis itself. This I do not wish to do either. For the most common view is that universals are abstract, whereas Spatiotemporally Homogenous Composition seems intuitive, and ought to seem plausible even to those who believe universals are abstract.

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Foundationism

This assumption concerns mainly Chap. 7, but is so fundamental that I prefer to mention it already here. In the Metaphysics, Aristotle famously said that relations are ‘least of all things a kind of entity or substance’ (1088a 22), and as is well known, during most of its history, Western philosophy reflected this inhospitality to relations. Foundationism is the congenial but harsher view that relations are not just to be downgraded, but that they are in some sense eliminable by being reducible to certain properties (‘foundations’) of their relata—a view which may go even further back than Aristotle (viz. to Plato’s Philebus). I shall assume that Russell, in The Principles of Mathematics, showed that this view is false.⁴ This assumption has two consequences for the present work. The first and relatively unimportant one is this. In Chap. 7, I shall myself argue that some relations are reducible in the weak sense I call ‘TM-reducible’, but in accordance with the present assumption that foundationism is false, I assume that these relations are not in addition reducible in the foundationist’s strong sense. The second and very important consequence is this. In Chap. 7, I shall also argue that some relations are what I call ‘TM-irreducible’, and again I assume that none of them is reducible in the foundationist’s strong sense. The reason this is very important is that in my view it is these, and only these, relations whose instantiations are polyadic states of affairs. But if they were reducible in the foundationist’s sense, despite not being TM-reducible, this could obviously not be the case: nothing, or at least nothing ontologically important, can be an instantiation of something eliminable.

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Lewis’s Razor

‘Lewis’s Razor’ is the principle of qualitative ontological economy that of two competing theories that explain the explananda equally well, we should choose the one that requires the smallest number of ontological categories, kinds or types (cf. Lewis, 1973, p. 87; and cf. Rodriguez-Pereyra 2002, pp. 204–7). The notions of ‘competing theories’, ‘explain’, ‘explananda’, and ‘ontological categories, kinds, or types’ can for our purposes be taken in an intuitive sense, which, I hope, accords with the individual cases where I shall invoke Lewis’s Razor. (Only at one unrelated point in the book, in Chap. 8, shall I appeal to a particular, ‘thick’ notion of ‘ontological category’). Consider an example. In the next chapter, I shall argue that (1) disjunctive truths can be made true without disjunctive truthmakers. But, by definition, (2) disjunctive truths can also be made true with disjunctive truthmakers. (1) and (2) explain the explanandum (disjunctive truths) equally well; (1) does not require the ‘ontological category, kind, or type’ of disjunctive truthmakers; hence, we should choose (1). Strictly speaking, it of course does not follow from Lewis’s Razor that what it tells us to choose is actually not just preferable, but also true, and that what it tells us to discard is not just worse, but also false. However, for pragmatic purposes, so to speak, which include ‘seeking the truth’, we can pretend that this is so.

Lewis’s Razor contrasts with Ockham’s Razor, which can be construed as a principle of quantitative ontological economy concerning the number of ‘tokens’ postulated by competing theories. Since I am uncertain about the status of this principle and since I shall only (briefly) invoke it at two points—in Chap. 4, in particular, on behalf of Mertz—it is not one of the assumptions to be stated here.

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Toy examples

I shall follow the common habit in the literature of using as examples of states of affairs instantiations of properties that are not ontologically fundamental, such as secondary qualities. Moreover, many examples cited in the literature are determinables (e.g. length and mass) whose existence is controversial, even if the existence of their determinates (e.g. 1.52 m and 9.82 kg) is not. This practice I shall follow too. A frequent type of example is colours, which are of course secondary qualities, and mostly it is their determinables that are mentioned, e.g. redness and blueness. However, it is convenient to pretend that such examples are ontologically fundamental properties, and nothing important for our purposes turns on it. A common type of examples of the particulars in states of affairs, physical, mid-sized objects of everyday experience, such as balls and chairs, are arguably not ontologically fundamental either, but, again, nothing important for our purposes depends on that.

1.2.3 Restrictions

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The problem of universals

In addition to the above assumption that the only alternatives to realism (in a version suitable for state of affairs ontology) as a solution to the problem of universals are trope theory and moderate realism, I shall not consider how any of them deals with this problem (except at most in passing). In other words, the problem of universals simply falls outside the scope of this work. Thus, my examination, and rejection, of trope theory and moderate realism in Chaps. 3 and 4, respectively, are, as I said above, independent of the problem of universals.

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Physical states of affairs

I shall consider only physical states of affairs, i.e. instantiations of physical properties and relations by physical particulars, such as the ball’s being white and Edinburgh’s being north of London. However, much of what I say is, I hope, so general that it applies, mutatis mutandis, to non-physical state of affairs.

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Contingent states of affairs

Perhaps every physical state of affairs is contingent, such that this restriction follows from (b). In any case, the states of affairs I shall consider are contingent, and so are the truths they make true. This, of course, does not rule out considering apparently necessary states of affairs in order to argue that this appearance is deceptive. This, for example, is what I shall do in Sect. 7.​1 when examining internal relations, whose ‘instantiations’ are not states of affairs.

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Time

Ignoring time is very common in the literature that is most relevant to state of affairs ontology. For instance, a monadic state of affairs is typically identified with the instantiation of a property F by a particular a, i.e. a’s being F, but this of course ignores that (contingent) particulars only instantiate properties at specific times. To accommodate time, state of affairs ontology would have to be extended, in a way that accords with the right philosophy of time (and existence in time). There are several options in this difficult area of philosophy, which would affect state of affairs ontology in different ways, but here I shall only sketch how the question of endurantism versus perdurantism perhaps would do this. If endurantism is true, times may well be constituents of states of affairs, such that a monadic state of affairs would have the form of a’s being F at t, where t is a time. If the more controversial perdurantism is true, it may instead be that the particulars in states of affairs are temporal parts, such that a monadic state of affairs would have the form at’s being F, where at is a temporal part of a. Similarly for polyadic states of affairs on either view. In any case, the state of affairs ontology of this book aims to be neutral with regard to these issues.⁵

1.3 The Main Problem of State of Affairs Ontology: Initial Thoughts

The problem of unity, i.e. how to account for the unity of a state of affairs (how its constituents are unified into it), is in my view the main problem of state of affairs ontology. Other proponents of states of affairs, notably William Vallicella (e.g. 2000, 2002b), likewise consider the problem of unity to occupy centre stage of the ontological investigations into states of affairs. And Donald Mertz (Chap. 4) rightly views his counterpart of the problem to be at the heart of his moderate realism. As we shall see below (Sect. 1.5), Arianna Betti (2015) also considers it to be central to states of affairs, although she claims to dissolve it as part of her rejection of them.

Indeed, if the problem of unity cannot be solved, states of affairs seem to be impossible entities, such that state of affairs ontology seems to be completely untenable. Although this is the topic of Part III, it will be helpful to have an initial sketch of it already here, as this enables us to explicate one of the most fundamental features of states of affairs. Since states of affairs are complexes, to account for the unity of a state of affairs is to account for the unity of a complex. To account for the unity of a complex is, roughly, to account for why it is one entity (Latin: unus). Why is this such a serious problem that I consider it the main problem of state of affairs ontology? The reason has to do with states of affairs having non-mereological existence conditions. What this means can be seen from the following. Call the ordinary, uncontroversial constituents of a state of affairs its ‘material constituents’ (as opposed to its ‘formal constituents’, if any), e.g. a, b, and R of the state of affairs R(a, b). The mere existence of the material constituents of a state of affairs does not entail the existence of the state of affairs. For if, to take a monadic example, (i) a is F, and (ii) a distinct particular b is G, and (iii) a is not G, then a and G coexist, but a is not G. Since a and G coexist, the (mereological) sum of them exists, but since a is not G, a’s being G does not exist. Similarly in other cases. Because of this difference in existence conditions between sums and states of affairs, I shall say that states of affairs are ‘non-mereological complexes’ and that sums are ‘mereological complexes’. I am leaving open the possibilities that some non-mereological complexes are not states of affairs—although I doubt it, pace Betti (2015)—and that some mereological complexes are not sums.⁶ It should come as no surprise that states of affairs also have non-mereological identity conditions, though we cannot consider this until much later (Sect. 7.​3.​2) when we have examined the topic of relations.

In thus contrasting the existence conditions of a sum with those of a state of affairs, I have assumed for the constituents of states of affairs something like David Lewis’s Principle of Unrestricted Composition, a thesis he describes as follows: ‘[W]henever there are some things, no matter how many or how unrelated or disparate in character they may be, they have a mereological [sum]’ (1991, p. 7). In line with what is mostly assumed in the literature, I shall take it that mereological sums have metaphysically unproblematic existence conditions (though this assumption has been questioned by Perovic 2014). It should be noted, however, that it is not inconsistent to affirm the existence of any number of entities E1, …, En and simultaneously deny the existence of the sum of them. A sum of E1, …, En is an item in addition to E1, …, En. True, denying the existence of the sum contradicts the Principle of Unrestricted Composition, but this principle is not a logical truth. What cannot be denied without contradiction when affirming the existence of E1, …, En is the plurality of them, since in affirming the existence of E1, …, En one ipso facto asserts this plurality, as they are this plurality (Simons 2003, p. 241). So the existence conditions of states of affairs of course are not only non-mereological, but also ‘non-plurality-like’. Might I have made illuminating use of this in characterizing the existence conditions of states of affairs? I think not. For firstly, speaking of complexes with ‘non-plurality-like’ existence conditions would be too coarse: it would group non-mereological complexes together with the mereological ones, given that the latter also have ‘non-plurality-like’ existence conditions. Secondly, and more importantly, since pluralities in the present sense are not complexes at all, it would be very confusing to speak of a ‘non-plurality-like’ complex.

One of the assumptions of this approach to states of affairs is that they are complexes composed of their constituents. Such an approach is sometimes called ‘constituent ontological’ or ‘compositional’ (Bynoe 2011). Armstrong favoured this approach in his middle period, but even then had doubts about it. He at the same time endorsed an incompatible view of universals and particulars being ‘abstractions’ from states of affairs. Eventually, he abandoned states of affairs (in our sense) concomitant with endorsing a ‘Leibnizian’ conception of apparently contingent predication as in fact necessary (2004). Adopting such a position might be the last resort if the problems of unity and Bradley’s regress are insurmountable. In any case, as I shall argue in Chaps. 9 and 10, they are not. However, readers who are skeptical about states of affairs might think they face a number of other important problems so that it therefore would be imprudent to focus so much on the problem of unity. In a thicker book than the present one, I could perhaps deal with all of these problems (for discussion of several of them, see e.g. Simons 2009; Butchvarov 2010; Betti 2015). At any rate, in the present one, it is not my job.

Returning to the problem of unity, as mentioned, the fact that it is so central is closely related to the non-mereological existence conditions of states of affairs. The seriousness of the problem is partly a result of these very existence conditions. Here I shall only give a prima facie reason for this: while mereological complexes exist ‘automatically’ given the existence of other entities (those that happen to be their ‘constituents’), such that any one of them exists ‘automatically’ given these entities, something more is needed for any one state of affairs to exist. As implied by my abovementioned answer to the problem of unity, I believe it is the relating of a unique relation that is needed.

The problem of unity is a cousin of what is often called the ‘problem of instantiation’. On one definition, the latter is, roughly, the problem of how particulars can possess properties (or relations)—given that neither are just bundles or aggregates of each other.⁷ More specifically, in our context, it is the problem of how particulars have properties in virtue of standing in the relation of instantiation to them. However, this problem is more specific than the problem of unity. For there are perhaps serious issues pertaining to instantiation, such as the fact that it is asymmetrical (or non-symmetrical), which are not essentially part of accounting for the unity of states of affairs.⁸ In any case, my aim is only to solve the problem of unity.

Incidentally, the problem of how to avoid Bradley’s regress—call it the problem of Bradley’s regress—is related to the problem of instantiation in an analogous way to how it is related to the problem of unity. But is seems preferable to formulate Bradley’s regress only in the context of the problem of unity, since for reasons I shall not go into here, the problem of unity is more fundamental than the problem of instantiation. Besides, everything I say regarding the regress in relation to the problem of unity applies, mutatis mutandis, to the regress in relation to the problem of instantiation. In any case, while the problem of unity and the problem of Bradley’s regress are closely related, they are different. This is something Chaps. 9 and 10 will demonstrate. Yet the two problems have often been mixed up, even by prominent philosophers. As Vallicella (2004, p. 163), who thinks Bradley himself did not make this mistake, eloquently puts it: ‘A regress-blocker is not eo ipso a unity-grounder, pace Russell, Alexander, Blanshard, Grossmann, et al.’

I mentioned above that there is a central point where Armstrong is too loose. This is it. Firstly, he is vague in the formulation of the problem of unity (which his state of affairs ontology faces just as much as mine): he describes it as the problem of how ‘to bind together the constituents of a state of affairs’ (1997, p. 119), and never gives a more precise formulation. Secondly, he is too loose in his attempt at solving the problem. Here he actually vacillates between two views. The first one is this. He says that ‘there is no relation of instantiation over and above the states of affairs themselves.’, that ‘[s]tates of affairs hold their constituents together’ (ibid., p. 118), and that ‘there is no call to bind together the constituents of a state of affairs by anything beyond the state of affairs itself. The instantiation of universals by particulars is just the state of affairs itself’ (ibid., p 119). This I shall interpret, not as the view that a state of affairs unifies itself (cf. my rejection of TM-irreducible reflexive relations in Sect. 7.​4), but as the view that states of affairs are unified primitively, a view that obviously should only be a last resort. His second attempt at a solution is the following. With inspiration from Frege, he construes universals as ‘unsaturated’ entities, e.g. _F, _G, _H, and R(_, _), R(_, _, _), which are ‘saturated’ by the particulars that instantiate them, thereby resulting in state of affairs. However, this obviously only displaces the problem of unity to the problem of what this ‘saturation’ consists in, and the latter he does not answer. Worse, he does not even provide a non-metaphorical counterpart of the notion of ‘saturation’.⁹ All he says about it are things like this: it ‘is the bringing together of a particular or particulars, on the one hand, and [universals] on the other, by inserting the particulars in the unsaturated structure [the universal]’ (ibid., p. 29). One might think that the motivation for this tack is a wish to avoid Bradley’s regress, which, as he rightly believes, only occurs if a relation is postulated as unifier of a state of affairs. This may have been a motivation for Armstrong at a psychological level, as it were, but it is not at a scientific level, for he believes—incorrectly, as we shall see—that this regress is non-vicious (ibid., pp. 118–19). In any case, since, as mentioned, the problem of unity is not identical to the problem of Bradley’s regress, it is plain that, given a rejection of Armstrong’s primitivist view, he has not even provided a metaphorical attempt at solving the problem of