This volume of papers about the metaphysics of relations and the history of the metaphysics of relations is dedicated to the memory of the late Jonathan Lowe. Drawing inspiration from Locke and Aristotle, Lowe performed an important role in stimulating 21st century interest in metaphysics, arguing that the discipline had a distinctive a priori method and subject matter of its own. Lowe was more radical than many other philosophers involved in the late 20th century metaphysical revolution – more radical than, say, Lewis, who remained methodologically beholden to common sense and to mid-century intellectual influences such as Quine. It is fitting that this volume contains one of Lowe's last papers (‘There Are (Probably) No Relations’), one in which Lowe sketches his own considered view on relations, arguing for their (probable) non-existence.
I'd like to dwell upon Lowe's arguments against relations. It wasn't an expected feature of recent philosophical culture that it now has become common to call relations into question. Some of the other contributors to this volume still believe in relations but several more share Lowe's outlook. Although Lowe was ahead of the curve, the curve has caught up. Before it had been considered a key doctrine of analytic philosophy that reflection upon modern mathematics and science compels us to admit relations. But whilst Lowe helped us take metaphysics seriously, I think that this particular development is regressive.
Lowe offers two lines of argument for why there are probably no relations. One is short: that there's no shred of intelligibility to even the idea of a relation conceived as a piece of the world's furniture. It's a short argument but doubtless influential and Heil strikes a similar note in his contribution to this volume (‘Causal Relations’). The other argument is longer: that we lack evidence for the existence of relations because relations are dispensable to our scheme, dispensable because we don't need to appeal to the existence of relations to account for what makes truths true. Both Heil and Simons deploy similar arguments in their contributions, although they differ from Lowe concerning exactly what non-relational existents do make truths true. Overall Simons takes a softer line than either Lowe or Heil. Simons thinks relations are intelligible qua tropes but it turns out we don't need them (‘External Relations, Causal Coincidence, and Contingency’).
Lowe's first argument is that ‘all putatively “real” relations […] seem to be ontologically weird’ (111), or as Heil expresses himself, ‘I find the ontology of external relations ontologically impenetrable’ (130). Why so? Lowe makes his case in terms of tropes but he thought the argument generalises to universals. A monadic trope is dependent upon the substance that bears it because it is ‘wholly within’ its bearer. The monadic case provides the benchmark of intelligibility. But a relational trope would have to exist ‘outside’ the substances it relates, because it holds between them, but would still have to be dependent upon them; ‘I consequently find it hard to conceive what such an entity could really be’ (111).
An immediate counter: why assume that monadic tropes provide the benchmark of intelligibility? Of course the monadic case may be one where creatures like us naturally begin – although even that psychogenetic claim is open to question (as William James emphasised in his descriptions of the flux of experience as things-in-relation). But it doesn't follow that no extension of that way of thinking is intelligible. We begin with finite numbers and infinite numbers obey different laws but this doesn't mean infinite numbers are unintelligible. The human spirit shouldn't be shackled to its beginnings. To advance our knowledge of the external world we have to be open to the possibility that sometimes it is necessary to learn new ways of thinking, i.e. to revise or even replace our internal settings, the standards of intelligibility to which we adhere. Of course relations don't behave like monadic tropes but this shouldn't preclude our understanding relations anymore than the fact that infinite numbers don't behave like finite numbers should preclude our understanding them.
Lowe might have conceded the point and still relied upon his second argument to hold the line against relations. To establish that relations are dispensable, Lowe proceeded down a list of candidate relations and argued that each of them is superfluous qua truth maker in the context of the other commitments of his favoured ontological scheme. Here's a straightforward case, at least by Lowe's lights. There's no need to recognise a same-height relation to explain the truth that Tom is the same height as Sally. It's solely in virtue of the existence of the two monadic height tropes (modes) of Tom and Sally, because ‘if those modes do in fact exist, then it follows of necessity, in virtue of the essence of these modes, that Tom is the same height as Sally’ (106, Lowe's italics). Lowe recognised that some of his conclusions were more speculative than others – for example, that we don't need temporal relations because only the present moment exists. But other claims he considered more robust: (1) that we don't need causal relations once we recognise an ontology of powers conceived as monadic attributes and (2) that we don't need spatial relations once we recognise that what we call ‘material objects’ aren't genuinely movable occupants of space but ‘just regions of variable density’ and that distance relations between regions ‘are “internal” and hence not “real”’ (109). Heil and Simons share views close to (1) and (2) respectively but expressed within the context of their own distinctive schemes of powers and processes.
Rather than delve into the details of these different schemes, explored in these papers, I'd like to raise a general concern about all of them. Lowe, Heil and Simons share a form of methodological monism. They assume that to be is to be a truth-maker. Hence, if there isn't reason to believe that relations are truth-makers there isn't reason to believe in them at all. But is it really plausible that we don't have any other reasons to believe in things? Don't we also have reason to believe in the existence of things which our best theories say there are even if they're not truth-makers? Since our best mathematical and scientific theories say that there are relations, don't we still have reason to believe in relations even if it is established that relations are dispensable qua truth-makers?
Of course I am presupposing here Quine's famous criterion of ontological commitment – that we are committed to whatever a theory we endorse quantifies over, i.e. to a domain of entities over which the quantifiers of the theory range. Heil rejects this way of thinking about Quine's criterion: ‘I prefer to think that what Quine's criterion yields is an accounting of truths to which our theories commit us’ (129). Heil concludes that attending to the quantificational structure of our best mathematical and scientific theories leaves untouched the question of what reality must be like if those theories are true. But truths are true sentences and sentences are true when things stand as the sentences describe them. If things don't stand as the sentences describe them then the sentences are false. Ergo, our best theories don't leave untouched the question of what reality must be like if those theories are true; since our best theories include sentences that quantify over relations then reality must contain relations if those theories are true. This line of thought might be resisted by offering an alternative account of truth or an alternative semantics for mathematics and science that eschews objectual quantification and reference, so the truth or falsity of our sentences doesn't turn on how things stand. But then Heil et al owe us such an account of truth or such a semantics for mathematics and science before we can take seriously their claim that relations don't exist because they are dispensable qua truth-makers – rather than dispensable tout court.
Let me briefly describe the remainder of the volume. By contrast to the foregoing, other papers in this volume take relations seriously because of the scientific roles they are posited to perform which have nothing to do with truth-making. Ladyman and Dorato both argue that modern physics reveals a profoundly relational reality (‘The Foundations of Structuralism and the Metaphysics of Relations’, ‘Rovelli's Relational Quantum Mechanics, Anti-Monism and Quantum Becoming’). Esfeld also maintains that quantum physics is committed to relations but, contra Ladyman, argues that quantum physics needs substances as well as relations (‘The Reality of Relations: The Case from Quantum Physics’). Briceño & Mumford argue that Ladyman has gone too far in characterising physical reality as relations all the way down because a reality with only relations would be metaphysically untenable as a purely Platonic entity (‘Relations All the Way Down? Against Ontic Structural Realism’). Yates argues that a theory of powers cannot provide non-relational truth-makers for all causal truths (‘Is Powerful Causation An Internal Relation?’). Berenstain argues that physical properties cannot be adequately characterised in causal terms but that higher-order mathematical and nomological properties must be built into their identity conditions (‘What a Structuralist Theory of Properties Could Not Be’). Donnelly defends the view that things are arranged thus-and-so in virtue of occupying different properties or roles relative to one another (‘Positionalism Revisited’). There are also three historical papers. Scaltas argues that Plato had a theory of plural-partaking in forms which obviated the need to posit any kind of relational form (‘Relations as Plural Predications in Plato’). Brower maintains that medieval philosophers, under the influence of Aristotle, exhibited a level of subtlety and sophistication in their thinking about relations that is usually missed (‘Aristotelian vs Contemporary Perspectives on Relations’). Penner reconstructs ancient and medieval reasons for refusing to admit relations (‘Why Do Medieval Philosophers Reject Polyadic Accidents?’).
The volume will doubtless be a useful resource for a range of different readers who will be able to find papers to interest them. But considered as a whole I had some misgivings. It is disappointing that the volume only contains papers on the history of philosophy up until the medieval period when there was far less reason to believe in relations. There aren't papers considering the history of philosophy after the advent of modern mathematics and science when there became far more reason to believe in them. So there is nothing devoted to Frege or Peirce or Russell. It is also disappointing that there is only one paper in this volume (Donnelly) devoted to the problem of order, accounting for the fact that things are arranged one way rather another. This is one of the primary reasons for believing in relations, there is a gamut of alternative explanations in the literature, and the problem of order is one of the issues that will need to be resolved before we can move forward on relations.
