The Relations Thesis might be thought to look dangerously similar to the infamous ‘axiom of internal relations’ criticised by Russell and Moore. Such a thought, though mistaken,
wouldn’t be entirely unjustified, as superficially speaking, there is a resemblance. Consider the following characterisation of the axiom by Russell (1994 p. 139):
‘Every relation is grounded in the natures of the related terms.’ Let us call this the axiom of internalrelations. If this axiom holds, the fact that two objects have a certain relation implies complexity in each of the two objects, i.e. it implies something in the ‘natures’ of the two objects, in virtue of which they have the relation in question.
Much of this description of the axiom could be taken to communicate what I wish to
communicate with the Relations Thesis. There is a sense in which I think it trivially true that “every relation is grounded in the natures of the related terms” and that there is “something in the ‘natures’ of the [related] objects, in virtue of which they have the relation in question” (Russell 1994 p. 139). But taken in the sense in which I would take them to be true, such
%*-!
claims are in no way incompatible with the position Russell (1994 p. 139) directly contrasts with that which he takes the axiom to express:
According to the opposite view, which is the one that I advocate, there are such facts as that one object has a certain relation to another, and such facts cannot in general be reduced to, or inferred from, a fact about the one object only together with a fact about the other object only: they do not imply that the two objects have any complexity, or any intrinsic property distinguishing them from two objects which do not have the relation in question.
The position Russell advocates is only at odds with the view that every relation is grounded
solely in the natures of the related terms, that there is something in the natures of the objects
solely in virtue of which they have the relation in question, the view that every relation is ‘intrinsic to its relata’, to appropriate Lewis’s (1999 p. 26) terminology. I definitely don’t think it trivial that relations are intrinsic to their relata. In fact, like Russell, I think it mistaken. I merely think there is a trivial sense in which every relation is at least partially grounded in the natures of the related terms, for concrete particulars, their nature qua
concrete particulars, for property instances, their nature qua property instances, for properties qua universals, their nature qua universals, for non-existents, their nature qua non-existents, and so on, and I take what suffices for it to be the case that there are such terms to be determinative of the requisite natures. On this score, Russell appears to be in complete agreement with me. Shortly after having given the axiom of internal relations short shrift, he claims that a judgement “that two terms have a certain relation” is true inasmuch as there is a corresponding “complex object” which “consists of the two terms related by the relation” (Russell 1994 p. 158 emphasis mine). In speaking of the related terms, he clearly means the related things themselves, so the truth-making object he speaks of consists of them, what they are, or, in the least, their natures in the foregoing sense. Their natures partially or wholly ground the relation by partially or wholly comprising that object.
%+.!
Might this be the kind of grounding relation that Moore (1922 p. 309) is speaking of when he issues the following comments at the end of his famous rebuttal of the axiom?
Yet it is worth noting, I think, that there is another sense of “grounded” in which it may quite well be true that every relational property is grounded in the nature of any term which possesses it. Namely that, in the case of every such property, the term in question has some quality without which it could not have had the property. In other words that the relational property entails some quality in the term, though no quality in the term entails the relational property.
It might be argued that my grounding requirement is more basic. It is not that possession of a relational property requires that a thing have some quality or other, it is that it requires that very thing, or its nature in the foregoing sense. To attribute a property to something, relational or otherwise, might not be tantamount to positing it qua existent, as Kant (2007 pp. 504, 505) famously claimed, but it is nonetheless the positing of it qua whatever kind of thing it is. Having said this, I think it reasonably obvious that my grounding requirement is entailed by Moore’s. The quoted passage appears shortly after Moore (1951 p. 308) has drawn a
distinction between a thing’s qualities and its relational properties. For something to have a quality, taken in Moore’s sense, is presumably for an aspect of reality making for the
instancing of such a quality to be an inherent part of an aspect of reality making for the being of that something. If the aspect of reality making for the instancing of the quality, taken alone or in conjunction with other aspects of reality, doesn’t make for the being of that something, then they surely can’t be said to be qualities of it. In saying this, I have weighed in on a metaphysical debate. I have assumed that there is no real distinction between a thing and what Moore calls its qualities. To quote Galen Strawson (2006b p. 207), “‘Inherence in a substance’ is ... a dummy phrase used simply to express the fact that the properties or
attributes in question are concretely instantiated (‘exist’)”. It might instead be maintained that quality possession is a matter of an instantiation relation pertaining between a quality qua
%+%!
universal and a thing qua bare particular. In such a case, Moore’s grounding requirement arguably doesn’t entail mine, as the possibility of such an instantiation relation pertaining without implicating what makes for the being of the quality instantiated or the thing
instantiating it hasn’t been ruled out (that’s what my grounding requirement does). I do not think the truth of the Relations Thesis in any way beholden to the truth of either account of quality possession; if the latter account is correct, then I think the Relations Thesis true of all relations including instantiation relations between universals and bare particulars. I could just as easily take the metaphysically inclusive high road here as well, but I think it worth noting that inasmuch as I am assuming Robust Realism regarding qualia in this thesis, I am
assuming the truth of the former account. In experience we encounter categorical phenomenal property instances, not some nexus between phenomenal properties qua universals and the bare particular that is the experience possessing them. It’s difficult to imagine why anyone whose metaphysics allowed for a non-relational property-instance-based account of quality possession in some cases might revert to a relational universal-and-bare-particular-based account at some other point.
Whether or not Moore is tacitly endorsing the Relations Thesis in the passage cited above, the asymmetry of entailment he appeals to is the crucial factor in distinguishing that thesis from the axiom of internal relations. Involvementis a not a symmetric notion; taking a bath involves getting wet, but getting wet needn’t involve taking a bath. Likewise, that the
pertaining of a relation necessarily involves what suffices for it to be the case that each of its relata exist, subsist, or whatever, doesn’t in any way imply that what thus suffices necessarily involves the pertaining of that relation. The claim that what thus suffices for the relata does in fact necessarily involve the pertaining of the relation is a more accurate rendering of the axiom of internal relations than that provided above by Russell. Moore characterises the axiom thusly: “in the case of every relational property, it can always be truly asserted of any
%+&!
term A which has that property, that any term which had not had it would necessarily have been different from A”.In case the difference isn’t immediately clear, Russell characterises the axiom as the claim that all relations are intrinsic to their relata taken collectively, Moore as the claim that all relations are intrinsic to their relata taken individually. On this
characterisation,every relation a thing has might be described as essential to and constitutive of its nature, taken in the foregoing sense. My piano’s maintaining whatever distance from the moon it does is something to which it owes its being, as anything not that distance from the moon would not be my piano.
Like Moore, and most philosophers that followed him, I think this view mistaken. Anything not the same distance from the moon as my piano is not my piano, as my piano, as a matter of fact, is that distance from the moon. But to say that anything not that distance from the moon
wouldn’t be my piano is an altogether different claim, a false one. Countless possible situations in which that distance relation is tinkered with leave my piano intact. In contrast, all situations bereft of appropriate counterparts to the localised intrinsic spatiotemporal components of my piano are situations in which my piano doesn’t exist. The Relations Thesis only claims that a constitutively sufficient set of those spatiotemporal components must be involved in the pertaining of any relation with my piano, not absolutely everything. That absolutely everything is thus involved is plausibly entailed by the axiom, as everything bears some relation or other to everything else, and, according to the axiom, owes its being to doing so, though it admittedly only follows that absolutely everything is therefore involved if the Relations Thesis holds as well. I think it likely that most advocates of the axiom would also have subscribed to the Relations Thesis, if only because it is intuitively highly plausible and I’ve found explicit rejection of it nowhere.121 But the Relations Thesis is equally compatible
121 In Bradley’s case, a better reason would be that the intuition that relations must implicate their relata is
%+'!
with rejection of the axiom, and taken in combination with such rejection it preserves the intuitive asymmetry of the part-whole relation. Absolutely everything owes its existence to every little thing, but every little thing doesn’t owe its existence to absolutely everything. As Moore (1922 pp. 288-289) pointed out, the axiom nullifies this intuitive asymmetry, as it arguably would the intuitive non-symmetry of involvement, taken in its most general sense. If the axiom were true, A’s involving B would be a relational fact belonging to B’s very nature. B’s nature would involve A’s involvement with it, plausibly thereby involving A itself (though once again, the plausibility of A’s involvement with B involving A itself is something I’m yet to argue for).