Alexander wrote:

I think it is clear that one thing being patterned on another, or having the other as its formal cause, seems a crucial part of this asymmetry. But maybe that just rephrases the problem, rather than pointing the way to a solution.

Yes, I think that's the heart of the matter. If resemblance is merely a matter of some sort of isomorphism, then if A resembles B, B also resembles A in the same way and to the same extent. But if resemblance is taken to involve copying or simulation (as etymologically and historically it does), then it matters which of the relata "came first," so to speak. On that view, human fatherhood would "resemble" the Fatherhood of God, but not vice versa.

Hi Dan,

I don't think there is an example. I think it's a necessary truth that if a resembles b, then b resembles a. If resemblance is a real relation, that causes problems for the view that creation is related to God, but God isn't related to creation. Resemblance is not, however, a real relation.

It's worth introducing the notion of an internal relation. Two or more particulars are internally related if and only if there exist properties of the particulars which logically necessitate that the relation holds. (Two or more particulars are externally related if and only if there are no properties of the particulars which logically necessitate that the relation holds.)

I'll also need Armstrong's reductive principle for internal relations. The reductive principle for internal relations states that if two or more particulars are internally related, then the relation is nothing more than the possession by the particulars of the properties which necessitate the relation.[1]

Resemblance relations are internal relations. There is, for instance, no possible world in which there exists some shade of red and another shade of red, and those two reds don't resemble each other. If each of those reds exist, it's necessary that they resemble each other. Hence, if the reductive principle for internal relations is correct, resemblance relations aren't real relations. 

If resemblance relations aren't real relations, then they aren't an example of a real relation God has to creation. Hence, if the reductive principle for internal relations is correct, resemblance relations aren't an example of a real relation God has to creation.

But suppose we try to analyze resemblance in terms of relation universals anyway. The idea with the real relations analysis is that classes of first-order universals, like the class of colours, are united by second-order resemblance relations. Since the different colours resemble each other more or less closely, the relations of resemblance would have to admit of degrees. But if the relations of resemblance admit of degrees, then it appears they all resemble each other (again, more or less closely) and, if we try to analyze those resemblances with yet higher-order real relations of resemblance, we're off on an infinite regress (that never manages to provide a completed analysis of the resemblances). So, the reductive principle for internal relations cuts against admitting resemblances as real relations, and analyzing resemblance in terms of real relations leads to a vicious infinite regress (and so doesn't work) anyway.

So, resemblance is symmetrical, but resemblance relations aren't real relations. (My preferred positive analysis is, in a nutshell, that we should analyze resemblance in terms of conjunctive properties and partial but strict identity, which, by the reductive principle for internal relations, doesn't involve real relations. But even if my preferred positive analysis is wrong, we have good reason for rejecting the view that resemblance relations are real.)


[1]Universals can also be internally related. Universals are internally related if and only if the relation which holds between them is logically necessitated by the existence of the universals. As with particulars, if two or more universals are internally related, then the relation is nothing over and above the universals themselves and their properties.

I don't have access to a copy of either Blanshard's “Reply to Marcus Clayton” or The Philosophy of Brand Blanshard (nor does the university have it). So, I haven't read the reply to Clayton in full.

But it seems to me Blanshard thinks resemblance relations are ultimate in the sense that they're not reducible to partial identities[1], not that they're ultimate in the sense of their breaking Kearns's regress[2]. If Blanshard does mean that his resemblance relations are ultimate in the sense that they break the regress, then he either needs to give some reason why it's okay to stop analyzing resemblances at the first level of resemblance relations or, as a reply, his account amounts to little more than a bare refusal to face the argument. 

Blanshard was a thorough guy, so I wouldn't be surprised to learn he at least tried to give this reason somewhere. But I don't know where, and I can't think of how.

Scott wrote:

I think this is true of "resemblance" understood as mere "being like" (or what I previously summarized as "isomorphism"). The medieval/scholastic notion was somewhat thicker, though, and implicitly involved a degree of intentionality in one thing's "copying" another. Arguably this is an altogether different relation, as I'm not at all sure it would make sense to say that orange "resembles" red in this way.

I think you're right. 

We may also need to draw a distinction between contemporary theories of relations and medieval theories of relations or respective entities (res respectivae). The contemporary debate assumes that a relation is a single intermediary between objects that are roughly ontological equals. In contrast, in the medieval debate, a respective entity wasn't thought of as a single intermediary at all. 

As Rondo Keele explains:

Instead, nominalists and realists alike said that respective entities were supposed to be Aristotelian accidents; that is, they are on par with qualities and other forms of dependent being [...]. Since an accident always inheres in exactly one substance, a respective entity could never “straddle” two relata by inhering in both of them. And yet a respective accident is not like an absolute accident (for example, whiteness) which simply inheres in its subject (a white thing). For, as we noted above, relations are multi-place, having two or more relata. Thus a respective accident corresponding to a two-place relation, say, would have to involve both its relata somehow, even though it only inheres in one of them; for this reason philosophers of this tradition tended to say that respectives are accidents that (1) inhere in a subject, as do all accidents, (2) are based on the subject in which they inhere or on some other, absolute accident which inheres in that same subject (e.g., a quality like whiteness), and (3) point to other relata in the relation or to their accidents. It is this “pointing” that makes respectives unique metaphysically, and the Latin terms used to refer to them often reflect precisely this feature: e.g., the Aristotelian category of relation was often called 'ad aliud' (literally, 'toward another'), and respectives were said to have 'esse ad' ('being toward').

Let us consider a concrete example. Suppose that Plato and Socrates are both pale. In precisely this respect then, 'Socrates is similar to Plato' is true. Many mediaeval realists thought of “similarity” as a respective entity which makes the two things similar, but they would claim that there are two “similarities” here, not one. Inhering in him but based on his absolute qualitative accident paleness, Socrates has a relative accident of similarity—call it 'S'—which “points toward” the paleness in Plato. But to complete the picture, it must be said that Plato too has a respective accident of similarity, S*, which inheres in him, is based on his paleness, and which points to the paleness of Socrates. Since an accident can inhere in but one subject, and Plato [is not identical to] Socrates, obviously, S [is not identical to] S*. Analogously, a realist might say that a one-meter stick and a two-meter stick will have inhering in them two distinct correlative accidents, “double” and “half,” based on their absolute accidental quantities.[3]

Once we have the right kind of entities and break relations up like the medievals, it makes way more sense (at least in the abstract) how there might be asymmetric resemblance.

Here's an omnipotence argument for the possibility of asymmetric resemblance (or, using Keele's terminology, similarity).[4] Consider the example of Plato and Socrates above. If God can annihilate anything that exists except Himself, then He can annihilate one respective entity in the pair of “similarity” respective entities (Plato's, say). From God's ontological ultimacy and the doctrine of divine conservation, God can annihilate anything that exists except Himself. Hence, God can annihilate Plato's respective entity in the pair of “similarity” respective entities.

If Plato's “similarity” respective entity doesn't ground anything else, then God can annihilate the respective entity without annihilating anything else. The respective entity doesn't ground anything else. It depends on a substance and an absolute accident (it inheres in Plato and is founded in Plato's paleness), but neither the substance nor the absolute accident depend on the respective entity. Hence, God can annihilate Plato's “similarity” respective entity without annihilating anything else. Hence, it's possible for God to create a situation where Socrates's paleness is similar Plato's, but Plato's paleness isn't similar Socrates's.

On one hand, since Socrates's “similarity” points towards Plato's paleness but Plato's “similarity” to Socrates's paleness no longer exists, we seem to have a case of asymmetric similarity (which seems like the same thing as asymmetric resemblance). On the other hand, this generates an oddity: Plato still has the same paleness as before despite Plato's paleness no longer being similar to Socrates's.


[1]He's arguing against F. H. Bradley's account of resemblances; Armstrong's account, which I prefer, also uses partial identities but differs from Bradley's.
[2]In Blanshard's reply to Kearns, he even goes so far as to “concede that an indefinite series of resemblances is entailed by the first resemblance”. An "indefinite series" isn't necessarily an infinite series, but does still seem telling.
[3]Keele, Rondo. Can God Make a Picasso? William Ockham and Walter Chatton on Divine Power and Real Relations, Journal of the History of Philosophy, 45.3. The whole paper is worth reading (and well written).
[4]Strictly, that resemblance is nonsymmetric.

Last edited by John West (1/01/2016 12:28 pm)