Coming to a pause in his arguments in Appearance and Reality, Bradley wonders if the reader may question “whether anything of what is understood by a thing is left to us,” given that at this point Bradley believes that what is generally thought of as a thing has been “undermined and ruined.” In particular, Bradley argues that “for a thing to exist it must possess identity; and identity seems a possession with a character at best doubtful.” (AR, p. 72).
Identity is a problem for Bradley with important, although perhaps unsettling consequences. Moreover, the problem of identity has, as Della Rocca (himself a careful reader of Bradley) shows in a recent article (here), important implications for the 3d’ist/4d’ist debate. I would also add that this was already a problem for Hume (as I’ve discussed here and here) and it is a problem that is critical to understanding Gilles Deleuze’s project.
In most of the cases mentioned above, the problem of identity is integrally connected to the problem of persistence and continuing identity in time. For Bradley, the identity of a thing entails that “A thing is a thing, in short, by being what it was.” (ibid. 73). But this immediately brings about an important consequence for Bradley since a thing, thus understood, “has become, in more senses than one, the relation of passages in its own history. And if we assert that the thing is this inclusive relation, which transcends any given time, surely we have allowed that the thing, though not wholly an idea, is an idea essentially.” (ibid.). Identity can thus not be reduced to, or explained in terms of, any given time, or any determinate fact, or, as Bradley puts it, “the identity of a thing…is a character which exists outside of and beyond any fact which you can take.” (ibid. 74). Rather than presupposing identity as an inexplicable given, a primitive fact, identity for Bradley is precisely the problem to be explained and accounted for.
It is on this point where Della Rocca and Deleuze are in agreement, which is not surprising given the importance they both give to Spinoza and to the principle of sufficient reason (PSR) in particular. In his article Della Rocca succinctly sums up the 3d’ist and 4d’ist positions. Whereas for both the 3d’ist and 4d’ist one can say that persistence occurs in virtue of qualitative and causal continuity between the state of an object, A, at time1 and object B at time2, for the 3d’ist this persistence occurs precisely because A is B while for the 4d’ist A and B are not the same and persistence occurs as a consequence of the succession of distinct objects. In short, for the 3d’ist, Della Rocca argues, persistence is explained by the persistence of the same object, and thus it is not really explained – “it is primitive” as Della Rocca puts it.
The problem then is if we are going to move beyond thinking of persistence as a primitive – in other words, if we push PSR and attempt to explain persistence itself – we will, Della Rocca argues, need “to insist on identity-free explanations of persistence; that is, it is to insist that in a case of persistence, A persists in virtue of some fact beyond the very persistence of A itself.” (p. 609). It is precisely this tactic that David Lewis and Ted Sider take, though Della Rocca argues, after a discussion of Armsrong’s famous example of homogenous disks in a symmetrical universe (of which more another time), that in the end Lewis and Sider ultimately retain a commitment to “primitive identity,” to an identity that is a brute, inexplicable fact.
For Deleuze, likewise, his acceptance of PSR demands that identity be explained rather than presupposed as an inexplicable primitive. His philosophy of difference is an attempt to provide such an explanation. I have discussed this theme in other posts (see here, here, and here), but it’s worth noting again that Deleuze derives much of his approach to this problem from Hume.
In his excellent book on Hume, Hume’s Difficulty: Time and Identity in the Treatise, Donald Baxter also addresses this problem while making a strong case for the importance of metaphysics for Hume. The problem of identity looms large for Hume, especially given the metaphysics of time Hume presupposes. The problem, in short, arises when one asks whether something is identical to something else. Bradley notes much the same problem when he claims that is “impossible to reply when we are asked if an object is really the same.” (p. 73). Leaving Bradley aside, the difficulty for Hume as Baxter reads him is that we need to somehow maintain two mutually exclusive viewpoints: on the one hand, the objects are taken to be identical and hence an object is not distinct from itself but is a unity, or they are distinct and we have two or more objects and they are thus not identical. What we need, Hume argued, is an understanding of identity that is a “medium betwixt unity and number,” but this is impossible, Hume claims, for “Betwixt unity and number there can be no medium; no more than betwixt existence and non-existence” (T200).
As Baxter reads the Treatise, Hume’s attempt to account for identity follows from his metaphysics of time, and most notably the distinction between steadfast objects which are unitary things without temporal parts and duration which consists of many things in succession. Identity as “a medium betwixt unity and number” thus results when we acquire the “unshakeable fiction” (to quote Baxter) that steadfast objects endure, or co-exist with a succession of objects.
Without going into detail, I would argue that whereas Baxter takes steadfast objects to be unitary existents, I would argue that to do the work that Baxter would have them do then steadfast objects are first and foremost identifiable, and hence the concerns that characterize Hume’s account of identity will also be the case with respect to steadfast objects—in other words, as identities they are fictions, or they are fictioned for Hume (as I argue in Deleuze’s Hume). And it is this fictioning process that offers the account or explanation of identity. A consequence of this explanation is that identity is not to be accounted for in terms of the metaphysical assumption that there “is no middle way between existing and non-existing” but rather the fictioning process inseparable from identity is a matter of degree. As Hume argues regarding identity (and thanks to Eric for reminding me of this passage),
Identity depends on the relations of ideas; and these relations produce identity by means of that easy transition they occasion. But as the relations, and the easiness of the transition may diminish by insensible degrees, we have no just standard, by which we can decide any dispute concerning the time, when they acquire or lose a title to the name of identity.” (220.127.116.11; T262).
For Baxter, however, there is a difference between the metaphysical status of existing objects and the idea of identity. An important strand of his argument is that Hume’s discussions of identity are concerned not with the identity of the intended objects that are thought about (this is thus not Frege's problem) but rather with the “intentional object” (as Baxter calls it, perhaps drawing a page from Husserl’s theory of the noema), or with “how many objects the ideas represent there as being.” (p. 53).
For Deleuze, by contrast, the problem of identity is not an issue confined to “intentional objects” but extends to the metaphysical status of existence itself, and as identity is a matter of degrees for Hume, so too is existence for Deleuze. In attempting to explain identity rather than presuppose it as an inexplicable primitive, one of Deleuze’s important influences here is Peirce, who argues quite bluntly that “There is no difficulty in conceiving existence as a matter of degree.” The “universe,” Peirce claims, “must be undergoing continuous growth from non-existence to existence.”
Peirce’s arguments, as well as Deleuze’s, are quite involved, but insofar as we seen them as working with the problem of identity then we have opened another possible point of contact between analytic and continental-focused philosophers, which has been an important concern of several of us here at this blog.