Identity, and So Forth
On the metaphysics and logic of interdependence
Identity conditions are the conditions by which a thing is the thing that it is. If a thing doesn’t maintain its identity conditions, it will no longer be the thing that it is.
Let me introduce the following terms: bidentity (or 2-dentity) conditions are the conditions by which two things are the two things that they are; tridentity (or 3-dentity) conditions are the conditions by which three things are the three things that they are. Let’s generalize: n-dentity conditions are the conditions by which n things are the n things that they are.
You are forgiven if you think that these new terms are philosophically uninteresting. Seemingly, it may be taken for granted that n things meet their n-dentity conditions simply in virtue of each of the n things meeting its own identity conditions. Call this the primacy of identity.
Thus begins (with some editing) one of my favorite pieces that I’ve published. It came out in 2013 in a special issue of the open access journal Essays in Philosophy on grounding. Articles that iron out details are often great for what they are, but I also enjoy provocative big-picture papers, which is what this one is. As you might suspect from the quote above and philosophers’ conventions in setting up foils, in the paper I go on to cast doubt on the primacy of identity. We shouldn’t presume that individuals are ontologically prior to collectives.
I’ll briefly summarize its main points. It’s going to be sketchy, but you can take a look at the paper if you’d like to see more details. This post is also going to be more technical than other Substack posts of mine, and the latter part of it may not be very intelligible to non-philosophers.
I used to engage a lot more with metaphysics, philosophy of language, and formal logic than I do now. I know that the things I talk about here connect with recent philosophical work, and I’d love to hear suggestions about how to move this project forward given the current state of the literature.
For a tl;dr version of this post, click on the footnote here1
Wood sorrel and pacific bleeding heart leaves, Silver Falls State Park, Oregon. Photo by me, Creative Commons License CC BY-NC4.0.
N-tets
According to Aristophanes’ myth in Plato’s Symposium, people are initially formed as pairs - one thing with two faces, four arms, and four legs. Then, they were split apart by Zeus, becoming the 2-legged creatures that we are today. However, people each spend their life trying to reconnect with their original mate. This, the story suggests, is the origin of love. I don’t share the view of the nature of romantic love suggested by this myth. But it certainly seems to be metaphysically coherent: the pair comes first, the individuals second.
Individual things can get their identity conditions from the n-dentity conditions of n-sized collectives - what I call n-tets - of which the individuals are parts, rather than the other way around. The Aristophanic pair form a 2-tet. Additionally, in this example, it is essential to each of the two individuals that they are connected to the other.
For Aristotle, a person’s left and right hands are not substances because they fail an independence criterion. But I think we should reject the independence criterion. If you disagree, then I invite you to at least play along with me to see where things go.
Ontological dependence and holism
There is a large literature in analytic philosophy on fundamentality and grounding, and my view intersects with some of what is said there. I don’t go as far as the priority monist to say that there is only one whole that is ontologically prior to all the other things. Rather, ontological priority of wholes obtains for some but not all collectives. There are lots of monist views out there, but I haven’t seen this kind of view developed elsewhere. (I’d be grateful if you gave me some references since I bet they are out there.)2
N-tets like Aristophanic pairs are cases of grounding-at-a-distance: sometimes x is a ground of y even though x and y are spatially (or temporally) non-overlapping. Further, they are cases that show that the grounding relation is not antisymmetric - x can be a (partial) ground of y while at the same time y is a (partial) ground of x.
I don’t pretend to have disproven the primacy of identity. Even I don’t accept that specific example. But it is useful to put a name on an unstated assumption underlying individualist metaphysics, and in so doing, raise the question of whether the assumption could be false. At the very least, we shouldn’t just take the primacy of identity for granted.
Towards a logic of ontological dependence
Now that I’ve named and briefly described an ontological category - n-tets - let’s see if it can do meaningful philosophical work. In the paper, I note three ways that we can put the notion of n-tets to use. One is in ethics, to make metaphysical sense of organic unities/wholes, as well as fulfilling a presupposition for value in systems with interconnected parts. A second is in the philosophy of biology, to understand what species are. The third is in formal logic, which I’ll focus on here.
In classical predicate logic, the way that we are taught to translate “There are exactly two Fs” into logical notation is (here, informally):
There is an x that is F and there is a y that is F, and x and y are not the same thing, and for all other things z, if z is F, then z is either x or y.
I’ve always found this to be really cool. But one thing you’ll notice is that it counts Fs by saying: over here is one individual F, and over there is a second individual F, and, looking at all the other individuals, none of them is an F.
For 2-tets, however, this is not the best way to go about things. The standard formalization is based in prioritizing individual elements of domains, in line with the primacy of identity. However, if one rejects the primacy of identity, then that gives reason to try to craft an extension of first-order classical predicate logic, an extension that allows there to be additional items in domains and requires new quantifiers and new rules of inference.
In particular, we should allow for the domain of discourse to include irreducibly plural n-tets, and not just individual objects represented by singular terms. There need to be quantifiers that quantify over n-tets and the items in them. And there should be a rule of inference, Decomposition, which is a kind of elimination rule, to go from the n-tet to the individual members. So, if F is a 2-tet, then the fact that there are two Fs will already be given in the domain of discourse. There should also be a Recomposition rule, which functions as a kind of introduction rule.
There’s more to it than this, since n-tets can be structured in various ways. In the paper, I discuss the metaphysics of rock bands. A band might essentially have one drummer, one bass player, one guitarist, and one lead singer. We can think, then, of at least some n-tets not as represented by sets with n members, but by ordered n-tuples. Because of this, further refinements in the logic must be made; in particular, there will have to be limits on the use of a Recomposition rule for structured n-tets, given that some objects can be recombined only into a specific place in the n-tet.
Now, there already is an extension of first-order logic known as plural logic which uses plural quantifiers. In plural logic, one can say: there exist some xx’s where the xx’s moved the piano. This is needed partly because there are cases where the group of people moved the piano, but the collective moving the piano doesn’t distribute down to every individual among the xx’s moving the piano (on their own).
However, plural logic doesn’t go far enough. For instance, in their book on the topic, Alex Oliver and Timothy Smiley write (78):
There is no monkey business with queer [plural] objects… ‘√4’ denotes 2 and -2; ‘the scientists who solved the structure of DNA’ denotes Watson and Crick. Nothing odd about them.
But I think we should want metaphysically weird objects to be allowed in the domain! Plural quantifiers do not account for the kind of metaphysical anti-individualism that I have in mind. This lack of monkey business in plural logic is, I take it, a limitation, not a perk. We shouldn’t let our metaphysics be limited by our logic.
This post is just a very brief summary of the project and where I would like it to head. I must confess I don’t have it all worked out, even after all these years. I am not a logician, and to bring the project to fruition would require a lot more technical skills, and also a lot more time, than I have. So if you happen to be, or know of, a logician who might want to help me out, I’d love to connect.
We should take seriously the idea that some, though not all, collectives are ontologically prior to their members. Call these n-tets.
Similarly, we should take seriously the idea that specific individuals are ontologically dependent on spatially distinct others. There may be (partial) grounding-at-a-distance.
This metaphysical view should be reflected in logic. In particular, there should be an extension of first-order logic that is similar to plural logic but allows for additional items in the domain as well as for structured collectives.
I need help from a logician to move this project forward!
Many different traditions around the globe accept the priority of wholes over individuals. Anglo-American thought is somewhat unusual in its metaphysical individualism. I’ve been delving into other traditions’ views of ontological dependence, and thinking about their relation to the tradition of analytic metaphysics that I am working within. I’m happy to hear suggestions for what I should look at.