Jiri Benovsky

“Primitives.” In The Routledge Handbook of Metametaphysics, edited by Ricki Bliss and J.T.M. Miller, 2020.

Primitives

“Problem-solvers”

Such primitives are what I call problem-solvers. A problem-solver is a primitive that is there to solve a problem. The theories we have seen above all answer the question of attribute agreement (i.e. the question about how two objects can “share the same property”) by appealing to their primitives: the relation of exact resemblance between tropes, the instantiation of the same universal, or the fact that a and b resemble each other. In the same crucial places, all three views introduce a primitive with the same function: primitively answer the question (“In virtue of what are a and b both F?”). Problem solved. With a problem-solver. Problem-solvers are commonplace in metaphysics, and in philosophy in general; without them we would not get very far. Primitive problem-solvers are the pillars that sustain the structures of our theories.

If, then, this is how the substratum theory explains numerical diversity and the particularity of particulars, the bundle theory (with universals) can do the same. According to the bundle theory, there are no substrata, rather there are only properties tied together by a special variably polyadic relation often called “compresence.” Here, compresence, instead of a substratum, plays the functional role of particularizing particulars: it is a “unifying device” (like the substratum, functionally speaking) whose role in the theory is to take properties to make up objects. Concerning the problem with the two indiscernible spheres, the relation of compresence does not contribute to the qualitative nature of objects and so it can very well be a numerically different relation in different objects without spoiling the two objects’ qualitative identity. It can thus account for numerical diversity of the two qualitatively identical spheres–in this way, the two spheres are numerically different in virtue of the numerical difference between the (instances of) relations of compresence that tie together the…

Realize here that not only are primitives like pillars that support the weight of our theories, by doing most of the work, but that they also are “points of contact” between the theories. Keep in mind the three answers above to the problem of attribute agreement (“sharing the same property”): the three theories all contain a primitive problem-solver at a crucial place in the theory that allows them to solve the problem. Their primitives are, of course, clearly different, but they have the same overall function within a given theory, and the role to explain how a and b can share the same property. In a very general sense, all three views do answer the question in the same way–a primitive way.

One can then raise the meta-metaphysical and methodological question: when it comes to the problem of attribute agreement, what difference does it really make to pick one theory rather than another? The current debate in metametaphysics provides a lot of discussion in the neighborhood of this question, even if the discussion typically does not focus on primitives. For instance, Hirsch (2005, 2007, 2008) defends a claim of equivalence between endurantism and perdurantism; in his view, these debates are merely verbal disputes. They seem to say different things but they are in fact making the same claims, merely formulated in different ways. Another example is Bennett (2008) who focuses on theories of composition and argues that there is little reason to embrace one side of the debate rather than the other, even if they are not just terminological variants, for, in her view, it is epistemically under-determined which one we should choose.

To come back to our examples above, in Benovsky (2008), I argue for an equivalence claim between (various versions of) the bundle theory and the substratum theory. In my view, the question that arises is: at the end of the day, if competing theories answer their theoretical challenges by appealing to their primitives, what difference does it make…?

View, then, even if two sides of a debate use problem-solvers that are functionally equivalent, they still have a different nature/content and so they are not metaphysically equivalent even if they are functionally/theoretically equivalent. In our example above, the idea here is that compresence is a relation and a substratum is not a relation, so they are not the same thing, even if their functions are so similar (or even entirely the same).

The functional view seems to behave better than the content view. Consider the idea that the problem-solver used by one theory is a substratum, while the problem-solver of another theory is a relation, and so they have a different nature. What is it that this idea captures? Does it say something about the substratum or the relation of compresence, like for instance the often-cited difference that properties cannot “float free” while a substratum can “stand alone” and support properties? But whatever this alleged difference between the two primitives means, it would be a functional difference–a difference in what a substratum can do, while compresence doesn’t.

So, here again, the functional view seems to be the adequate story. Here, we would have a difference between the two primitives, and so they would not be equivalent, but they would not be equivalent for functional reasons. To repeat: this is no surprise at all–primitives being there to do a job, it’s only natural that they are individuated in terms of their functions.

For this reason, any difference between primitives will always be a functional one–their functions are the very reason for introducing them in the first place. In the content view, we would be forced to say that in addition to their functions primitives have a non-functional content, but this would objectionably mean that there is a difference that makes no difference–a somewhat prejudiced attitude towards one of the primitives and against the other, where one would stick too heavily…

“…are correlated with each other; and what we thought were distinct correlated phenomena run out to be one and the same. Here the apparent correlation is understood as identity.”

(Kim 2006, p. 85)

In this example, the relation between the explanandum and the explanans is simply identity. We have a similar situation in the case of our example concerning attribute-agreement: for instance, we can say that the explanandum is the sharing of the same property, while the explanans is the instantiating of the same immanent universal. In this case, we can say that sharing the same property just is instantiating the same universal, exactly as lightning just is atmospheric electric discharge.

To have another example, according to the substratum theory, numerical diversity of the two spheres in Black’s world just is or consists in their having a numerically different substratum. So, can we say that the relation between a primitive problem-solver and the phenomenon it explains is identity? There are two problems with this view.

First, as Ruben (1990, p. 219) claims, not all identities are explanatory. The identity claim “lightning is lightning” is not explanatory, while the identity claim “lightning is atmospheric electric discharge” is, because in the second case, even if there is only one phenomenon involved, it is conceptualized in two different ways. We see here that explanation is (and identity isn’t) an irreflexive relation.

Second, perhaps even the claim “lightning is atmospheric electric discharge” is not explanatory. This is the skeptical challenge: if the relation between “sharing the same property” and “instantiating the same universal” is identity, how does this explain anything? We encounter this worry in many places; for instance, when discussing the psychoneural identity theory, Kim (2006, pp. 97–98) says:

“Our conclusion, therefore, has to be that both forms of the explanatory argument are open to serious difficulties. Their fundamental weak…”

An “ontological free lunch” in Armstrong’s (1997) sense; the “ontological price” you pay for a and b is just whatever you would pay for b alone. Only in this particular sense can one talk about identity between a and b. This kind of relation is found in many cases of metaphysical theories.

For instance, according to a version of perdurantism, a’s persisting through time just is a’s having temporal parts at different times, where the latter is taken to be a more fundamental phenomenon than the former. Quite often, the terminology that is used in such cases appeals to the locution “in virtue of”: a persists through time in virtue of having temporal parts at different times.

If we took this idea involving the notion of grounding on board, we would then be in a situation where we step on a primitive in our effort of understanding the nature of explanation–indeed, the notion of grounding is typically taken as being primitive itself (as well as other related notions such as the notion of “being nothing over and above,” the notion of an “ontological free lunch,” and similar).

In the case of lightning and the explanation in terms of atmospheric electric discharge, the chain of explanation goes on until the most fundamental level is reached–the most fundamental level being largely dependent here on empirical matters. The situation is different in the case of explanations found in metaphysical theories involving problem-solvers–we are not limited here by empirical matters. Rather, we reach the bottom of our metaphysical inquiry when we arrive at a notion that is unanalysable any further without circularity. The examples we have seen include a substratum, a non-relational instantiation, resemblance, and others. These notions are taken by our theories to be too fundamental to be further explained.

In this sense, what is at stake in metaphysical inquiry is to find out which is the best primitive, and what is more fundamental than what; what explains what and how. Ultimately, it is a matter of deciding which primitive we want to posit to do the job, or which set of primitives we want to adopt, and on which basis. This leads us to further meta-metaphysical considerations about theoretical virtues, parsimony, and how to weigh them in deciding which primitives (and how many) are worth including in our ontology.

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