The Abstract and the Concrete is a collection of nine essays (eight of which have been previously published) on a variety of different topics in ontology and metaontology. The essays in metaontology broadly defend a “neo-Quinean” approach to metaontology by critiquing various alternative approaches. The essays in ontology mostly focus on defending a particular theory of abstract objects, which van Inwagen calls “Lightweight Platonism. ”A central component of Quine’s metaontology is that there is only one way to exist. The goal of the first essay is to defend this view against “ontological pluralism, ” which says that there is more than one way to exist. The kind of ontological pluralism at issue in this chapter can be thought of as endorsing the fundamentality of at least two existential quantifiers, which we can symbolize as ∃1 and ∃2. These distinct quantifiers nonetheless function grammatically like the standard first-order existential quantifier, in that they bind variables in nominal position (as opposed to the kinds of quantifiers in higher-order logic). Van Inwagen argues that the “generic” existential quantifier, which ranges over absolutely everything across different ways of being, is indispensable for the ontological pluralist. For example, if the ontological pluralist wishes to state that everything exists in one of two ways, they would seem to need a generic quantifier. Van Inwagen also argues that in order to construct a satisfactory logic that accounts for the validity of “mixed” inferences that use different fundamental quantifiers, the ontological pluralist must (either explicitly or implicitly) appeal to generic quantifiers. The fact that generic quantifiers are indispensable for ontological pluralists (while “specific” quantifiers are not indispensable for neo-Quineans) is, van Inwagen argues, a reason to be skeptical of ontological pluralism. This kind of argument against pluralism has since been further discussed and defended by Trenton Merricks (2017) and David Builes (2019). Finally, van Inwagen also argues that the primary motivation behind ontological pluralism is not persuasive. Although it is true that (say) numbers and tables are extremely different entities, that is not a good reason to think that they exist in different ways. One only needs to appeal to the vastly different properties had by numbers and tables to capture how different they are. The goal of the second essay, as well as the eighth, is to defend neo-Quineanism against “neo-Carnapianism. ” A central component of Carnap’s metaontology is that many ontological debates can be trivially or analytically settled by appealing to a “linguistic framework. ” For example, one might argue that there are conceptual truths that guarantee the existence of numbers, properties, mereological sums, propositions, and so on. Such conceptual truths might include, for example, “If there are no dinosaurs, then the number of dinosaurs is zero, ” “If an apple is red, then it has the property of redness, ” or “If there are particles-arranged-table-wise, then there are tables. ” Van Inwagen raises a number of initial difficulties for this view. Here are three of them. First, the kinds of conceptual truths that lead to the existence of properties quickly lead to contradictions that are similar to Russell’s paradox. Consider the predicate “non-self-applicable. ” The property of wisdom is non-self-applicable, since the property of wisdom is itself not wise. But, if the property of being non-self-applicable exists, is it non-self-applicable? Either way, a contradiction follows. Second, how exactly are truths about numbers supposed to be guaranteed by adopting a particular linguistic framework? Given Gödel’s incompleteness theorems, it seems like any finitely specifiable list of linguistic rules will fail to capture all the truths of arithmetic. So it’s hard to see how the truths of arithmetic could be guaranteed by the adoption of some linguistic framework. Third, even if the bare existence of these various entities is guaranteed by linguistic rules, there seem to be many questions about these entities that are not settled by linguistic rules. For example, what are the persistence conditions of tables? What kinds of de re modal properties do tables have? More generally, accepting the existence of an entity results in the theoretical burden of assigning a consistent and complete (and preferably nonarbitrary and independently motivated) set of properties to that entity. Of course, there are ways to resist these initial problems. Philosophers have developed many different ways to resist Russell’s paradox, there are ways to defend the determinacy of arithmetic without giving up on neo-Carnapianism (e. g. , see Warren 2020), and there are ways to deflate questions about the temporal and modal properties of objects (e. g. , via temporal or modal counterpart theory or via a plenitudinous ontology that contains objects with “all possible” temporal and modal profiles). However, each of these further replies comes with its own distinctive set of philosophical challenges. A last and more general point that van Inwagen raises is that philosophers have given many different arguments against the existence of numbers, properties, mereological sums, and so on. Appealing to conceptual truths does nothing to show where these arguments are supposed to go wrong (if anywhere). The third and final topic in metaontology that van Inwagen discusses is whether we should adopt a “hierarchical” model of ontology, according to which some entities are more fundamental than, and metaphysically ground, other entities. Van Inwagen’s main criticism of this kind of view is methodological. Oftentimes a hierarchical model of ontology is motivated by giving some intuitive examples of entities that are supposed to ground other entities, such as Socrates grounding Socrates. Van Inwagen instead argues that we should be deciding on the merits of a hierarchical model of ontology by comparing global systematic metaphysical theories that utilize a hierarchical model of ontology with global systematic metaphysical theories that do not utilize such a hierarchical model. A second point that van Inwagen makes is that eliminativist views about Fs have important advantages over views that recognize the nonfundamental existence of Fs. For example, van Inwagen argues that the various philosophical puzzles that come with giving a full theory of events are avoided if one is an eliminativist about events, whereas recognizing the nonfundamental existence of events doesn’t seem to do anything to address those puzzles. Although these two points are well taken, I would have liked to hear more about how van Inwagen addresses the usual paradigmatic examples of metaphysical grounding. Van Inwagen’s preferred ontology does not include sets, so the example of Socrates will not get off the ground. But van Inwagen does accept the existence of composite living organisms. The defender of metaphysical grounding would say that there is a systematic correlation between the kinds of properties that composite living organisms have and the intrinsic properties and relations of the simples that compose that living organism. Moreover, this systematic correlation seems to hold of metaphysical necessity. It is natural to think there should be an explanation of this systematic necessary correlation. Proponents of metaphysical grounding will say that what explains this necessary correlation is that the properties of composite objects hold in virtue of the properties of their constituent parts, where this “in virtue of” tracks an important kind of explanation that is ubiquitous in metaphysics. In the absence of an explanatory connection of this kind, the necessary connection between a composite object and its parts can seem mysterious. Moving on to “first-order” ontology, three of the essays in the book (essays 4, 5, and 6) defend and describe van Inwagen’s preferred theory of abstract objects, while one essay (essay 7) critiques a rival account of “fictionalist nominalism. ”Van Inwagen’s primary motivation for believing in abstract objects is a familiar Quinean reason. Much of what we say in ordinary life seems to quantify over abstract objects, and there doesn’t seem to be a successful way to “paraphrase away” this ontological commitment. One nominalist response to this challenge is to say that, although much of what we say in ordinary life might be strictly speaking false, the “nominalistic content” of what we say (roughly: how the concrete world would intrinsically have to be in order for our sentences to come out true) is still true, and this is good enough both for ordinary life and scientific purposes. One criticism of this view in the literature, defended by Mark Colyvan (2010), is to argue that this kind of view cannot account for the explanatory role that mathematics plays in science (just as scientific antirealists cannot account for the explanatory role of unobservable scientific posits). Van Inwagen comes close to this kind of criticism in his seventh essay, “Fictionalist Nominalism and Applied Mathematics, ” where he argues that nominalists cannot account for why applied mathematics is so successful at letting us draw conclusions about the concrete world. However, by now there are several existing replies to this explanatory challenge by nominalists in the literature, which, unfortunately, van Inwagen does not address (e. g. , see Leng 2012). With respect to his own positive views, van Inwagen defends a theory of abstract objects with several different components. First, he argues that abstract objects are all necessarily existent. Although this view is fairly standard, it has its detractors. For example, one could think that “haecceitistic” properties like being Socrates are abstract objects that only exist in worlds where Socrates exists. In response, van Inwagen argues that denying that properties exist necessarily leads to the implausible view that the accessibility relation among possible worlds is not symmetric (103–4). A second component of van Inwagen’s view is that abstract objects do not stand in any causal relations. This view is also standard, although again it has its detractors (e. g. , one might think that fictional characters are abstract objects that are causally brought into existence by their authors). Third, he argues that all abstract objects are “universals” rather than “tropes, ” where the relevant conception of universals is “transcendent” rather than “immanent, ” in that universals do not in any way depend on the concrete world for their existence. Fourth, van Inwagen rejects the idea, defended by David Armstrong, that universals are explanatory posits that are meant to explain (say) facts about objective similarity. He also rejects the idea that (say) an apple is red in virtue of or because it instantiates the abstract property of redness. For van Inwagen, the only explanation for why an apple is red will be a scientific causal explanation, not a metaphysical explanation. One of the more distinctive aspects of van Inwagen’s view of abstract objects is that they are all relations. Here, “relations” is meant to be understood broadly to not only include n-place relations where n is greater than 1, but also 1-place relations (“properties”), 0-place relations (“propositions”), and variably polyadic relations. Van Inwagen describes his version of Platonism as a “truth-centered” ontology, since all these abstract objects are closely connected to the concept of truth. Propositions are of course things that can be true or false, and properties and relations are things that can be true or false of some other thing (s). Van Inwagen’s truth-centered ontology does not include ordinary mathematical objects like numbers and sets. So how does van Inwagen account for mathematics? He does this by introducing a structurally similar “replacement” for set theory that he calls “proxy set theory, ” or “proxet theory” for short. The rough idea behind proxet theory is to replace sets with properties and membership with instantiation. Socrates is associated with the haecceity of Socrates, or the property of being Socrates. So “Socrates is a member of Socrates” is translated as “Socrates instantiates the property of being Socrates. ” More generally, a nonempty set of things is associated with a disjunctive property, which is the disjunction of the haecceities of its “members, ” so Socrates, Plato will be associated with the disjunctive property of being either Socrates or Plato. Finally, the empty set can be associated with an arbitrary impossible property that is not instantiated by anything, such as the property of being non-self-identical. Overall, this collection of essays contains many interesting and important arguments in ontology and metaontology, and I would recommend anyone interested in those topics read it. In some cases, the essays feel a bit dated and not responsive to the contemporary literature on the relevant topics, but that is only to be expected since the volume contains many essays that were written roughly a decade ago. For example, recent discussions of “higher-order metaphysics” are, of course, very relevant to both metaontology and the reality of abstract objects, but they are not discussed in any detail in the present volume. Readers interested in what van Inwagen has to say about higher-order quantification (and, in particular, why he finds such quantification unintelligible if it is not paraphrased away) can find his thoughts on the topic in chapter 5 of his previous book, Being: A Study in Ontology.
David Builes (Mon,) studied this question.