“In One”: The Bearer Issue and the Principles of Exemplification

Traditionally, the so-called exemplification or the relation between the particular and the universal has been one of the three central problems making up the classical problem of universals: (1) What is a particular? (2) What is a universal? (3) What is the relation between the particular and the universal? I used the expression “classical problem of universals” instead of “the problem of universals” since the classical formulation of the problem could be said to contain a questionable assumption, namely that substance should be the bearer “in” which are the entities of (other) categories. Under these circumstances, a neutral approach to the problem of universals could consist in reformulating the three problems of the classical problem as follows: (4) What is the fundamental bearer of categories? (5) What categories are there? (6) What is the relation between the fundamental bearer and the categories? My purpose in this paper is to answer the latter three questions. In order to accomplish this task, I shall discuss the views of two leading figures in substance-ontology, Aristotle and Jonathan Lowe, and the views of two leading figures in fact-ontology, Gustav Bergmann and Reinhardt Grossmann. I shall answer the first question by claiming that the fundamental bearer of categories is facts; the second, by pointing out that it depends on the answer to the previous one; and the third, by showing that the relation between the fundamental bearer and the categories is the one between facts and its constituents, not between a substance or particular and its accidents or properties. In this connection, I shall argue that the “in” of property exemplification should be categorially reconstructed in order for entities other than properties, say, particulars, relations, connectives, numbers, and even facts, to be “in” facts. This categorial reconstruction will also argued for with respect to the Principle of Exemplification.     

Emergentism and supervenience physicalism

I argue that it is intuitive and useful to think about composition in the light of the familiar functionalist distinction between role and occupant. This involves factoring the standard notion of parthood into two related notions: being a parthood slot and occupying a parthood slot. One thing is part of another just in case it fills one of that thing's parthood slots. This move opens room to rethink mereology in various ways, and, in particular, to see the mereological structure of a composite as potentially outreaching the individual entities that are its parts. I sketch one formal system that allows things to have individual entities as parts multiple times over. This is particularly useful to David Armstrong, given Lewis's charge that his structural universals must do exactly that. I close by reflecting upon the nature and point of formal mereology.     

Structure-Making

Friends of states of affairs and structural universals appeal to a relation, structure-making, that is allegedly a kind of composition relation: structure-making ‘builds’ facts out of particulars and universals, and ‘builds’ structural universals out of unstructured universals. D. M. Armstrong, an eminent champion of structures, endorses two interesting theses concerning composition. First, that structure-making is a composition relation. Second, that it is not the only (fundamental) composition relation: Armstrong also believes in a mode of composition that he calls mereological, and which he takes to be the only kind of composition recognized by his philosophical adversaries, such as David Lewis. Armstrong, accordingly, is a kind of pluralist about compositional relations: there is more than one way to make wholes from parts. In this paper, I critically evaluate Armstrong's compositional pluralism.     

Referring to Natural Kind Thingamajigs,and What They Are: A Reply to Needham

Natural kind terms appear to behave like singular terms. If they were genuine singular terms, appearing in true sentences, that would be some reason to believe that there are entities to which the terms refer, the natural kinds. Paul Needham has attacked my arguments that natural kind terms are singular, referring expressions. While conceding the correctness of some of his criticisms, I defend and expand on the underlying view in this paper. I also briefly sketch an account of what natural kinds in fact are—natural complexes of sparse (natural) universals.     

Exemplification and Universal Realism

The relation between universal and particular is considered to be the Achilles’ heel of universal realism. However, modern universal realism with facts does not have the difficulties which traditional Platonic universal realism had. Its exemplification relation connecting particulars and universals in atomic facts is very different from Platonic participation. Bradley’s regress argument against the exemplification relation can be refuted in two different ways. Nevertheless, there are good reasons to avoid the assumption of an exemplification relation and thus to go without the Achilles’ heel altogether.     

The location problem in social ontology

Mental, mathematical, and moral facts are difficult to accommodate within an overall worldview due to the peculiar kinds of properties inherent to them. In this paper I argue that a significant class of social entities also presents us with an ontological puzzle that has thus far not been addressed satisfactorily. This puzzle relates to the location of certain social entities. Where, for instance, are organizations located? Where their members are, or where their designated offices are? Organizations depend on their members for their existence, but the members of an organization can be where the organization is not. The designated office of an organization, however, need be little more than a mailbox. I argue that the problem can be solved by conceptualizing the relation between social entities and non-social entities as one of constitution, a relation of unity without identity. Constituted objects have properties that cannot be reduced to properties of the constituting objects. Thus, my attempt to solve the Location Problem results in an argument in favor of a kind of non-reductive materialism about the social.     

Universals

In this paper, I argue that there are universals. I begin (Sect. 1) by proposing a sufficient condition for a thing’s being a universal. I then argue (Sect. 2) that some truths exist necessarily. Finally, I argue (Sects. 3 and 4) that these truths are structured entities having constituents that meet the proposed sufficient condition for being universals.     

Structural Universals as Structural Parts: Toward a General Theory of Parthood and Composition

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological composition. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail.     

The Permeability of Causal Criteria of Identity for Universals

To analyze the concept of a human merely in terms of the concept of a primate is to let all kinds of monkeys and apes into a category reserved for humans. Criteria of identity for universal attributes formulated merely in terms of causal roles associated with universals involve a similar permeability, since they cannot distinguish universals from non-universal attributes. Without appealing to the existence of noncausal universals or resorting to charges of circularity, I will show that causal criteria of identity for universals are insufficiently informative because they cannot capture a distinctive feature of universals.     

Ostrich Nominalism and Peacock Realism: A Hegelian Critique of Quine

Abstract

My aim in this paper is to offer a Hegelian critique of Quine’s predicate nominalism. I argue that at the core of Hegel’s idealism is not a supernaturalist spirit monism, but a realism about universals, and that while this may contrast to the nominalist naturalism of Quine, Hegel’s position can still be defended over that nominalism in naturalistic terms. I focus on the contrast between Hegel’s and Quine’s respective views on universals, which Quine takes to be definitive of philosophical naturalism. I argue that there is no good reason to think Quine is right to make this nominalism definitive of naturalism in this way – where in fact Hegel (along with Peirce) offers a reasonably compelling case that science itself requires some commitment to realism about universals, kinds, etc. Furthermore, even if Hegel is wrong about that, at least his case for realism is still a naturalistic one, as it is based on his views on concrete universality, which is an innovative form of in rebus realism about universals.     

Nomic Universals and Particular Causal Relations: Which are Basic and Which are Derived?

Armstrong holds that a law of nature is a certain sort of structural universal which, in turn, fixes causal relations between particular states of affairs. His claim that these nomic structural universals explain causal relations commits him to saying that such universals are irreducible, not supervenient upon the particular causal relations they fix. However, Armstrong also wants to avoid Plato’s view that a universal can exist without being instantiated, a view which he regards as incompatible with naturalism. This construal of naturalism forces Armstrong to say that universals are abstractions from a certain class of particulars; they are abstractions from first-order states of affairs, to be more precise. It is here argued that these two tendencies in Armstrong cannot be reconciled: To say that universals are abstractions from first-order states of affairs is not compatible with saying that universals fix causal relations between particulars. Causal relations are themselves states of affairs of a sort, and Armstrong’s claim that a law is a kind of structural universal is best understood as the view that any given law logically supervenes on its corresponding causal relations. The result is an inconsistency, Armstrong having to say that laws do not supervene on particular causal relations while also being committed to the view that they do so supervene. The inconsistency is perhaps best resolved by denying that universals are abstractions from states of affairs.

The Concrete Universal and Cognitive Science

Cognitive science depends on abstractions made from the complex reality of human behaviour. Cognitive scientists typically wish the abstractions in their theories to be universals, but seldom attend to the ontology of universals. Two sorts of universal, resulting from Galilean abstraction and materialist abstraction respectively, are available in the philosophical literature: the abstract universal—the one-over-many universal—is the universal conventionally employed by cognitive scientists; in contrast, a concrete universal is a material entity that can appear within the set of entities it describes, of which it represents the essential, paradigmatic case. The potential role of concrete universals in cognitive science is discussed.     

Rationality,Relativism, and Religion: A Reinterpretation of Peter Winch

Many point to Peter Winch’s discussion of rationality, relativism, and religion as a paradigmatic example of cultural relativism. In this paper, I argue that Winch’s relationship to relativism is widely misinterpreted in that, despite his pluralistic understanding of rationality, Winch does allow for universal features of culture in virtue of which cross-cultural understanding and even critique is possible. Nevertheless, I also argue that given the kind of cultural universals that Winch produces, he fails to avoid relativism. This is because in order to provide the standards without which relativism ensues, one requires a certain kind of criteria of rationality, namely, what I here call substantive universals, a kind of criteria which Winch rejects.     

Setting the Facts Straight

Substantial facts (or states of affairs) are not well-understood entities. Many philosophers object to their existence on this basis. Yet facts, if they can be understood, promise to do a lot of philosophical work: they can be used to construct theories of property possession and truthmaking, for example. Here, I give a formal theory of facts, including negative and logically complex facts. I provide a theory of reduction similar to that of the typed λ-calculus and use it to provide identity conditions for facts. This theory validates truthmaker maximalism: it provides truthmakers for all truths. I then show how the usual truth-in-a-model relation can be replaced by two relations: one between models and facts, saying that a given fact obtains relative to the model, and the other between facts and propositions: the truthmaking relation.     

A First Order Theory of Functional Parthood

This paper contains a formal theory of functional parthood. Since the relation of functional parthood is defined here by means of the notion of design, the theory of functional parthood turns out to be a theory of design. The formal theory of design I defend here is a result of introducing a number of constraints that are to express the rational aspects of designing practice. The ontological background for the theory is provided by a conception of states of affairs. The theory is accompanied with a formal model. I prove that the theory is sound and complete with respect to this model.     

Scattered Exemplification and Many-Place Copulas

Can there be relational universals? If so, how can they be exemplified? A monadic universal is by definition capable of having a scattered spatiotemporal localization of its different exemplifications, but the problem of relational universals is that one single exemplification seems to have to be scattered in the many places where the relata are. The paper argues that it is possible to bite this bullet, and to accept a hitherto un-discussed kind of exemplification relation called ‘scattered exemplification’. It has no immediate symbolic counterpart in any Indo-European natural language or in any so far constructed logical language. In order to remedy this, a notion called ‘many-place copula’ is introduced, too.     

Two Models of the Trinity?

Contrary to a common assumption, I argue that there is full agreement between East and West on the issue of the relation between the divine essence and the divine persons. I defend this claim by using the understanding of universals found in D. M. Armstrong to cast light on the theories. Taking Gregory of Nyssa and John of Damascus as representatives of the Eastern tradition, I show that this tradition sees the divine essence as a numerically singular object that is wholly present in each divine person. The Eastern tradition explicitly sees this object as a universal. The Western tradition – exemplified in Augustine and Aquinas – likewise sees the divine essence as a numerically singular object that is wholly present in each divine person. But this tradition customarily denies that such an object could be a universal, on the merely philosophical grounds that universals are divided amongst the particulars that share them, and thus cannot be numerically one. Having shown the fundamental consonance of the two traditions, I argue by way of conclusion that differences between social and non–social theories of the Trinity depend entirely on the nature and extent of the features that are supposed to distinguish the persons from each other.     

Structural Universals And Formal Relations

I will consider Armstrong's problems in trying to account for structural universals,i.e., a kind of complex universal whose instantiation by particulars involves differentparts of those particulars instantiating several basic properties and relations, such asthe property of being a molecule of methane. I present and criticise Armstrong's mostrecent attempt to explain structural properties by means of the identification of universals with types of states of affairs and I state my own solution to the problem by appealing to formal relations holding between particulars.     

Parthood and naturalness

Is part of a perfectly natural, or fundamental, relation? Philosophers have been hesitant to take a stand on this issue. One reason for this hesitancy is the worry that, if parthood is perfectly natural, then the perfectly natural properties and relations are not suitably “independent” of one another. (Roughly, the perfectly natural properties are not suitably independent if there are necessary connections among them.) In this paper, I argue that parthood is a perfectly natural relation. In so doing, I argue that this “independence” worry is unfounded. I conclude by noting some consequences of the naturalness of parthood.     

Sinnott-Armstrong,Walter, ed., Moral Psychology Volume 2. The Cognitive Science of Morality: Intuition and Diversity,Cambridge, Mass.: MIT Press, 2008, pp. xviii + 585, US$30 (paper)

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of denying each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive.