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The notion of a formal ontological relation is introduced and illustrated. Distinctions are drawn between various types of ontological dependence relations. The hierarchical character of systems of ontological categories is examined, together with the ontological status of such categories themselves. It is argued that neither ontological categories nor formal ontological relations, such as instantiation and characterization, should be regarded as elements of being, that is, as entities in their own right. A distinction is drawn between form and content in ontology, paralleling but distinct from a similar distinction commonly made in logic.

F. P. Ramsey’s objections to the universal/particular distinction, especially as advocated by Bertrand Russell, are examined in depth and rebutted. At the same time, certain important lessons are drawn from his arguments concerning how best to articulate the distinction. In response to related arguments recently directed against the four-category ontology by Fraser MacBride, it is shown how each of the four categories can be uniquely identified in terms of the characteristic pattern of ontological dependence relations that its members bear to members of other ontological categories.

This chapter focuses on the view that works of music are not types, but continuants or (as they are sometimes called) historical individuals. Two versions of the continuant view are discussed: musical perdurantism (which has been defended by Ben Caplan and Carl Matheson), and which takes a work of music to have its performances, playings, and other ‘embodiments’ as temporal parts; and the kind of view defended by Rohrbaugh, which takes a musical work to be a higher-level object, ontologically dependent upon, but not constituted by, its embodiments. The chapter outlines compelling objections to both versions of the continuant view, and argues that neither version can adequately explain what the repeatability of a work of music consists in.

Wedin considers the relation between the ontological commitment in the Categories and the semantical theory of underlying ontological configurations for standard categorical statements. According to Wedin, Aristotle's fourfold division of beings, which divides things according to whether they are, or are not, said of, and/or present in a subject, is a meta‐ontology that is concerned with beings per se, i.e. the fundamental things that are. Wedin explains that the primacy of c‐substance involves an asymmetry in the relation between c‐substance and everything else, or between the substantial and the nonsubstantial. This is because there is an ontological dependence of non‐substances, and also of secondary substances, on substances: everything is either said of, or in, primary substance. The argument of this chapter, then, is that the world of the Categories is a world of individuals: all ontological relations needed for semantics can be accommodated by appeal to individuals only.

Implicit in the criticism of mereological theories which permit the existence of arbitrary sums is the view that something cannot count as an individual, as one object, unless it is possessed of a certain degree of integrity or internal connectedness. There are problems with this criticism, however. First, arbitrary sums may be bizarre or ontologically wasteful, but they are algebraically neatening and appear not to lead to contradictions. Second, the properties said to keep individuals on the right side of respectability are hardly very clear. Integrity or connectedness, whatever they are, presumably come in degrees. Yet it seems to be counter-intuitive to suppose that there are degrees of being an individual. This chapter discusses ontological dependence, independence, substance, accident, disturbance, non-modal theories of foundation and dependence, and unconditional existence.

This chapter focuses on the question of whether concrete particular objects deserve to be classified as substances within a hylomorphic ontology, despite their metaphysical complexity, and, if so, according to what criterion of substancehood or “ontological privilege.” It is common to conceive of the substances as ontologically independent, following some preferred sense of “independence.” But what is this sense of “ontological independence” and do matter–form compounds qualify as substances when this notion is applied to them? This chapter discusses various relations defined in the literature under the heading of ontological dependence, beginning with existential construals of ontological dependence and turning next to construals of ontological dependence that are formulated in terms of a non-modal conception of essence. When evaluated against various plausible measures of success, it turns out that even the most promising candidate relations are open to objections.

If both the external and the internal world turn out to be less solid than we initially thought, one thing we can still hold on to is the certainty that something is real, even if the external world is not, and even if we and our internal world are not. This, of course, is the belief in the existence of an ultimate foundation that grounds all existence. This chapter considers a series of challenges to this idea. It begins by evaluating possible arguments for the existence of such a foundation, and then describes attempts to establish its opposite, a non-foundational view of reality, also considering what role this non-foundational view plays in particular sciences, such as mathematics, physics, and cognitive science.

The human mind often relies on external mechanisms for carrying out its cognitive processes, for example by using a calculator. Vehicle externalism and in particular the Extended Mind theory (Clark and Chalmers 1998) explore whether such external mechanisms, under specified conditions, are more than mere instruments for the mind; the claim is that they are parts of the mind and thus extend it beyond its outer boundaries of skin and skull. This chapter argues that high degrees of interdependence between the mind and its extensions give rise to ontological entanglements, with respect to which there is at present no theory of individuation which can tell us how many entities there are in the entanglement and what type of entity the entanglement is. The chapter argues that the Extended Mind theory sheds light on the problem of the incarnation by motivating, in a more intuitively compelling way, the need for new ways of thinking about oneness and distinctness. The problems we encounter with the metaphysics of the incarnation are not peculiar to it; the solutions might not be either.

I argue that Kit Fine’s essence-based account of ontological dependence is subject to various counterexamples. I first discuss Fine’s distinctive “schema-based” approach to metaphysical theorizing, which aims to identify general principles accommodating any intelligible application of the metaphysical notion(s) at issue. I then raise concerns about the general principles Fine takes to schematically characterize the notions of essence and dependence, which principles enter into his account of ontological dependence. The problem, roughly speaking, is that Fine supposes that an object’s essence makes reference just to what it ontologically depends on, but various cases suggest that an object’s essence can also make reference to what ontologically depends on it. As such, Fine’s essence-based account of ontological dependence is subject to the same objection he raises against modal accounts of essence and dependence—that is, of being insufficiently ecumenical.

In this chapter, a generic definition of fundamentality as an ontological minimality thesis is sought and its applicability examined. Many discussions of fundamentality are focused on a mereological understanding of the hierarchical structure of reality, which may be combined with an atomistic, object-oriented metaphysics. But recent work in structuralism, for instance, calls for an alternative understanding and it is not immediately clear that the conception of fundamentality at work in structuralism is commensurable with the mereological conception. However, it is proposed that once we understand fundamentality as an ontological minimality thesis, these two as well as further conceptions of fundamentality can all be treated on a par, including metaphysical infinitism of the ‘boring’ type, where the same structure repeats infinitely.

This chapter discusses and evaluates the role of truthmaking in articulating an unproblematic concept of emergence—specifically, the proposal that emergent properties should be characterized as those that, while “ontologically dependent”, are yet needed as truthmakers. It argues that while emergence so understood appears to avoid several well-known concerns about emergence and emergent properties, including those that stem from the alleged “brute determination” of emergent properties, this result is secured through the weak notion of dependence that it employs. The appeal to truthmaking, in contrast, proves largely superfluous. While truthmaking may thus not be able to play a significant role in emergentist metaphysics, it is argued that it is consistent with this verdict that truthmaking can play a more significant role in characterizing an attractive middle ground between reductive and nonreductive approaches to physicalism.

This chapter argues that commentators have misunderstood Spinoza’s claim that particular things are modes of God by holding that modes are either accidents that inhere in God or objects that do not inhere but are merely caused by God. Instead, it argues that modes in Spinoza must be understood as objects that inhere in God. Modes stand to substance as waves stand to the ocean, fists stand to hands, and wrinkles stand to carpets. It further argues that, in addition to avoiding criticisms to which others are subject, this interpretation allows an attractive account of inherence in terms of constitution. It concludes by considering the question of the reality of the modes: are the modes genuine beings or are they mere illusions?

Functionalism, or non-reductive physicalism, presupposes the possibility of multiple realization. Multiple realization, in turn, suggests an analysis of realization as an ontological dependence relation between entities that is distinct from other kinds of relations, such as identity, composition, or constitution. When seeking to discover whether a given entity is realized, one must ask a specific question: Is X realized by Y; similarly, questions about multiple realization will be contrastive: Is X realized by Y and Z? Within cognitive science, the questions of interest are whether psychological states are realized by brain states, and whether they are multiply realized by brain states as well as other kinds of states. Answers to these questions will depend on how the taxonomy of psychological states relates to the taxonomies of neuroscience as well, perhaps, as other sciences.

This chapter expands on the basic theory, which is presented in the Categories. It offers a treatment of the mereotopological properties of bodies, for instance, what belongs to them insofar as they are bodies of physical substances. Bodies are complete and perfect in virtue of being three‐dimensional. Body is prior to surfaces and lines and, because bodies are complete, there cannot be a four‐dimensional magnitude. The explanation offered is that certain topological properties are linked to and determined by the nature of the object in question. Body is a composite of the boundary and the interior or extension. A formal characterization of boundaries as limit entities is offered and it is argued that boundaries are dependent particulars. Similarly, the extension is ontologically dependent on bodies. Aristotle’s argument that the extension of objects is divisible into ever‐divisibles is revisited.