Relations

In numerous works, Dame Professor Marilyn Strathern has written of the concept of a relation in her discipline, social anthropology. This paper was prompted by Strathern’s 2025 description of how, as a student, she needed to be told by Esther Goody that societies in conflict are in a relationship: a relationship of enmity. I present an attractive thesis on the Victorian debate between evolutionism versus diffusionism, according to which only the latter always requires the concept of a relation in all (...) its explanations of shared features. I then introduce how relations are normally understood in contemporary analytic philosophy. If we work with this normal understanding, the thesis must be rejected. (shrink)

This paper develops a structural critique of classical theism by formalizing a mapping failure between the modal architecture of the divine nature and the branching structure of the actual world. Moving beyond propositional contradictions, I argue that classical theism suffers from two fundamental grounding failures. -/- First, External Misalignment: using a rooted branching-time model and the Axiom of Historical Priority (AHP), I demonstrate that no structure-preserving mapping exists between the divine modal system and the actual world. The "Hard Anchor" of (...) actualized history—containing gratuitous suffering and epistemic opacity—generates modal vectors that the divine nature cannot ground without violating its own essential necessities. -/- Second, Internal Incoherence: I argue that because grounding is hyperintensional, the necessities generated by distinct divine attributes (such as Goodness, Freedom, and Relationality) interact to produce incompatible modal commitments prior to creation. -/- These results yield a Structural Trilemma: one cannot simultaneously maintain a unitary necessary ground, a branching historical root, and grounding-theoretic consistency. Beyond theism, the paper establishes a novel meta-metaphysical category of "Structural Impossibility"—worlds that are propositionally consistent but architecturally ungroundable—offering a new diagnostic tool for formal ontology. (shrink)

In his Examination of Relations (Sambandhaparīkṣā), Dharmakīrti rejects the existence of mind-independent relations. Instead, on his view, all relations are merely conceptual constructs. While this is a significant conclusion on its own, several of Dharmakīrti’s Indian and Tibetan commentators argue that his denial of real relations has far-reaching implications for the ontological status of everything that we generally take to populate the world—both persons and ordinary objects. This paper focuses on the case of persons. After providing an overview of Dharmakīrti’s (...) own view on the status of persons and relations, I show how three of his commentators rely on the rejection of a different kind of relation to rule out the possibility of an autonomous self: Śaṅkaranandana’s argument turns on rejecting an inherence relation, Chomden Reldri’s on an agential relation, and Gyaltsab Darma Rinchen’s on an autonomy relation. I develop an analysis of Gyaltsab’s apparently novel proposal of an autonomy relation, and I argue that, of these three commentators, Gyaltsab’s argument looks the most promising. I conclude by considering how the claims of these commentators may be reconciled with the prima facie incompatible conclusions of Dharmakīrti himself concerning the nature of things. (shrink)

I develop and defend a new theory of naturalness according to which relations can be natural to different degrees relative to their different positions. Set-membership, for example, is more natural relative to its set-position than to its member-position. I call this view position-relativism. The alternative view, position-absolutism, implies that existential derivatives of the same non-symmetric relation—such as being a member of something, and having something as a member—must always have the same degree of naturalness. But this is false. Position-relativism avoids (...) this problem and promises to do more. (shrink)

According to directionalism, non-symmetric relations are distinct from their converses. Kit Fine (2000) argues that the directionalist faces a dilemma; they must either (i) reject the principle Uniqueness, which states that no completion (fact, state of affairs, or proposition) is a completion of more than one relation, or (ii) reject the principle Identity, which states that each completion of a relation is identical to a completion of its converse (e.g., Dante’s loving Bice is identical to Bice’s being loved by Dante). (...) Fine’s argument has been regarded as a decisive blow to directionalism. But new strategies for replying to it can be developed with the tools of the postmodal metaphysician, who is comfortable individuating relations and their completions hyperintensionally, allowing for necessary connections between distinct entities, and making use of hyperintensional notions like essence and grounding. In what follows, I develop postmodal strategies for denying both horns of Fine’s dilemma, concluding that the postmodal directionalist need not be concerned with Fine’s argument. (shrink)

In this paper, I first argue for a relational account of the concept of ontological form and its difference from being. The former is explicated by the concepts of character-neutral internal relation and existence or being and that the ontological forms of entities consist in these formal ontological relations in which the entities stand. Secondly, I apply this account to ontological categories and their membership-determination, existence and reality. Here I also defend a relational view that categories are construed as pluralities (...) of entities standing in the same formal ontological relations in the same order. Formal ontological relations are not additional entities to their relata because they are internal relations. Therefore, categories do not exist as entities numerically distinct from their members. Yet their membership is determined by formal ontological relations actually holding among entities. My accounts are nominalist since ontological forms and categories are not universal or general entities of any sort. (shrink)

In this review I take to task the related views of E.J. Lowe, John Heil and Peter Simons according to which relations don't exist because they're dispensable qua truth-makers. I argue that this view is methodologically unstable because we also have reason to believe that relations exist because our best mathematical and scientific theories say so, i.e. quantify over them.

‘Substance’ (substantia, zelfstandigheid) is a key term of Spinoza’s philosophy. Like almost all of Spinoza’s philosophical vocabulary, Spinoza did not invent this term, which has a long history that can be traced back at least to Aristotle. Yet, Spinoza radicalized the traditional notion of substance and made a very powerful use of it by demonstrating – or at least attempting to demonstrate -- that there is only one, unique substance -- God (or Nature) -- and that all other things are (...) merely modes or states of God. Some of Spinoza’s readers understood these claims as committing him to the view that only God truly exists, and while this interpretation is not groundless, we will later see that this enticing and bold reading of Spinoza as an ‘acosmist’ comes at the expense of another audacious claim Spinoza advances, i.e., that God/Nature is absolutely and actually infinite. But before we reach this last conclusion, we have a long way to go. So, let me first provide an overview of our plan. In the first section of this paper we will examine Spinoza’s definitions of ‘substance’ and ‘God’ at the opening of his magnum opus, the Ethics. Following a preliminary clarification of these two terms and their relations to the other key terms defined at the beginning of the Ethics, we will briefly address the Aristotelian and Cartesian background of Spinoza’s discussion of substance. In the second section, we will study the properties of the fundamental binary relations pertaining to Spinoza’s substance: inherence, conception, and causation. The third section will be dedicated to a clarification of Spinoza’s claim that God, the unique substance, is absolutely infinite. This essential feature of Spinoza’s substance has been largely neglected in recent Anglo-American scholarship, a neglect which has brought about an unfortunate tendency to domesticate Spinoza’s metaphysics to more contemporary views. The fourth section will study the nature of Spinoza’s monism. It will discuss and criticize the interesting yet controversial views of the eminent Spinoza scholar, Martial Gueroult, about the plurality of substances in the beginning of the Ethics; address Spinoza’s claim in Letter 50 that, strictly speaking, it is improper to describe God as “one”; and, finally, evaluate Spinoza’s kind of monism against the distinction between existence and priority monism recently introduced into the contemporary philosophical literature. The fifth and final section will explain the nature, reality, and manner of existence of modes. We therefore have an ambitious plan; let’s get down to business. (shrink)

Facts (and, more generally, states of affairs) are plausibly individuated in an at least moderately coarse-grained way: the fact that this rose is red should not be distinguished from the fact that this rose fails to fail to be red. Something similar can be said for properties and relations. It is relatively easy to formulate principles that entail that the individuation of states of affairs, properties, and relations—in brief, intensional entities—is coarse-grained enough to conform to this idea. It is less (...) easy to devise a complementary principle that imposes an *upper* bound on the coarse-grainedness of intensional entities. A promising approach to this problem is to formulate a principle according to which the *fundamental* entities (including fundamental properties and relations) are freely recombinable or ‘logically independent’; but certain special provisions that have to be made with regard to relations tend to render such a principle unattractively complex. In this paper I put forward a simpler principle, based on a broadly positionalistic conception of relations. (shrink)

I propose a novel metaphysical explanation of identity and distinctness facts called the Modal Proposal. According to the Modal Proposal, for each identity fact – that is, each fact of the form a=b – that fact is metaphysically explained by the fact that it is necessary that the entities involved are indiscernible, and for each distinctness fact –that is, each fact of the form a≠b – that fact is metaphysically explained by the fact that it is possible for the entities (...) involved to be discernible. I argue that the Modal Proposal has greater payoffs at less cost than any of its competitors. It gives simple, uniform, and intuitive explanations of identity and distinctness that conserve longstanding philosophical insights about identity that go back to Leibniz. It does this while making our fundamental base more parsimonious, determining whether controversial cases of identity or distinctness are possible, and expanding our understanding of these central philosophical relations. It does all this while avoiding controversial ontological commitments. (shrink)

A large number of diversity measures have been proposed in the literature, almost all of which are designed for sets with elements that differ in multiple aspects. However, these types of measures are not appropriate for sets with elements that differ in a single aspect only, such as duration, value or probability. In this essay I present a new measure of diversity, designed specifically for single aspect diversity. The measure captures the intuitive idea that single aspect diversity is affected by (...) the maximal dissimilarity between the elements, the number of different elements, and the even spacing of the elements’ aspect values, when represented as points in one dimension. I show that the measure satisfies six plausible conditions for a single aspect diversity measure, which concern scale independence, minimal diversity, maximal dissimilarity, restricted function growth, strict monotonicity, and even spacing. The measure is also characterised. (shrink)

This dissertation defends the existence of relations and their role in constructing structural universals���complex, multiply-located properties. Chapter 1 reviews historical debates on the existence of relations, advocates for a truth-making approach to ontology, and argues that relations are required as truth-makers for relational claims. Chapter 2 examines two competing theories of relations—Positionalism and Anti-Positionalism—as potential truth-makers for relational claims, showing that Positionalism provides a more satisfactory account. Chapter 3 critiques contemporary theories of structural universals and demonstrates how Positionalist relations overcome (...) these critiques by abstracting structural universals from complex states of affairs constructed through Positionalist relations. Chapter 4 defends the abstract nature of Positionalist relations, showing that Positionalism possesses greater explanatory power in addressing the problems of multiple realizability, order, and converse relations. (shrink)

Contemporary ontology faces a fundamental challenge: How can entities exist in relation to their environments without reducing them to mere relations or isolated substances? This paper develops a spatial ontology that goes beyond the relationism-substantialism debate by examining how entities relate to their surroundings through what I term “spatial weavings”. Drawing on phenomenological analysis and biological examples, I argue that entities exist through dynamic spatial engagements that are neither reducible to network effects nor explicable as interactions between pre-given objects. Using (...) Heidegger’s analysis of spatial existence and Sartre’s inversion of essence and existence, I demonstrate that spatiality is not a container for entities, but the fundamental structure through which entities become what they are. This approach contributes to post-correlationist ontology by grounding ontology in the concrete spatial practices through which entities encounter their environments. The paper concludes by extending this analysis beyond human existence to develop a general theory of spatial being that encompasses biological, technical, and material entities. (shrink)

Can we, in keeping with Fine’s celebrated distinction between essential and merely-necessary properties, account for essence in terms of necessity plus something else? One appealing idea is that essence can be accounted for in terms of necessity plus intrinsicality. However, as brought out recently by Zylstra, if intrinsicality is treated as a feature which properties and relations possess tout court, a necessity-plus-intrinsicality account will not deliver the goods on Fine’s celebrated example of Socrates and the set containing him. I argue (...) that, if we have available a notion of intrinsicality which applies to relations in a place-relative way, we avoid the problem. I give independent motivation for the idea that intrinsicality is place-relative, and discuss the philosophical options for understanding place-relative intrinsicality in a way that is suitable for a necessity-plus-intrinsicality account of essence. (shrink)

In this article, we pursue the definition of an ontological framework and a species of ontologies called “epistemic ontologies” by focusing on the complex entities, physical and mental, that populate the world. These entities unify other entities on which they unilaterally existentially depend. These complex entities include states of affairs (in the physical sphere) and propositions and events (in the mental sphere). To account for their unity, we appeal to the ontological figure of ‘connection’, in reference to Gustav Bergmann's notion (...) of nexus. On the physical side, we identify different kinds of connections, namely connections of particular qualities to their carrier object, and connections of objects and processes to each other. We conjecture that physical states of affairs are exclusively connections. On the mental side, we equate relations with the conceptual constituents of our knowledge of the world, whose role is to put together entities. We conjecture that there are no physical relations. (shrink)

I begin by explaining the four contexts in which relations are discussed in Summa logicae, and giving some basic terminology. After explaining the difference between metaphysical realism and nominalism relevant to these contexts, I will briefly exposit the logical, theological, and methodological tools Ockham uses to obtain his own conclusions. Finally, I show where in the text he applies these tools to each of the four contexts, and close by speculating on the interesting differences between Ockham’s treatment of relations in (...) Summa logicae as opposed to his theological works. (shrink)

One of the main ontological challenges posed by quantum mechanics is the problem of the indistinguishability of so-called “identical” particles, that is, particles that share the same state-independent properties. In the framework of this philosophical problem, a quasi-set theory was formulated to provide a proper metalanguage to deal with quantum indistinguishability; this theory included certain Urelemente called m-atoms, representing essentially indistinguishable objects. In turn, over the last two decades, the Modal Hamiltonian Interpretation proposed an ontology of properties, totally devoid of (...) objects, where quantum systems are bundles of instances of universal properties. Therefore, the original quasi-set theory, with its m-atoms, does not adequately reflect the structure of an ontology devoid of objects. The purpose to the present article is to introduce a new quasi-set theory that does not include atoms at all: elementary items correspond to properties and are also represented by quasi-sets, which can be only numerically different. The final aim is to apply this new quasi-set theory to the MHI ontology. (shrink)

This book addresses the issue of natural simultaneity of relatives, discussed by Aristotle in Categories 7, 7b15-8a12. Natural simultaneity is a form of symmetrical ontological dependence that holds between items that are not causally linked. In this section of the Categories, Aristotle introduces this topic in his analysis of relatives and maintains that, although relatives seem to be for the most part simultaneous by nature, there seem to be some exceptions. He mentions two pairs of relatives as exceptions, namely the (...) pairs knowledge/knowable and perception/perceptible, and argues at length for the priority of the second relative over the first one in each case. Through a close reading of this text, the author analyses Aristotle's arguments for the thesis of the exceptional character of these pairs and shows that all of them are unsuccessful in supporting the thesis. In order to draw this conclusion, the author highlights and carefully considers the properties that Aristotle is committed to attributing to relatives, taking into account the metaphysical framework of the Categories as well as their specificities within the set of non-substantial categories. Then, he shows that Aristotle's mature views on relatives in the Metaphysics can be construed as committing him to the rejection of such a thesis. Although the issue of natural simultaneity is just one of several that Aristotle considers in his discussion of relatives throughout Categories 7, it is a particularly relevant issue, since it involves a number of puzzles whose analysis allows for a better understanding of the very notion of relativity in Aristotle. This is the first book to explore this issue from the perspective of illuminating the Aristotelian views on relatives. Aristotle on Natural Simultaneity of Relatives in the Categories will appeal to scholars and graduate students working on Aristotle, ancient philosophy in general, and metaphysics. (shrink)

2025 update of the entry "Properties".

I discuss Rooney’s criticisms of structural hylomorphism and defend the later form of hylomorphism. I argue that the problems raised by Rooney are not unique to structural hylomorphism but also affect other forms of hylomorphism that treat forms as non-structural and non-relational entities. A plausible solution lies in understanding structures as external relational modes, which avoids the problematic regresses. I then challenge Rooney’s identitarian hylomorphism, arguing that material substances cannot be numerically identical with composites of a form and matter. This (...) position, which I label "active nihilism," holds that material substances are simple entities, yet still assigns crucial roles to composites of form and matter. (shrink)

This book provides an exhaustive overview of the ontology of relations. Moreover, it offers a detailed defense of the existence of irreducible relations in the universe and shows that entities such as powers should be better thought of as relations. At first, the author discusses many classical arguments for and against the existence of relations and draws preliminary distinctions between internal and external relations and symmetrical and non-symmetrical relations. He defends the existence of irreducible relations against several objections, most notably (...) three Bradleyan regresses. In response to these objections, the author argues that both internal and external relations should be thought of as relational modes and that intentional, temporal and spatial relations are external. He also presents several problems that are typically taken to affect non-symmetrical relations and introduces one new version of a theory to deal with them-the O-role theory. Finally, the author explores essential dependence relations and causal dependence relations and defends the view that power are relational modes. The Ontology of Relations will be of interest to scholars and advanced students working in metaphysics, philosophy of science, and history of philosophy. (shrink)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorising about properties, relations, and states of affairs – or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, (...) understood as a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Objects have, and themselves are, parts. If we endorse a sufficiently liberal notion of object, anything is an object and anything, excluding the universe, is a part of some larger one. If we think that the universe, too, is an object, then any object is a part of it. What is it, then, for an object to be a part? Contra the orthodoxy, in my dissertation I argue that to be a part is no more a relation than to exist (...) is a property. In fact, to be a part is just to be the value of a variable in the range of a quantifier whose interpretation has been extended. When I say that, for instance, my hand is a part of my body, I am not making the claim that two objects in the domain of quantification my hand and my body—stand in a certain relation of ordering—being a part of—to one another. Rather, I am making the claim that the domain of quantification, which used to include my body but not my hand, has been expanded and now includes my hand. For the hand to be a part (of my body, but most importantly of the universe) is for it to exist in an expansion of the quantification domain. As I construe it, the operation of re-interpreting the quantifiers—and, so, of individuating parts of objects—is both modal (the interpretations of the quantifiers are indefinitely extensible) and actuality-bound (the modality at play operates across interpretations, rather than across possible worlds). In the resulting ontology, the universe itself (i.e. effectively, the actual world) is the only object that exists before we start individuating its parts—that is to say, before we start expanding our domain. As such, individuating parts is an operation that is generative (with each re-interpretation, the domain includes new objects, which replace the previous ones, and its cardinality is higher than that of the domains associated with previous, less extended interpretations); maximally general (any new object is a part); and world-bound (every new object is a part of the universe). Insofar as it is indefinitely extensible, the interpretation of our quantifiers can always be extended, but does not need to be. Insofar as individuating the parts of any object is expanding the domain of quantification, the universe, which is the only object that exists in the non-expanded domain, is itself part-less, albeit extended. Similarly, the objects existing at further levels of expansions are, too, themselves part-less, for individuating their parts is, once again, expanding the domain. Mereological complexity is, strictly speaking, quantificational complexity. The dissertation is written as three papers. In the first paper, “Composition as Analysis: The Meta-Ontological Origins and Future of Composition as Identity” I argue that a non-trivial formulation of the claim that a composite object is the same as its parts requires that we construe parthood quantificationally. I then suggest that we construe the system of domain expansions as an information ordering and interpret the corresponding many-one identity statements as metaphysically informative. In the second paper, “Parthood Without Mereology,” I present an antinomic result for parthood: that we cannot both construe coincident objects as numerically distinct and mereologically indiscernible while also claiming that absolutely every object coincides with at least one other object. I blame a relational account of parthood for this result and argue that switching to a quantificational account is needed both to make sense of the problem and to find a solution. In the third and last paper, “To be said of as a quantifier: quantity, parts, and the invention of ontology in Aristotle’s Categories,” I take on an interpretive challenge from Aristotle’s Categories and show that the challenge could be met by appreciating that Aristotle has a non-relational notion of parthood and re-thinking his account of quantity on that basis. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

This paper will examine the Küng-Armstrong trilemma against Class Nominalism. We will see that combining Class Nominalism and Zermelo-Fraenkel set theory (ZF) can provide us with a sophisticated version of Class Nominalism, namely ZF-Class Nominalism, which successfully addresses the objection and leads to a moderate version of ineffabilism about the putative set-membership relation.

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of functional (...) decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

Is second-order logic logic? Famously Quine argued second-order logic wasn't logic but his arguments have been the subject of influential criticisms. In the early sections of this paper, I develop a deeper perspective upon Quine's philosophy of logic by exploring his positive conception of what logic is for and hence what logic is. Seen from this perspective, I argue that many of the criticisms of his case against second-order logic miss their mark. Then, in the later sections, I go beyond (...) Quine to develop a novel case that quantification into polyadic predicate position, understood as requiring quantifiers to range over relations, isn't intelligible. (shrink)

There is an ongoing debate on the ontology of relations, which features four main competing approaches: directionalism, positionalism, anti-positionalism, and primitivism. This paper focuses on a particular version of positionalism, namely role positionalism, and proposes the results of an experimental philosophy research concerning aspects of it. We tested the intuitions of ordinary subjects regarding the inter-relational generality of the roles typically assumed for spatial and kinematic relations, namely source, destination, theme, location. According to a 2014 paper by Orilia, this generality (...) is rather wide, as it encompasses relations of temporal order, causation, quantitative order, transaction, possession, and parthood. Our findings do not support this proposal, except for parthood, and, in a limited way, for temporal order. We also tested the intuitions of ordinary subjects regarding the contrast between the pro-converses option, according to which non-symmetric relations split into distinct converse relations, and the anti-converses option, according to which non-symmetric relations have no distinct converses. Although traditionally positionalism is associated to the latter option, in recent works by Orilia role positionalism is associated to the former option for at least some relations, while remaining anchored to the latter option for other relations. Our findings support this mixed line to some extent, but not quite in the way suggested by Orilia in such works. (shrink)

This essay critically discusses the rising interest in process philosophy in recent years. I argue that the appeal of process philosophy lies in its ability to circumnavigate the binary dichotomies pervasive in European philosophy and defend an interpretation of process philosophy in terms of relationality, difference, and change. After outlining the central tenets of process philosophy, Graham Harman’s critique of a relational account of process philosophy is examined, particularly his assertion that this type of philosophy cannot fully explain genuine change. (...) Despite the merits of Harman’s critique, I will show that his object-oriented ontology faces similar limitations. Turning to Graham Priest’s dialethism I suggest that philosophy, instead of striving for a consistent representation of fundamental metaphysics, must embrace paradox to some extent. This leads the philosophical discipline to understand itself as a transformative process. (shrink)

The paper presents an extension of the metaphysics of self-subsisting structures set out in a companion paper to the realm of non-relativistic quantum physics. The discussion is centered around a Pure Shape Dynamics model representing a relational implementation of a de Broglie-Bohm N-body system. An interpretation of this model in terms of self-subsisting structures is proposed and assessed against the background of the debate on the metaphysics of quantum physics, with a particular emphasis on the nature of the wave function. (...) The analysis shows that elaborating an appropriate Leibnizian/Machian metaphysics of the quantum world requires a substantial revision of the notion of world-building relation. (shrink)

Dharmakīrti’s (c. seventh century) Examination of Relations (Sambandhaparīkṣā) is unique in the Indian Buddhist canon for its being the only extant root text devoted entirely to the topic of the ontological status of relations. But the core thesis of this treatise—that relations are only nominally real—is in prima facie tension with another claim that is central to Dharmakīrti’s epistemology: that there exists some kind of “natural relation” (svabhāvapratibandha) that reliably underwrites inferences. Understanding how Dharmakīrti can consistently rely on natural relations (...) to prop up his presentation of inferential reasoning while at the same time advancing an anti-realist account of relations is critical for making sense of his system of logic and epistemology, which came to be nearly universally adopted in Tibetan Buddhism cutting across traditions. Chomden Rikpé Reldri (1227–1305), who was perhaps the most prolific commentator on logic and epistemology in the history of Tibetan philosophy, composed two texts commenting on the Examination of Relations, neither of which have received any scholarly attention to date. In this paper, I provide an introduction to Chomden Reldri’s two commentaries and consider how they may illuminate Dharmakīrti’s text and also what they reveal about the understanding of Dharmakīrti’s account of relations in early Tibetan scholasticism. I then present a translation of Dharmakīrti’s Examination of Relations together with Chomden Reldri’s commentary, Annotations and Topical Outline of the Examination of Relations (’Brel pa brtag pa’i mchan dang sa bcad gnyis). (shrink)

There are two ways to characterize symmetric relations. One is intensional: necessarily, _Rxy_ iff _Ryx_. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do ‘strictly symmetric’. Is there is a difference between the notions of necessary and strict symmetry that would prevent them (...) from being used interchangeably in such discussions? I show that there is. While the notions coincide assuming an intensional account of relations and their completions, according to which relations/completions are identical if they are necessarily coinstantiated/equivalent, they come apart assuming a hyperintensional account, which individuates relations and completions more finely on the basis of relations’ real definitions. I establish this by identifying two definable relations, each of which is necessarily symmetric but nonetheless results in distinct facts when it applies to the same objects in opposite orders. In each case, I argue that these facts are distinct because they have different grounds. (shrink)

At least since Russell, mainstream analytic philosophy has distinguished internal and external relations and acknowledged the existence of both. This seems in line with both the manifest and scientific images of the world. However, there is a recent deflationary trend about relations, which focuses on the truthmakers of relational statements in order to show that putative external relations are in fact internal, and that internal relations do not really exist. Lowe’s posthumous 2016 paper is a thorough presentation of this line (...) of thought. This article critically analyzes Lowe’s arguments in that paper, and some related arguments in recent works. It finds them wanting and thus reaffirms the irreducible reality of relations. (shrink)

I shall refine in this article Jaegwon Kim's theory of events by appealing to modes, i.e., particular properties that also depend on their 'bearers' for their identity. Events will turn out to be occurrent modes, i.e., relational modes having further modes and times as their relata. In Section 1 I shall briefly present Kim's theory and some difficulties that affect it. In Section 2, after having made some preliminary assumptions on modes and universals, I shall introduce occurrent modes. In Section (...) 3 I shall show how my theory can deal with the difficulties discussed in Section 1. (shrink)

Relationism holds that objects entirely depend on relations or that they must be eliminated in favour of the latter. In this article, I raise a problem for relationism. I argue that relationism cannot account for the order in which non-symmetrical relations apply to their relata. In Section 1, I introduce some concepts in the ontology of relations and define relationism. In Section 2, I present the Problem of Order for non-symmetrical relations, after distinguishing it from the Problem of Differential Application. (...) I also examine four main existing strategies to solve it. In Section 3, I develop my argument. The first step consists in arguing that—among those strategies—relationism can only accept directionalism. The second step consists in arguing that directionalism is affected by a serious problem: the Problem of Converses. I also show that relationists who embrace directionalism cannot solve this problem. In Section 4, I introduce and rebut several strategies on behalf of relationists to cope with my argument. In Section 5, I briefly draw some conclusions. (shrink)

It is a metaphysical orthodoxy that interesting non-symmetric relations cannot be reduced to symmetric ones. This orthodoxy is wrong. I show this by exploring the expressive power of symmetric theories, i.e. theories which use only symmetric predicates. Such theories are powerful enough to raise the possibility of Pythagrapheanism, i.e. the possibility that the world is just a vast, unlabelled, undirected graph.

Foundational relations play an important role in the ontological foundations of conceptual modeling. Their investigation has been theoretically addressed in philosophical/ontological theories, and empirically offered in foundational ontologies (FOs). FOs are comprehensive theories that model the world as top-level entities and relations. Empirically, for modelers aiming to use foundational relations without an urge for entity types, FOs seem to be complex to comprehend, comply with, and integrate in practice. And since the practice of these relations is critical for conceptual modeling (...) tasks, we present an approach that builds a well-founded entity-type free relations theory within a first-order-logic formalization, besides large complex FOs. The theory contributes to a minimal set of foundational ontological relations (FORT) by importing extant theories (mereotopology and location) and (re-)formalizing other relations (dependence, membership, constitution, and entity-location), while no FO has compromised this set. (shrink)

Since the publication of Hume’s Treatise, scholars have been divided on how to interpret the ontology of Humean relations. In particular, is Hume’s theory of relations consistent with positivism, (skeptical) realism, or anti-realism? In this essay, I propose a novel distinction separating impressions and ideas from relations such that relations are construed as forming a distinct category equal to impressions and ideas. In so doing, I interpret Hume as fundamentally agnostic toward the ontology of relations.

Hume’s account of contrariety in Book I of the Treatise poses several interpretive puzzles. I consider each in turn and offer a novel interpretation of contrariety based on Hume’s discussion of the passions. That Book II and Book I form a complete chain of reasoning suggests that the way in which passions are related is analogous to the way in which ideas are related in the understanding. I argue that Hume identifies three species of empirical contrariety in Book II: contraries, (...) oppositions, and contradictions. All three species help clarify Hume’s remarks concerning contrariety in Book I. I further identify a second genus I call logical contrariety by drawing on Hume’s discussion of fictitious duration and distance. (shrink)

Maureen Donnelly has recently argued that directionalism, the view that relations have a direction, applying to their relata in an order, is unable to properly treat certain symmetric relations. She alleges that it must count the application of such a relation to an appropriate number of objects in a given order as distinct from its application to those objects in any other ordering of them. I reply by showing how the directionalist can link the application conditions of any fixed arity (...) relation, no matter its arity or symmetry, and its converse(s) in such a way that directionalism will yield the correct ways in which it can apply. I thus establish that directionalism possesses the same advantage Donnelly’s own account of relations, relative positionalism, has over traditional positionalist accounts of relations, which do not properly treat symmetric relations. I then note some advantages that directionalism has over its closest competitors. This includes Donnelly’s relative positionalism, since directionalism is not, like relative positionalism, committed to the involvement of relative properties in every irreducibly relational claim. I close by conceding that, as Donnelly notes, directionalism is committed to the primitive relation of order-sensitive relational application. But I don’t find this notion as mysterious as Donnelly does. I conclude that, even if one construes this feature of directionalism as a drawback, the two views are at worst at a draw, other things being equal, since this drawback is mitigated by the advantage directionalism has over relative positionalism. (shrink)

David Lewis is typically interpreted as a class nominalist. One consequence of class nominalism, which he embraced, is that the reduction of ordered pairs, triples, etc to unordered sets of sets is conventional. The reaction by his Australian counterparts D.M. Armstrong and Peter Forrest was that Lewis was not being ontologically serious. This chapter evaluates this debate over serious ontology. It is argued that in one sense Lewis is ontologically serious, but that his additional commitment to structuralism about classes should (...) push him to adopt a trope-theoretic account of naturalness, which opens up another way to respond to the charge of not doing serious ontology. This conclusion is supported by certain remarks he makes in his correspondence, thus revealing how his thinking about properties appears to have evolved from property-egalitarianism to a sparse theory of tropes. (shrink)

I formulate an account, in terms of essence and ground, that explains why atomic Russellian propositions have the truth conditions they do. The key ideas are that (i) atomic propositions are just 0-adic relations, (ii) truth is just the 1-adic version of the instantiation (or, as I will say, holding) relation (Menzel 1993: 86, note 27), and (iii) atomic propositions have the truth conditions they do for basically the same reasons that partially plugged relations, like being an x and a (...) y such that Philip gave x to y, have the holding conditions they do. The account is meant to be mainly of intrinsic interest, but I hope that it goes some distance toward answering an objection to classical theories of propositions put forward by King (2014), who writes that ‘since the classical conception of propositions as things that have truth conditions by their very natures and independently of minds and languages is incapable of explaining how or why propositions have truth conditions, it is unacceptable’ (2014: 47). Propositions do have their truth conditions ‘by their very natures’ and ‘independently of minds and languages’. But a fact about a given entity can hold by the very nature of that entity without being a fundamental fact. I argue that this is plausibly the case for atomic Russellian propositions and the facts about their truth conditions. A fact about the truth conditions of such a proposition holds by the very nature of the given proposition but is metaphysically grounded in facts about that proposition’s parts and their essences. If my account is correct, then the supposedly intractable problem of explaining why the given propositions have the truth conditions they do reduces to the problem of explaining why relations have the holding essences they do, which few seem to have found worrisome . (shrink)

F. H. Bradley’s relation regress poses a difficult problem for metaphysics of relations. In this paper, we reconstruct this regress argument systematically and make its presuppositions explicit in order to see where the possibility of its solution or resolution lies. We show that it cannot be answered by claiming that it is not vicious. Neither is one of the most promising resolutions, the relata-specific answer adequate in its present form. It attempts to explain adherence (relating), which is a crucial component (...) of the explanandum of Bradley’s relation regress, in terms of specific adherence of a relational trope to its relata. Nevertheless, since we do not know the consequences and constituents of a trope adhering to its specific relata, it remains unclear what specific adherence is. It is left as a constitutively inexplicable primitive. The relata-specific answer only asserts against Bradley. This negative conclusion highlights the need for a metaphysical account of the constitution of the holding of adherence. (shrink)

Contrary to widely shared opinion in analytic metaphysics, E.J. Lowe argues against the existence of relations in his posthumously published paper There are probably no relations (2016). In this article, I assess Lowe’s eliminativist strategy, which aims to show that all contingent “relational facts” have a monadic foundation in modes characterizing objects. Second, I present two difficult ontological problems supporting eliminativism about relations. Against eliminativism, metaphysicians of science have argued that relations might well be needed in the best a posteriori (...) motivated account of the structure of reality. Finally, I argue that, by analyzing relational inherence, trope theory offers us a completely new approach to relational entities and avoids the hard problems motivating eliminativism. (shrink)

We argue that traditional formulations of the reduction thesis that tie it to privileged relational operations do not suffice for Peirce’s justification of the categories and invite the charge of gerrymandering to make it come out as true. We then develop a more robust invariant formulation of the thesis, one that is immune to that charge, by explicating the use of triads in any relational operations. The explication also allows us to track how Thirdness enters the structure of higher order (...) relations and even to propose a numerical measure of it. Our analysis reveals new conceptual phenomena when negation or disjunction are used to compound relations. (shrink)

A many-faceted beast, the metaphysics of relations can be approached from many angles. One could begin with the various ways in which relational states are expressed in natural language. If a more historical treatment is wanted, one could begin with Plato, Aristotle, or Leibniz. In the following, I will approach the topic by first drawing on Russell’s Principles of Mathematics [-@russell_b:1903] (still a natural-enough starting point), and then turn to a discussion mainly of positionalism. The closing section contains an overview (...) of the six contributions to this Special Issue. (shrink)

There is a tension in Santayana's ontological system, one that is generated by the interactions of his doctrine of existence, doctrine of systematization, and critical agnosticism on the infinity of material substance. From and, in conjunction with what will be called the expansionist postulate, an infinite material expansion is generated, one that is in conflict with. This tension is remediated by a coherentist proposal regarding Santayanan existence, the relevant feature of which is that existents at distinct orders of organization are (...) in symmetrical dependence relations. "Metaphysical coherentism," which has recently been described as "one of the least explored areas in contemporary... (shrink)

The model of a closed linear measure space, which can be used to model Aristotle’s treatment of motion (kinesis), can be analogically extended to the qualitative ‘spaces’ implied by his theory of contraries in Physics I and in Metaphysics Iota, and to the dimensionless ‘space’ of the unity of matter and form discussed in book Eta of the Metaphysics. By examining Aristotle’s remarks on contraries, the subject of change, continuity, and the unity of matter and form, Aristotle’s thoughts on motion, (...) on contraries, and on the unity of substance can be brought together under a single interpretive framework, which can provide an approach to interpreting his ontology. (shrink)