Relations

I think it would be fair to say that, until about 1900, philosophers were generally reluctant to admit the existence of what are nowadays called polyadic properties.1 It is important to recognize, however, that this reluctance on the part of pre-twentieth-century philosophers did not prevent them from theorizing about relations. On the contrary, philosophers from the ancient through the modern period have had much to say about both the nature and the ontological status of relations. In this paper I examine (...) the views of one such philosopher, namely, Albert the Great. (shrink)

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses. He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that each slot (...) may be occupied by at most one entity. Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems. I fully develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which are first considered by Yi (1999: 168 ff.). Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations. Pocket theory also avoids a serious drawback of anti-positionalism. (shrink)

In this article, we propose a new trope nominalist conception of determinate and determinable kinds of quantitative tropes. The conception is developed as follows. First, we formulate a new account of tropes falling under the same determinates and determinables in terms of internal relations of proportion and order. Our account is a considerable improvement on the current standard account (Campbell 1990; Maurin 2002; Simons 2003) because it does not rely on primitive internal relations of exact similarity or quantitative distance. The (...) internal relations of proportion and order hold because the related tropes exist; no kinds of tropes need be assumed here. Second, we argue that there are only pluralities of tropes in relations of proportion and order. The tropes mutually connected by the relations of proportion and order form a special type of plurality, tropes belonging to the same kind. Unlike the recent nominalist accounts, we do not identify kinds of tropes with any further entities (e.g. sets) or abstractions from entities (e.g. pluralities of similar tropes). (shrink)

In the following paragraphs, I will describe ten strategies through which we can show the weaknesses of every form of theism, while postulating that the Trinity is a good solution. This approach follows up on Swinburne’s claims about the existence of a priori and a posteriori proofs for the existence of the Trinity (his proofs are part of the sixth strategy). Clearly, these strategies are not “new”: they have been advocated by many thinkers in the past and in the present. (...) I merely revived them, and brought them together in a kind of cumulative reasoning: the strength of the Kantian Argument arises when these strategies are considered together, showing that the Trinity is a reasonable hypothesis even though it is contradictory. (shrink)

Causal structuralism is the view that, for each natural, non-mathematical, non-Cambridge property, there is a causal profile that exhausts its individual essence. On this view, having a property’s causal profile is both necessary and sufficient for being that property. It is generally contrasted with the Humean or quidditistic view of properties, which states that having a property’s causal profile is neither necessary nor sufficient for being that property, and with the double-aspect view, which states that causal profile is necessary but (...) not sufficient. Shoemaker’s (1998) and Hawthorne’s (2001) arguments in favor of causal structuralism primarily focus on problematic consequences of the other two views. I argue, however, that causation does not provide an appropriate framework within which to characterize all physical properties for two main reasons. First, there are physical properties that do not have causal profiles and properties whose causal profiles do not exhaust their essences. Second, there is no unified notion of causation across the sciences. After distinguishing between the causal and the nomological, I suggest that what is needed is a structuralist view of properties that is not merely causal but that incorporates a physical property’s higher-order mathematical and nomological properties into its identity conditions. Such a view retains the naturalistic motivations for causal structuralism while avoiding the problems it faces. (shrink)

We propose a novel ontological analysis of relations and relationships based on a re-visitation of a classic problem in the practice of knowledge repre- sentation and conceptual modeling, namely relationship reification. Our idea is that a relation holds in virtue of a relationship's existence. Relationships are therefore truthmakers of relations. In this paper we present a general theory or reification and truthmaking, and discuss the interplay between events and rela- tionships, suggesting that relationships are the focus of events, which emerge (...) from the context (the scene) they occur in. (shrink)

The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the holding of relational inherence to the (...) obtaining of certain other facts about entities of the trope theoretical category system. Moreover, I show that the analysis can deal with asymmetric and non-symmetric relations by assuming that all relation-like tropes are quantities. Finally, I provide an account of the spatial location of tropes in the difficult case in which tropes contribute to determining of the location of other entities. (shrink)

In this paper, I elaborate on the Strong Nuclear Theory (SNT) of tropes and substances, which I have defended elsewhere, using my metatheory about formal ontology and especially fundamental ontological form. According to my metatheory, for an entity to have an ontological form is for it to be a relatum of a formal ontological relation or relations jointly in an order. The full fundamental ontological form is generically identical to a simple formal ontological relation or relations jointly in an order. (...) Regarding generic identity, I follow Fabrice Correia and Alexander Skiles, who consider it a form of generalized identity as distinguished from numerical identity. The SNT states that for any trope to have the full fundamental ontological form is for it to be a strongly rigidly or generically (existentially) dependent individual simple part. Therefore, the common dichotomous set-up of asking whether tropes are fundamentally properties rather than objects or vice versa is a non-starter to me in formal ontological terms. The elaboration of the SNT also supplies me with the resources to respond to the arguments against tropes by Douglas Ehring, Robert K. Garcia and Herbert Hochberg. Finally, I argue that non-fundamentally but necessarily, every trope is a proper part of a substance and is concrete in the SNT. (shrink)

Trope theories aim to eschew the primitive dichotomy between characterising (properties, relations) and characterized entities (objects). This article (in Finnish) presents a new trope theoretical analysis of relational inherence as the best way out of the impasse created by the alleged necessity to choose between an eliminativist and a primitivist ("relata-specific") view about relations in trope theory.

The Greek model of the Trinity, based on the Theological Orations of Gregory of Nazianzus, treats the Trinitarian relations as connections between the Father and the two other persons: the Son and the Holy Spirit. The two relations have to be heteronymous, and have to be interpreted from the extreme realistic position. The Latin Trinitarian model, based on Boethius’ De Trinitate, treats relations as three subsistent persons. The relations have to be unidirectional: from the Father to the Son, and from (...) both of them to the Holy Spirit. Both models are adequate and effective, but incompatible. One of the consequences of this incompatibility is the problem of filioque: the introduction of an additional relation of procession into the Greek model as well as the exclusion of this relation from the Latin model result in the inadequacy of the models. From the point of view of the complementability of a model, the Greek model allows introduction of new elements, while the Latin model does not. The soteriological consequences are such that the Greek model welcomes a human person to establish a unique relation with the person of the Father, which leads to the theosis of a creature. The Latin model requires the saving relation to be established with the whole Trinity, and theosis is not supported. (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)

In Kapitel 5 dieses Buches wurde mit dem ontologischen Sextett eine Klassifizierung der Realität vorgestellt, die das klassische Aristotelische Viereck erweitert, indem sie Einzeldinge und Universalien in insgesamt sechs Kategorien umfaßt. Zwischen den Entitäten dieser Kategorien sind bestimmte Beziehungen postuliert worden, wie zum Beispiel Inhärenz, Partizipation, Instantiierung, Exemplifizierung und Charakterisierung. In diesem Kapitel soil der Frage nachgegangen werden, wie eben diese Beziehungen zwischen den Entitäten dieser Kategorien genauer charakterisiert und die sie bezeichnenden relationalen Ausdrücke eindeutig formal definiert werden konnen.

In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes are, as determinate (...) particular natures, internally related by certain relations of proportion and order. By being determined by the nature of tropes, the relations of proportion and order remain invariant in conventional choice of unit for any quantity and give rise to natural divisions among tropes. As a consequence, tropes fall under distinct determinables and determinates. Our conception provides an accurate account of quantitative distances between tropes but avoids commitment to determinable universals. In this important respect, it compares favorably with the standard conception taking exact similarity and quantitative distances as primitive internal relations. Moreover, we argue for the superiority of our approach in comparison with two additional recent accounts of the similarity of quantity tropes. (shrink)

An introduction to our edited volume, The Metaphysics of Relations, covering a range of issues including the problem of order, the ontological status of relations, reasons for ancient scepticism about relational properties, and two ways of drawing the distinction between internal and external relations.

Is a bank note identical with the piece of paper of which it consists? On the one hand, John Searle, in his reply to Barry Smith, suggests that they are “one and the same object” that is a social or non-social object only under certain descriptions. On the other hand, Lynne Rudder Baker puts forward the claim that bank note and paper are distinct entities that are bound together by the relation of material constitution. I suggest two possible analyses for (...) Searle’s description relativity claim, the Alternative Subject Analysis and the Predicate Modification Analysis. On both accounts his identity claim gets into serious trouble. While Baker’s definition of material constitution deals well with the bank note example, it fails to account for the constitution of bearerless social entities and groups. I point out five respects in which social constitution can differ from Baker’s account of material constitution and discuss compositional, institutional and interactional constitution as additional varieties of social constitution. (shrink)

The Metaphysics of Relations is an anthology of thirteen original papers plus an introduction, addressing the philosophical issue of relations from a contemporary and historical perspective. The result is a remarkably coherent whole, where the different papers shed light on each other even though very few of them explicitly address interconnections. As a consequence, the book works really well as an introduction to the philosophical issue on relations, while the individual papers represent cutting edge research on the particular issues that (...) they focus on. The mix of contemporary and historical perspectives means you get a snapshot view of the contemporary issues, as well as insights into their historical development. (shrink)

‘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)

According to standard trope nominalism, there are simple tropes that do not have parts or multiply distinct aspects. Douglas Ehring’s reductio ad absurdum against this standard view concludes that there are no simple tropes. In this paper, we provide a response to Ehring defending the standard view. Ehring’s argument may be refuted by (1) distinguishing the ontological form of tropes from their contribution to the ontological content of the world, and (2) construing tropes as having primitive identity. At the same (...) time, standard trope nominalism is elaborated on by distinguishing between ontological form and content, for which there are also independent reasons. (shrink)

I call anti-resemblism the thesis that independently of any contextual specification there is no determinate fact of the matter about the comparative overall similarity of things. Anti-resemblism plays crucial roles in the philosophy of David Lewis. For instance, Lewis has argued that his counterpart theory is anti-essentialist on the grounds that counterpart relations are relations of comparative overall similarity and that anti-resemblism is true. After Lewis committed himself to a form of realism about natural properties he maintained that anti-resemblism is (...) true about the relations of overall similarity that enter his counterpart theory and his analysis of counterfactuals. However, in this article I argue that Lewis’s account of degrees of naturalness for properties combined with his modal realism entails that anti-resemblism is false. The Lewisian must amend Lewis’s system if she aims to benefit from the alleged virtues of anti-resemblism. I consider two ways of amending it, neither of which is a free lunch. (shrink)

Vallicella’s influential work makes a case that, when formulated broadly, as a problem about unity, Bradley’s challenge to Armstrongian states of affairs is practically insurmountable. He argues that traditional relational and non-relational responses to Bradley are inadequate, and many in the current metaphysical debate on this issue have come to agree. In this paper, I argue that such a conclusion is too hasty. Firstly, the problem of unity as applied to Armstrongian states of affairs is not clearly defined; in fact, (...) it has taken a number of different forms each of which need to be carefully distinguished and further supported. Secondly, once we formulate the problem in more neutral terms, as a request for a characterization of the way that particulars, universals, and states of affairs stand to one another, it can be adequately addressed by an Armstrongian about states of affairs. I propose the desiderata for an adequate characterization and present a neo-Armstrongian defense of states of affairs that meets those desiderata. The latter relies on an important distinction between different notions of fundamentality and existential dependence. (shrink)

In this talk, I propose a new account of ontological form, formal ontological relations, modes of being and hence of specifying the subject matter of metaphysics.

Speaks defends the view that propositions are properties: for example, the proposition that grass is green is the property being such that grass is green. We argue that there is no reason to prefer Speaks's theory to analogous but competing theories that identify propositions with, say, 2-adic relations. This style of argument has recently been deployed by many, including Moore and King, against the view that propositions are n-tuples, and by Caplan and Tillman against King's view that propositions are facts (...) of a special sort. We offer our argument as an objection to the view that propositions are unsaturated relations. (shrink)

It is commonly held that Bradley’s regress has a solution within a trope ontology. This seems to happen when a bundle is understood as constituted by non-transferable tropes. It also seems to happen when a bundle is understood as constituted by transferable tropes related by a relational trope of compresence whose existence specifically depends on those relata. In this article I demonstrate that these proposals fail in addressing the essential question that underlies the regress, incurring in a question-begging response already (...) anticipated by Bradley. (shrink)

We propose a formalization of a realist ontology using first order logic with identity and allowing quantification over terms representing both individuals and universals. In addition to identity, the ontology includes also relational predicates such as subtype, instantiation, parthood, location, and inherence. Inspired in part by Davidson’s treatment of events, the ontology includes also various relations linking events to their participants and to the times at which they occur.

In this paper, we argue that formal ontological relations avoid Bradley's reductio of relations, including his famous relation regress.

In the present article, I show that sounds are properties that are not physical in a narrow sense. First, I argue that sounds are properties using Moorean style arguments and defend this property view from various arguments against it that make use of salient disanalogies between sounds and colors. The first disanalogy is that we talk of objects making sounds but not of objects making colors. The second is that we count and quantify over sounds but not colors. The third (...) is that sounds can survive qualitative change in their auditory properties, but colors cannot survive change in their chromatic properties. Next, I provide a taxonomy of property views of sound. As the property view of sound has been so rarely discussed, many of the views available have never been articulated. My taxonomy will articulate these views and how they are related to one another. I taxonomize sounds according to three characteristics: dispositional/non-dispositional, relational/non-relational, and reductive/non-reductive. Finally, mirroring a popular argument in the color literature, I argue that physical views in the narrow sense are unable to accommodate the similarity and difference relations in which sounds essentially stand. I end replying to three objections. (shrink)

Intrapersonal variation due to color contrast effects has been used to argue against the following intuitive propositions about the colors: No object can be more than one determinable or determinate color of the same grade all over at the same time ; external objects are actually colored ; and the colors of objects are mind-independent. In this article, I provide a defense of Incompatibility, Realism, and Objectivism from intrapersonal variation arguments that rely on color contrast effects. I provide a novel, (...) ecumenical response to such arguments according to which typical variants are right, and which respects Incompatibility, Realism, and Objectivism, using the thesis that the colors of objects depend on the colors of objects in their surrounds. (shrink)

La thèse du présent article est que l’opposition factice entre James, repré- sentant supposé des « relations externes », d’une part, et Bradley, représen- tant supposé des « relations internes », d’autre part, est due à une mauvaise appréhension des thèses de ce dernier. Ce premier contresens conduit alors à manquer le propos même de James.

Color relationalism holds that the colors are constituted by relations to subjects. The introspective rejoinder against this view claims that it is opposed to our phenomenally-informed, pre-theoretic intuitions. The rejoinder seems to be correct about how colors appear when looking at how participants respond to an item about the metaphysical nature of color but not when looking at an item about the ascription of colors. The present article expands the properties investigated to sound and taste and inspects the mentioned asymmetry, (...) with a particular focus on the principle of charity. Using a metaphysical item, we find that color and sound are no different from shape, our control for a clearly anti-relational property. Taste, on the other hand, is no different from likability, our control for a clearly relational property. Importantly, we find that the disparity between metaphysical and ascription items is due to participants using a principle of charity to interpret disagreement cases such that both parties can be correct. (shrink)

In his recent book, The Universe As We Find It, John Heil offers an updated account of his two-category ontology. One of his major goals is to avoid including relations in his basic ontology. While there can still be true claims positing relations, such as those of the form “x is taller than y” and “x causes y,” they will be true in virtue of substances and their monadic, non-relational properties. That is, Heil’s two-category ontology is deployed to provide non-relational (...) truthmakers for relational truths. This paper challenges the success of Heil’s project with respect to causation. The arguments here are not entirely negative, however. An option is made available to Heil’s ontology so that it might, at least to some extent, regain non-relational causings. (shrink)

In this paper I consider whether a powers ontology facilitates a reduction of causal relations to intrinsic powers of the causal relata. I first argue that there is a tension in the view that powerful causation is an internal relation in this sense. Powers are ontologically dependent on other powers for their individuation, but in that case—given an Aristotelian conception of properties as immanent universals—powers will not be intrinsic on several extant analyses of ‘intrinsic’, since to possess a given power (...) P requires the existence of other concrete particulars as bearers of the powers that individuate P. I suggest several ways for Aristotelians to resolve this tension, but all tenable options involve individuative type-level causal relations between powers. While these individuative relations between powers are internal in the sense that the powers are essentially related, this is a different sense of ‘ internal ’ to the one that entails reducibility. The proposed reduction of token-causal relations to powers succeeds only at the cost of irreducible type-level causal relations between the powers themselves. (shrink)

In "How to Define Intrinsic Properties" I offered a relational account of the intrinsic/extrinsic distinction. The basic idea is that F is an intrinsic property of an item x just in case x’s having F consists entirely in x’s having certain internal properties, where an internal property is one whose instantiation does not consist in one’s relation to any distinct items (items other than oneself and one’s proper parts). I still think that this relational analysis is largely correct, and here (...) I provide additional support for it and defend it against some objections that have been raised. In the process I aim to make the account somewhat more precise, especially by contrasting it with a grounding approach to defining the intrinsic/extrinsic distinction. (shrink)

I argue that the fundamental dogma that all necessary relations are internal is ungrounded. To motivate my argument, I analyse Moore’s classic ideas on internal relations and take them as an illustration of the common form of reasoning that can mislead us to conclude that all necessary relations are internal. That reasoning illicitly smuggles the idea that necessary properties and relations reflect on identity—in the sense that the loss of a necessary property/relation is a loss of identity—into the separate idea (...) that the loss of a necessary property/relation is a loss of essence. Essence, however, is not identity. So the way seems to be open for the existence of necessary properties/relations which do not belong to the essence of entities; that is, the existence of necessary but external relations. I then offer some examples of such relations. (shrink)

This paper provides an axiomatic formalization of a theory of foundational relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the is-a relation among universals and the part-of relation among individuals as well as cross-category relations such as instance-of, member-of, and partition-of. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is critical (...) for formal ontology. We provide examples to support this thesis from the domain of biomedicine. (shrink)