We study the logical structure of relations, and in particular the notion of occurrences of objects in a state. We start with formulating a number of principles for occurrences and defining corresponding mathematical models. These models are analyzed to get more insight in the formal properties of occurrences. In particular, we prove uniqueness results that tell us more about the possible logical structures relations might have.

In the ordinary way of representing relations, the order of the relata plays a structural role, but in the states themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relations, different assignments of objects to the positions can give exactly the same states. This is a puzzling situation. (...) The question is what is the internal structure of relations? Is the use of positions still justified, and if so, what is their ontological status? In this paper mathematical models for relations are developed that provide more insight into the structure of relations “out there” in the real world. (shrink)

A new logic is presented without predicates—except equality. Yet its expressive power is the same as that of predicate logic, and relations can faithfully be represented in it. In this logic we also develop an alternative for set theory. There is a need for such a new approach, since we do not live in a world of sets and predicates, but rather in a world of things with relations between them.

The present paper is the result of a long struggle to understand how the notion of compositionality can be used to motivate the structure of a sentence. While everyone seems to have intuitions about which proposals are compositional and which ones are not, these intuitions generally have no formal basis. What is needed to make such arguments work is a proper understanding of what meanings are and how they can be manipulated. In particular, we need a definition of meaning that (...) bans all mentioning of syntactic structure; it is not the task of semantics to state in which way things are put together in syntax. The present paper presents such a theory of meaning. This, in tandem with some minimal assumptions on the syntactic process (that there can be no deletion) yield surprisingly deep insights into natural language. First, it rehabilitates a lot of linguistic work as necessary on semantic grounds and defends it against potential claims of redundancy. For example, θ-roles and linking are an integral part of semantics, and not syntax. To assume the latter is to put the cart before the horse. Second, as a particular example we shall show that Dutch is not strongly context free even if weakly context free. To our knowledge, this is the first formal proof of this fact. (shrink)

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...) In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (shrink)

This paper explores the impact of quantification into predicate position on the metaphysics of properties, arguing that two familiar debates about properties are fundamentally altered by recasting them in a second-order setting. Two theories of properties are outlined, differing over whether the existence of properties is expressed using first-order or second-order quantifiers. It is argued that the second-order theory: provides good reason to regard debate about the locations of properties as contentless; resolves debate about whether properties are particulars or universals (...) in favour of universals. (shrink)

What is exemplification? A proposition that attributes a property to an object is true if the object exemplifies the property. But according to the correspondence theory, a proposition is true if the corresponding fact exists. So if the correspondence theory is correct, an exemplification of a temporal property by an object is simply the concrete circumstance of the object’s having the property. But since not all properties are temporal, not all exemplifications are circumstances, and we need to recognise timeless as (...) well as temporal facts. This distinction allows us to solve the problem of converse relations, and to give an account of the logically complex facts which deduction allows us to know. (shrink)

Putative counterexamples to the Principle of Identity of Indiscernibles (PII) are notoriously inconclusive. I establish ground rules for debate in this area, offer a new response to such counterexamples for friends of the PII, but then argue that no response is entirely satisfactory. Finally, I undermine some positive arguments for PII.

If Sophroniscus is the father of Socrates, then Socrates is the son of Sophroniscus. If Socrates is similar to Plato, then Plato is similar to Socrates. But how many relations does Sophroniscus and Socrates being so related involve? How many does Plato and Socrates being thus related? Is there a difference between the two cases? These are questions that have featured prominently in discussions of relations in recent years, but they are by no means new. Focusing on a text by (...) the later Archbishop of Canterbury, Robert Kilwardby, this paper explores some of the replies and main arguments advanced by a number of philosophers working in the Latin west in the mid-to-late thirteenth century. (shrink)

The identity predicate can be defined using second-order quantification: a=b =df ∀F(Fa↔Fb). Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ϕ≡ψ =df ∀X(Xϕ↔Xψ), where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? -/- I will argue that reality is not structured in anything like (...) the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell’s paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege’s theory of structured thoughts to be inconsistent, to which Frege replied that Russell’s argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented. (shrink)

Recent years have seen an explosion of interest in metaphysical explanation, and philosophers have fixed on the notion of ground as the conceptual tool with which such explanation should be investigated. I will argue that this focus on ground is myopic and that some metaphysical explanations that involve the essences of things cannot be understood in terms of ground. Such ‘essentialist’ explanation is of interest, not only for its ubiquity in philosophy, but for its being in a sense an ultimate (...) form of explanation. I give an account of the sense in which such explanation is ultimate and support it by defending what I call the inessentiality of essence. I close by suggesting that this principle is the key to understanding why essentialist explanations can seem so satisfying. (shrink)

Is there an explanation of why the state of x's bearing the non-symmetric binary relation R to y is different from its differential opposite, the state of y's bearing R to x? One traditional view has it that the explanation is that non-symmetric relations hold of objects in an essentially directional way, ordering the relevant relata. We call this view ‘directionalism’. Kit Fine has suggested that this approach is subject to significant metaphysical difficulties, sufficient to motivate seeking an alternative analysis. (...) He considers two such alternative explanations, which he labels ‘positionalism’ and ‘anti-positionalism’. Of these he endorses the latter. We argue that anti-positionalism fails to provide a coherent explanation of the distinction between differential opposites, and that one should simply hold the minimalist position that there is no explanation for this metaphysical difference. (shrink)

We present here the papers selected for the volume on the Unity of Propositions problems. After summarizing what the problems are, we locate them in a spectrum from those aiming to provide substantive, reductive explanations, to those with a more deflationary take on the problems.

Editorial comment on the relations between philosophy and cognitive science.

An argument going back to Russell shows that the view that propositions are structured is inconsistent in standard type theories. Here, it is shown that such type theories may nevertheless provide entities which can serve as proxies for structured propositions. As an illustration, such proxies are applied to the case of grounding, as standard views of grounding require a degree of propositional structure which suffices for a version of Russell’s argument. While this application solves some of the problems grounding faces, (...) it introduces problematic limitations: it becomes impossible to quantify unrestrictedly over the relata of ground. The proposed proxies may thus not save grounding, but they shed light on what exactly Russell’s argument does and does not show. (shrink)

I apply the theory of embodiment to various questions concerning the identity of social groups.

The problem, or cluster of problems, of the unity of the proposition, along with the cluster of problems that tend to go under the name of Bradley’s regress, has recently again become a going concern for philosophers, after having for some time been regarded as primarily of historical interest. In this paper, I distinguish between the different problems that tend to be brought up under the heading of the unity of the proposition, and between different related regress arguments. I present (...) my favored solutions to these problems. (shrink)

‘Instantiation-directed slot theorists’ believe that properties/relations have slots which are filled by their instances/relata e.g., where Abigail is taller than Bronia, there are two slots in the relation Taller Than such that Abigail fills the first slot and Bronia fills the second. This crude statement of the theory runs into ‘The Problem of Filling’, whereby a natural understanding of the relation between slots, filling, and instantiation leads to absurd results. This paper examines a variety of solutions to that problem, one (...) of which is an extension of slot theory that adds an additional category of entities, ‘slotites’. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Non-symmetric relations like loves or between can apply to the same relata in non-equivalent ways. For example, loves may apply to Abelard and Eloise either by Abelard’s loving Eloise or by Eloise’s loving Abelard. On the standard account of relations, different applications of a relation to fixed relata are distinguished by the direction in which the relation applies to the relata. But neither Directionalism nor its most popular rival, Positionalism, offer accounts of differential application that generalize to relations of arbitrary (...) symmetry structure. Here, I develop an alternative account, Relative Positionalism, which distinguishes different applications of a relation to fixed relata in terms of the ways in which the relata are characterized relative to one another. In presenting and defending Relative Positionalism, this paper covers some of the same ground as my [2016], but avoids the latter’s algebraic approach and focuses on interpretative issues—in particular, how to make sense of relative property instantiation—that were not addressed in the earlier paper. (shrink)

Realists about universals face a question about grounding. Are things how they are because they instantiate the universals they do? Or do they instantiate those universals because they are how they are? Take Ebenezer Scrooge. You can say that Scrooge is greedy because he instantiates greediness, or you can say that Scrooge instantiates greediness because he is greedy. I argue that there is reason to prefer the latter to the former. I develop two arguments for the view. I also respond (...) to some concerns one might have about the view defended. I close by showing that analogous views regarding the truth of propositions and the existence of facts are supported by analogs of one of these arguments. (shrink)

Maureen Donnelly’s (2016) relative positionalism correctly handles any fixed arity relation with any symmetry such a relation can have, yielding the intuitively correct way(s) in which that relation can apply. And it supplies an explanation of what is going on in the world that makes this the case. But it has at least one potential shortcoming — one that its opponents are likely to seize upon: it can only handle relations with fixed arities. It is unable to handle relations with (...) variable arities. I argue that, all else being equal, relative positionalism ought nonetheless to be preferred to its closest competitors — at least to the extent that the explanation it supplies of relational application is plausible — even though those competitors can handle variable arity relations in addition to fixed arity relations. (shrink)

Both through his own work and that of his students, Franz Clemens Brentano had an often underappreciated influence on the course of 20 th - and 21 st -century philosophy. _The Routledge Handbook of Franz Brentano and the Brentano School_ offers full coverage of Brentano’s philosophy and his influence. It contains 38 brand-new essays from an international team of experts that offer a comprehensive view of Brentano’s central research areas—philosophy of mind, metaphysics, and value theory—as well as of the principal (...) figures shaped by Brentano’s school of thought. A General Introduction serves as an overview of Brentano and the contents of the volume and three separate bibliographies point students and researchers on to further avenues of inquiry. Systematic and detailed, _The Routledge Handbook of Franz Brentano and the Brentano School_ provides readers with a valuable reference to Brentano’s work, and to his lasting importance in the history of philosophy and in contemporary debates. (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)

John Cook Wilson (1849–1915) was Wykeham Professor of Logic at New College, Oxford and the founder of ‘Oxford Realism’, a philosophical movement that flourished at Oxford during the first decades of the 20th century. Although trained as a classicist and a mathematician, his most important contribution was to the theory of knowledge, where he argued that knowledge is factive and not definable in terms of belief, and he criticized ‘hybrid’ and ‘externalist’ accounts. He also argued for direct realism in perception, (...) criticizing both empiricism and idealism, and argued for a moderate nominalist view of universals as being in rebus and only ‘apprehended’ by their particulars. His influence helped swaying Oxford away from idealism and, through figures such as H. A. Prichard, Gilbert Ryle, or J. L. Austin, his ideas were also to some extent at the origin of ‘moral intuitionism’ and ‘ordinary language philosophy’ which defined much of Oxford philosophy until the second half of the twentieth-century. Nevertheless, his name and legacy were all but forgotten for generations after World War II. Still, his views on knowledge are with us today, being in part at work in the writings of philosophers as diverse as John McDowell, Charles Travis, and Timothy Williamson. (shrink)

Seeing-in is the experience of seeing something in a picture. This experience is single and unified. It is not like the disjoint experience of perceiving one thing while simultaneously visualizing another. This is so despite the fact that, like the latter experience, seeing-in is twofold. It involves being visually aware of two distinct objects at the same time – an array of ink-marks, on the one hand, and the depicted scene, on the other. Plausibly, it also involves being aware of (...) them in two distinct ways: while we perceive the ink-marks before us, the manner of our visual awareness of the depicted object is not perceptual. In this paper, I offer a novel way of reconciling these two features of seeing-in. I argue that the modes of visual awareness operative in seeing-in have to be understood on the model of converse relations, like lighter and heavier, in the sense that the same state arises from the obtaining of each. (shrink)

In this paper I provide a state of the art survey and assessment of the contemporary debate about relations. After (1) distinguishing different varieties of relations, symmetric from non-symmetric, internal from external relations etc. and relations from their set-theoretic models or sequences, I proceed (2) to consider Bradley’s regress and whether relations can be eliminated altogether. Next I turn (3) to the question whether relations can be reduced, bringing to bear considerations from the philosophy of physics as well as metaphysics. (...) Finally, (3) I consider in what sense relations have order, and whether to make sense of this we are required to conceive of relations as having direction or argument positions. (shrink)

This accessible essay treats knowledge and belief in a usable and applicable way. Many of its basic ideas have been developed recently in Corcoran-Hamid 2014: Investigating knowledge and opinion. The Road to Universal Logic. Vol. I. Arthur Buchsbaum and Arnold Koslow, Editors. Springer. Pp. 95-126. http://www.springer.com/birkhauser/mathematics/book/978-3-319-10192-7 .

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)

This is a commentary on the article by Augusto (2022; this issue) on categories and foundation ontology (FO). We agree that the notion of categories of kinds of elements to devise a FO deserves more attention than it has received to date. From a practical point of view sensu developing domain ontologies, however, it probably does not matter much as long as a FO is used and that that one was understood.

The purpose of this thesis is to provide a metaphysic for moral realism and moral perception. This thesis is in two parts. The first is concerned with basic ontology. I begin in chapter 1 with an analysis of causation, demonstrating that substance theory is superior to Humeanism at accounting for our observations; thus I defend a substance ontology. In chapter 2, I address human agency, demonstrating that reasons internalism does not allow for incompatibilist freedom; hence, I affirm reasons are states (...) of affairs. I move on to qualia in chapter 3, demonstrating that arguments both for and against qualia realism involve question begging. In response, I argue that qualia realism is just as reasonable as anti-realism, and affirm realism. Given this, I address the mind-body problem in chapter 4, demonstrating the failure of physicalists to account for mental causation. I conclude that panpsychism, idealism, and substance dualism are equal reasonable alternatives: each allows for intrinsic properties, which are integral to substance ontology. The second part builds a moral ontology, along with an account of moral perceptual knowledge, compatible with the above basic ontology. In chapter 5, I reject moral properties as monadic since this would bar mapping moral concepts onto mind-independent reality. Instead, I argue that moral properties are relations. More specifically, in chapter 6, I make the case that they are features of relations, relations themselves being the total complex states of affairs between one or more substances. This allows moral properties to have their own nonreducible phenomenal quality. To account for moral normativity, I argue that moral features are actually a class of causal features, and briefly argue that final causes determine the normative causal trajectory of all substances. In chapter 7, I conclude this thesis with addressing possible objections to my theory of perception and perceptual knowledge. (shrink)

Båve has argued that act-type theories of propositions entail unwanted ambiguity of sentences such as ‘Donald loves Joan’. King has argued that act-type theories of propositions entail an unwanted abundance of propositions. I reply that a version of the act-type theory can avoid these objections. The key idea is that grammar constrains the acts that can be performed by the utterance of a sentence. I present enough of the details of this version of the act-type theory to show how it (...) can be used to respond to Båve's and King's objections. I conclude that this is a promising way to develop the act-type theory of propositions. (shrink)

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...) advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

Plural Logic is an extension of First-Order Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the first-order domain of quantification. Given that Plural Logic is equi-interpretable with Monadic Second-Order Logic, it gives us its expressive power at the low ontological cost of a first-order language. This (...) makes it a valuable tool in various areas of philosophy. Some authors believe that Plural Logic can be extended into an even more expressive logic, Higher-Level Plural Logic, by adding higher-level plural terms and quantifiers to it. The basic idea is that second-level plurals stand to plurals like plurals stand to singulars. Allegedly, Higher-Level Plural Logic enjoys the expressive power of type theory while, again, committing us only to the austere ontology of a first-order language. Were this really the case, Higher-Level Plural Logic would be a very useful tool, extending and strengthening some of the applications of Plural Logic. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with scepticism. The main objection raised against them is that higher-level plural reference is unintelligible. This has been argued, among others, on the grounds that there are no higher-level plurals in natural language and that, if there were any, they could be eliminated. In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to defending the legitimacy of the notion of higher-level plural reference. To this end, in Chapter 3, I present and elucidate the notion. Next, in Chapter 4, I show that some natural languages clearly contain these expressions and that they do so in an ineliminable manner. Finally, in Chapters 5 and 6, I develop a semantics for higher-level plurals that employs only devices previously well-understood by English speakers. To finish, in Chapter 7, I describe an application of Higher-level Plural Logic: a strengthening of the neo-Fregean programme. After describing my proposal, I turn to the issue of the logical status of this formalism and defend an optimistic take on the matter. (shrink)

I reassess the famous arguments of Frank Plumpton Ramsey (1925) against the tenability of the distinction between particulars and universals and discuss their recent elaboration by Fraser MacBride. I argue that Ramsey’s argument is ambiguous between kinds and properties and that his sceptical worries can be resolved once this distinction is taken into account. A crucial role in this dissolution is a notion of what is essential to a property. I close by some epistemological considerations.

Este texto tem como objetivo apresentar a principal motivação filosófica para se defender uma teoria causal da memória, que é explicar como pode um evento que se deu no passado estar relacionado a uma experiência mnêmica que se dá no presente. Para tanto, iniciaremos apresentando a noção de memória de maneira informal e geral, para depois apresentar elementos mais detalhados. Finalizamos apresentando uma teoria causal da memória que se beneficia da noção de veritação (truthmaking).

One of the hottest philosophical debates in recent years concerns the nature of the semantics/pragmatics divide. Some writers have expressed the reserve that this might be merely terminological, but in my view it ultimately concerns a substantive issue with empirical implications: the scope and limits of a serious scientific undertaking, formal semantics. In this critical note I discuss two arguments by Recanati: his main methodological argument --viz. that the contents posited by what he calls 'literalists' play no relevant role in (...) communication--, and some phenomenological considerations regarding the "Availability Principle" that he appeals to in order to buttress that main argument. /// Uno de los más encarnizados debates filosóficos recientes atañe a la naturaleza de la distinción entre semántica y pragmática. Aunque algunos autores han expresado reservas en el sentido de que èste pudiera ser sólo terminológico, en mi opinión tiene que ver con una cuestión sustantiva con implicaciones empíricas: el alcance y los límites de una empresa científica seria, la semántica formal. En este texto discuto dos argumentos de Recanati: su principal argumento metodológico, que los contenidos postulados por los autores que él denomina "literalistas" no desempeñan ningùn papel relevante en la comunicación, y, en segundo lugar, ciertas consideraciones fenomenológicas en torno a su "Principio de Accesibilidad", a las cuales apela para apoyar el argumento metodológico. (shrink)

This paper extends the definition of strong supervenience to cover classes of relations of any adicity, including transworld relations. It motivates that project by showing that not all interesting supervenience claims involving relations are global supervenience claims. The proposed definition has five welcome features: it reduces to the familiar definition in the special case where the classes contain only monadic properties; it equips supervenience with the expected formal properties, such as transitivity and monotonicity; it entails that a relation supervenes on (...) its converse; it classifies certain paradigms correctly; it makes distinctions even in the realm of the non-contingent, as witnessed by the fact that identity does not supervene on any class of relations. Finally, the paper applies the defined concept, and the related concept of orthogonality, to the study of internal and external relations. (shrink)