We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of (...) quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of settheoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items. (shrink)

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics for plural logic (...) that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)

In recent literature on plurals the claim has often been made that the move from singular to plural expressions can be iterated, generating what are occasionally called higher-level plurals or superplurals, often correlated with superplural predicates. I argue that the idea that the singular-to-plural move can be iterated is questionable. I then show that the examples and arguments intended to establish that some expressions of natural language are in some sense higher-level plurals fail. Next, I argue that these and some (...) other expressions should instead be classified as plurals whose reference is articulated, an idea explained and elaborated in the paper. I also show that the related categories of plural and superplural predicates collapse to that of ordinary predicates. In the process we also see that the law of substitutivity salva veritate should be elaborated for cases involving expressions more complex than singular ones. (shrink)

The consensus in the philosophical literature on joint action is that, sometimes at least, when agents intentionally jointly φ, this is explicable by their intending that they φ, for a period of time prior to their φ-ing. If this be granted, it poses a dilemma. For agents who so intend either severally or jointly intend that they φ. The first option is ruled out by two stipulations that we may consistently make: (i) that at least one of the agents non-akratically (...) believes that, all things considered, the agents ought not to φ, and (ii) that an agent is akratic, if she intends a thing that she believes, all things considered, ought not to be done. But the second option seems to entail the existence of a mental state with multiple subjects, which, in turn, seems to commit us to the existence of a group mind modified by that state: an incautious posit to say the least. I resolve the dilemma by noting that ‘They jointly intend’ is indeterminate between ‘They intend, jointly’, which does indeed entail that some mental state is an intention with multiple subjects, and ‘Jointly, they intend’, which entails a weaker claim, viz. that some mental state or states is an intention with multiple subjects. I then sketch an account of how a plurality of mental states, distributed among subjects, might, collectively, do service as their intention that they φ. It makes novel use of notions of participation and of doing a thing jointly with others. A corollary is that either intentions are not attitudes towards propositions, or propositions are individuated more finely than is often assumed. (shrink)

Nozick provides us with a compelling characterization of romantic love, but, as I argue, he under-describes the phenomenon, for he fails to distinguish it from attitudes that those who are not romantically involved may bear to each other. Frankfurt also offers a compelling characterization of love, but he is sceptical about its application to the case of romantic love. I argue that each account has the resources with which to complete the other. I consider a preliminary synthesis of the two (...) accounts, which I find wanting. The synthesis I then favour relies upon two thoughts: each romantic partner has loving concern for a plural object viz. the two of them, and romantic partners are, in addition, beloved of a plural subject, viz. the two of them. A corollary is that Frankfurt is wrong to think that, whilst self-love is a pure form of love, romantic love is an impure form of love, for romantic love just is a form of self-love. In an appendix, I defend the coherence of the thought that love can have plural relata. (shrink)

I address what I call the Number Issue, which is raised by our ordinary talk and beliefs about certain social groups and institutions, and I take the Hallé orchestra as my example. The Number Issue is that of whether the Hallé is one individual or several individuals. I observe that if one holds that it is one individual, one faces an accusation of metaphysical extravagance. The bulk of the paper examines the difficulty of reconciling the view that the Hallé is (...) several individuals with two prima facie plausible theses about the manner of its persistence through time. The paper is structured around some remarks made by Peter Simons about groups, and the Hallé in particular, in his 'Parts'. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...) that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

where ‘aa’ is a plural term, and ‘F’ a plural predicate. Following George Boolos (1984) and others, many philosophers and logicians also think that plural expressions should be analysed as not introducing any new ontological commitments to some sort of ‘plural entities’, but rather as involving a new form of reference to objects to which we are already committed (for an overview and further details, see Linnebo 2004). For instance, the plural term ‘aa’ refers to Alice, Bob and Charlie simultaneously, (...) and the plural predicate ‘F’ is true of some things just in case these things cooperate. A natural question that arises is whether the step from the singular to the plural can be iterated. Are there terms that stand to ordinary plural terms the way ordinary plural terms stand to singular terms? Let’s call such terms superplural. A superplural term would thus, loosely speaking, refer to several ‘pluralities’ at once, much as an ordinary plural term refers to several objects at once.1 Further, let’s call a predicate superplural if it can be predicated of superplural terms. It is reasonably straightforward to devise a formal logic of superplural terms, superplural predicates, and even superplural quantifiers (see Rayo 2006). But does this formal logic reflect any features of natural languages? In particular, does ordinary English contain superplural terms and predicates? The purpose of this article is to address these questions. We examine some earlier arguments for the existence of superplural expressions in English and find them to be either.. (shrink)

in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions between (...) different contexts of utterance. I present an alternative response which involves the negation of that claim, and argue that it is preferable to van Inwagen’s. (shrink)

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...) but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote Principia (...) Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)

This paper aims to characterise properly entanglement as an external relation obtaining between multiple quantum degrees of freedom. In particular, we argue that the entanglement relation is a unique relation fully characterised by mutual information, i.e. a quantity standardly used as a measure of entanglement. This analysis leads us to propose a new metaphysical account of entanglement, which we call Relational Entanglement Tesseract. Such an account characterises entanglement for both bipartite and multipartite cases, and, at the same time, it satisfies (...) what we argue are three important desiderata of any metaphysical account of entanglement. (shrink)

A number of natural language constructions seem to provide access to structured pluralities — that is, pluralities of pluralities. A body of semantic work has debated how to model this additional structure and the extent to which it depends on pragmatics. In this article, after controlling for the distinction between ambiguity and underspecification, we present new data showing that structured pluralities are sometimes but not always available, depending on the form of the plural noun phrase used. We show that these (...) results challenge two longstanding theories of plurality. We sketch two different ways to account for these data and describe some of the diverging predictions they make. (shrink)

Most of the theories of location on the market appear to be ideologically parsimonious at least in the sense that they take as primitive just one locative notion and define all the other locative notions in terms of it. Recently, however, the possibility of some exotic metaphysical scenarios involving gunky mixtures and extended simple regions of space has been argued to pose a significant threat to parsimonious theories of locations. The aim of this paper is to show that a theory (...) taking as primitive a notion of plural pervasive location and allowing for irreducibly plural locative facts can account for all the putatively problematic scenarios for parsimonious theories of location. Furthermore, I will also argue that the notion of plural pervasive location is compatible with the possibility of multilocation. (shrink)

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (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)

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)

Knowledge representation is a central issue for Artificial Intelligence and the Semantic Web. In particular, the problem of representing n-ary relations in RDF-based languages such as RDFS or OWL by no means is an obvious one. With respect to previous attempts, we show why the solutions proposed by the well known W3C Working Group Note on n-ary relations are not satisfactory on several scores. We then present our abstract model for representing n-ary relations as directed labeled graphs, and we show (...) how this model gives rise to a new ontological pattern (parametric pattern) for the representation of such relations in the Semantic Web. To this end, we define PROL (Parametric Relational Ontology Language). PROL is an ontological language designed to express any n-ary fact as a parametric pattern, which turns out to be a special RDF graph. The vocabulary of PROL is defined by a simple RDFS ontology. We argue that the parametric pattern may be particularly beneficial in the context of the Semantic Web, in virtue of its high expressive power, technical simplicity, and faithful meaning rendition. Examples are also provided. (shrink)

In its simplest form, a Spritz is an aperitif made with (sparkling) water and (white) wine. A ‘gunky Spritz’, as I will call it, is a Spritz in which the water and the wine are mixed through and through, so that every proper part of the Spritz has a proper part containing both water and wine. In the literature on the notion of location the possibility of mixtures like a gunky Spritz has been thought of as either threatening seemingly intuitive (...) locative principles, or as requiring the position of multiple primitive locative relations. In this paper I present a new theory of location which assumes as primitive only the notion of pervasive location and show that it can account for the possibility of gunky Spritz in an intuitive and adequate way. (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)

According to Minkoswki, Einstein's special theory of relativity reveals that ‘space by itself, and time by itself are doomed to fade away into mere shadows’. But perceptual experience represents objects as instantiating shapes like squareness — properties of ‘space by itself’. Thus, STR seems to threaten the veridicality of shape experience. In response to this worry, some have argued that we should analyze the contents of our spatial experiences on the model of traditional secondary qualities. On this picture—defended in recent (...) work by Chalmers —an experience of squareness just represents whatever property usually causes such experiences. This view salvages the veridicality of shape experience, but leaves the nature of the properties we perceive outside our ken. I argue that such a move is unwarranted: STR is compatible with the idea that shape experience acquaints us with the spatial character of our world. In defending this claim, I propose a view on which shape experience presents familiar Euclidean spatial properties veridically, while implicitly representing those properties as instantiated in a particular manner — namely, relative to our own frame of reference. (shrink)

The resemblance nominalist says that the truthmaker of 〈Socrates is white〉 ultimately involves only concrete particulars that resemble each other. Furthermore he also says that Socrates and Plato are the truthmakers of 〈Socrates resembles Plato〉, and Socrates and Aristotle those of 〈Socrates resembles Aristotle〉. But this, combined with a principle about the truthmakers of conjunctions, leads to the apparently implausible conclusion that 〈Socrates resembles Plato and Socrates resembles Aristotle〉 and 〈Socrates resembles Plato and Plato resembles Aristotle〉 have the same truthmakers, (...) namely, Socrates, Plato and Aristotle. I shall argue that the resemblance nominalist can say that those conjunctions have the same truthmakers but these truthmakers make them true in different ways. I shall also use this view to account for the truthmakers of propositions like 〈Socrates is white〉, and respond to previous objections by Cian Dorr and Jessica Wilson. (shrink)

I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.

This paper outlines a semantic account of attitude reports and deontic modals based on cognitive and illocutionary products, mental states, and modal products, as opposed to the notion of an abstract proposition or a cognitive act.

Two grams mass, three coulombs charge, five inches long – these are examples of quantitative properties. Quantitative properties have certain structural features that other sorts of properties lack. What are the metaphysical underpinnings of quantitative structure? This paper considers several accounts of quantity and assesses the merits of each.

Abstract: Friends of plural logic—like Oliver & Smiley (2001), Rayo (2002), Yi (2005), and McKay (2006)—have argued that a semantics of plurals based on mereological sums would be too weak, and they have adduced several examples in favor of their claim. However, they have not considered various possible counter-arguments. So how convincing are their own arguments? We show that several of them are easily answered, while some others are more problematic. Overall, the case against mereological singularism—the idea that mereological sums (...) can serve as the semantic values of plurals—turns out to be much less strong than what it is usually presented to be. (shrink)

Following Russell, philosophers like Moltmann, Jubien, Boër, and Newman analyse ‘John believes that Mary is French’ as ‘R ’, instead of analysing it as ‘R ’. Thus, for these philosophers, instead of relations holding between agents and truth-bearing entities, propositional attitude verbs, like ‘belief’, express relations holding between agents and the properties and objects our thoughts and speech acts are about. This is also known as the Multiple Relation Theory. In this paper, I will discuss the Multiple Relation Theory primarily (...) in connection with a problem known as Schiffer’s puzzle. Schiffer first presented the puzzle to argue against the so called direct-reference theory of belief reports advocated, among others, by Salmon and Braun. I will argue that, unlike the direct-reference theory of belief reports, the Multiple Relation Theory does not provide a solution to Schiffer’s puzzle. In this connection, I will also discuss a slight modification of the Multiple Relation Theory according to which the ways the properties and objects our thoughts and speech acts are about are presented to us are part of the truth-conditions of sentences like ‘John believes that Mary is French’. We will see that prima facie such a contextualist version of the Multiple Relation Theory provides a solution to Schiffer’s puzzle. However, concluding, I will argue with new Schiffer cases that, ultimately, also a contextualist version of the Multiple Relation Theory cannot explain all instances of Schiffer’s puzzle. This will undermine the Multiple Relation Theory in general. (shrink)

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...) the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

That there is no substance causation is often treated as the default position. My aim in this paper is primarily one of burden shifting: opponents of substance causation must do more to defend their position. After outlining the thesis I wish to defend, I present a simple argument for substance causation, arguing that opponents of substance causation owe us an explanation of why this argument is unsound. I end by answering objections to the view that substances can be causes.

Sentences that exhibit sensitivity to order (e.g. 'John and Mary arrived at school in that order' and 'Mary and John arrived at school in that order') present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference (Hewitt 2012) and articulated reference (Ben-Yami 2013). The aim of this article is to show that sensitivity to order should be accounted for (...) without altering the standard formulation of plural logic. In particular, sensitivity to order does not call for a fine-grained notion of plural reference. We point out that the phenomenon in question is quite broad and that current proposals are not equipped to deal with the full range of cases in which order plays a role. Then we develop an alternative and unified account, which locates the phenomenon not in the way in which plural terms can refer, but in the meaning of special expressions such as 'in that order' and 'respectively'. (shrink)

According to the singular conception of reality, there are objects and there are singular properties, i.e. properties that are instantiated by objects separately. It has been argued that semantic considerations about plurals give us reasons to embrace a plural conception of reality. This is the view that, in addition to singular properties, there are plural properties, i.e. properties that are instantiated jointly by many objects. In this article, I propose and defend a novel semantic account of plurals which dispenses with (...) plural properties and thus undermines the semantic argument in favor of the plural conception of reality. (shrink)

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

According to Frege, expressions shift their reference when they occur in indirect contexts: in “Anna believes that Plato is wise” the expression “Plato” no longer refers to Plato but to what is ordinarily its sense. Many philosophers, including Carnap, Davidson, Burge, Parsons, Kripke and Künne, believe that on Frege's view the iteration of indirect context creating operators gives rise to an infinite hierarchy of senses. While the former two take this to be problematic, the latter four welcome the hierarchy with (...) open arms. In this paper I argue that the hierarchy should be avoided and that it can be avoided. (shrink)

In this contribution, we will present some results concerning the connectives of bi-intuitionistic logic in the setting of Arnold Koslow’s implication structures. Furthermore, we will present soundness and completeness results of Koslow’s implication structures with respect to bi-intuitionistic logic.

This paper attempts a conceptualisation of authority intended to be useful across all areas where the concept is relevant. It begins by setting off authority against power, on the one hand, and respect, on the other, and then spells out S1’s authority as consisting in S2’s voluntary action performed in the belief that S1 would approve of it. While this definition should hold for authority generally, a distinction is made between three different kinds of authority according to what grounds them: (...) personal, acquired and bestowed authority. Authority thus defined is then used as an example to argue that there is a kind of property that is response-dependent , but, consisting in all and only a response, is ontologically different from both secondary qualities and value judgments. While secondary qualities are interactive in that they depend on both the object and the perceiver and on what they are like, genuinely R-D qualities depend ontologically and metaphysically only on the responder. And whil.. (shrink)

Most of the theories of location on the market appear to be ideologically parsimonious at least in the sense that they take as primitive just one locative notion and define all the other locative notions in terms of it. Recently, however, the possibility of some exotic metaphysical scenarios involving gunky mixtures and extended simple regions of space has been argued to pose a significant threat to parsimonious theories of locations. The aim of this paper is to show that a theory (...) taking as primitive a notion of plural pervasive location and allowing for irreducibly plural locative facts can account for all the putatively problematic scenarios for parsimonious theories of location. Furthermore, I will also argue that the notion of plural pervasive location is compatible with the possibility of multilocation. (shrink)