Whether collective agency is a coherent concept depends on the theory of agency that we choose to adopt. We argue that the enactive theory of agency developed by Barandiaran, Di Paolo and Rohde (2009) provides a principled way of grounding agency in biological organisms. However the importance of biological embodiment for the enactive approach might lead one to be skeptical as to whether artificial systems or collectives of individuals could instantiate genuine agency. To explore this issue we contrast the concept (...) of collective agency with multi-agent systems and multi-system agents, and argue that genuinely collective agents instantiate agency at both the collective level and at the level of the component parts. Developing the enactive model, we propose understanding agency – both at the level of the individual and of the collective – as spectra that are constituted by dimensions that vary across time. Finally, we consider whether collectives that are not merely metaphorically ‘agents’ but rather are genuinely agentive also instantiate subjectivity at the collective level. We propose that investigations using the perceptual crossing paradigm suggest that a shared lived perspective can indeed emerge but this should not be conflated with a collective first-person perspective, for which material integration in a living body may be required. (shrink)

This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.

This paper outlines a novel solution to the problem of the many and a conception of ordinary objects that implies it. The solution is that many collections of particles can simultaneously constitute a single object. The proposed conception of ordinary objects maintains that they are fundamentally subjects of change: the changes an object is able to survive explain its constitution.

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)

Say that some things compose something, if the latter is a whole, fusion, or mereological sum of the former. Then the thesis that composition is identity holds that the composition relation is a kind of identity relation, a plural cousin of singular identity. On this thesis, any things that compose a whole are identical with the whole. This article argues that the thesis is incoherent. To do so, the article formulates the thesis in a plural language, a symbolic language that (...) includes counterparts of plural constructions of natural languages, and shows that it implies that nothing has a proper part. Then the article argues that the thesis, as its proponents take it, is incoherent because they take it to imply or presuppose that some things have proper parts. (shrink)

Self-consciousness in non-human animals is a complex phenomenon which raises both conceptual and methodological problems. First, what do we mean by the concept of ‘self-consciousness’? Secondly, what is the best experimental approach to self-consciousness? This paper gives a short overview of the concept of self-consciousness in section 1. We can understand the concept of self-consciousness as capturing the ability of subjects to consciously think about themselves as themselves. If this is accurate, then it is prudent to look at a broad (...) bundle of abilities which are related to this ability. The paper then focuses on advantages and problems of the multipronged approach, a kind of empirical approach which uses several different test criteria to determine whether a subject is self-conscious or not. Section 2 briefly contrasts this kind of approach with other possibilities. The main disparity is to singlepronged approaches, which have been discussed and dismissed in greater detail elsewhere. Section 3 discusses the advantages of a multipronged approach, whereas section 4 is dedicated to the discussion of some of its problems. (shrink)

The aim of this paper is to introduce, elucidate and defend the usefulness of a variant of grounding, or metaphysical explanation, that has the feature that the grounds explain of some states of affairs that one of them obtains without explaining which one obtains. I will dub this variant arbitrary grounding. After informally elucidating the basic idea in the first section, I will provide three metaphysical hypotheses that are best formulated in terms of arbitrary grounding in the second section. The (...) third section will be concerned with the relation between arbitrary grounding and non-arbitrary grounding. The fourth section will compare arbitrary grounding to two extant proposals in the literature. (shrink)

The Platonic account of modality says, roughly, that truths about alien possibilities are grounded in uninstantiated universals. Recently, Ingram has raised a problem for this kind of view, which is that it apparently requires negative facts to play a truthmaking role. Ingram offers an alternative Platonic account which makes use of modal instantiation relations. In this paper, I highlight some of the costs of Ingram’s new account and argue that a more appealing version of Platonism—and modal theory in general—is one (...) that is supplemented with an ontology of totality facts. (shrink)

European Journal of Philosophy, EarlyView.

Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the (...) help of definitions, just as the logicist thesis maintains. (shrink)

It is natural to think that social groups are concrete material particulars, but this view faces an important objection. Suppose the chess club and nature club have the same members. Intuitively, these are different clubs even though they have a common material basis. Some philosophers take these intuitions to show that the materialist view must be abandoned. I propose an alternative explanation. Social groups are concrete material particulars, but there is a psychological explanation of nonidentity intuitions. Social groups appear coincident (...) but nonidentical because they are perceived to be governed by conflicting social norms. (shrink)

I propose a way of thinking aboout content, and a related way of thinking about ontological commitment. (This is part of a series of four closely related papers. The other three are ‘On Specifying Truth-Conditions’, ‘An Actualist’s Guide to Quantifying In’ and ‘An Account of Possibility’.).

Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.

This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...) discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications. (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)

Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...) if only because mathematicians take many-valued functions seriously. We assess the objection (by Russell, Frege and others) that many-valued functions are illegitimate because the corresponding terms are ambiguous. We also assess the various methods proposed for getting rid of them. Finding the objection ill-founded and the methods ineffective, we introduce a logical framework that admits plural reference, and use it to answer some earlier questions and to raise some more. (shrink)

A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but plural logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets when characterizing their semantics, we arrive at a Russellian paradox. And if we use predicate logic and mereoogical ums, the semantics turns out (...) to be too weak. We then develop an account where mass nouns are treated as non-singular terms. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: "The silverware that is on the table comes from Italy." We show that this account provides a satisfactory semantics for a wide range of sentences. (shrink)

A dilemma put forward by Schein (1993) and Rayo (2002) suggests that, in order to characterize the semantics of plurals, we should not use predicate logic, but non-singular logic, a formal language whose terms may refer to several things at once. We show that a similar dilemma applies to mass nouns. If we use predicate logic and sets, we arrive at a Russellian paradox when characterizing the semantics of mass nouns. Likewise, a semantics of mass nouns based upon predicate logic (...) and mereological sums is too weak, since it cannot characterize the “intermediary” construals that sentences containing mass nouns may receive. We then develop an account where mass nouns are treated as non-singular terms, which may refer to several things at once. This semantics is faithful to the intuition that, if there are eight pieces of silverware on a table, the speaker refers to eight things at once when he says: “The silverware that is on the table comes from Italy”. We show that this account provides a satisfactory semantics for a wide range of sentences, including cases often seen as difficult, like “The gold on the table weighs seven ounces” (Bunt 1985) and “All phosphorus is either red or black” (Roeper 1983). (shrink)

This paper motivates and defends a principle which captures a systematic connection between essence, truth, and grounding. It says that if a proposition expresses an essential truth, i.e., if it is true in virtue of the nature of some objects, then there are grounds for its truth which involve these objects. Together with the assumption that a fact can only be grounded in facts which are relevant to it, this principle is then applied in an argument against the monotonicity of (...) the Essentialist notion ‘true in virtue of the nature of’. (shrink)

Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things (...) as “It is indeterminate whether this particle is part of Kilimanjaro”. After reviewing some of the limitations of this approach, I will propose an alternative account, based on a new semantic relation—multiple reference—capable of holding in a one-many pattern between a term and several objects in the domain. I will explain how multiple reference works, what differentiates it from plural reference and how it might be used to accommodate at least some aspects of our ordinary discourse about vague objects. (shrink)

Propositional contingentism is the view that what propositions there are is a contingent matter—certain propositions ontologically depend on objects which themselves only contingently exist. Possible worlds are, loosely, complete ways the world could have been. That is to say, the ways in which everything in its totality could have been. Propositional contingentists make use of possible worlds frequently. However, a neglected, but important, question concerns whether there are any notions of worlds which are both theoretically adequate and consistent with propositional (...) contingentism. Some notion of a possible world is adequate if the systematic connection between, at least, possibility and truth at some possible world holds. Here, I argue that no adequate notion of a possible world is available to at least those who subscribe to one natural formulation of propositional contingentism. I also show that this result contrasts with a simple and adequate definition of a possible world available to the necessitist—those who hold that necessarily everything necessarily exists. (shrink)

Plural constructions in mathematical speech are no rarity. E.g., when we want to say that the real numbers are the basis on which we construct Calculus (cf. [16], p. 6), and that the integers are an integral domain (cf. [14], p. 237), we are not talking about one thing, namely the set of the real numbers and the set of the integers, respectively, but we are talking about several things, namely the real numbers and the integers, respectively. In the present (...) paper, we introduce a semantics which takes the use of plural constructions in mathematical speech as a basis and thus avoids sets and attributes. (shrink)

In this paper I address two important objections to the theory called ‘ Composition as Identity’ : the ‘wall-bricks-and-atoms problem’, and the claim that CAI entails mereological nihilism. I aim to argue that the best version of CAI capable of addressing both problems is the theory I will call ‘Atomic Composition as Identity’ which consists in taking the plural quantifier to range only over proper pluralities of mereological atoms and every non-atomic entity to be identical to the plurality of atoms (...) it fuses. I will proceed in three main steps. First, I will defend Sider’s Composition as identity. Oxford University Press, Oxford, pp 211–221, 2014) idea of weakening the comprehension principle for pluralities and I will show that :219–235, 2016a) it can ward off both the WaBrA problem and the threat of mereological nihilism. Second, I will argue that CAI-theorists should uphold an ‘atomic comprehension principle’ which, jointly with CAI, entails that there are only proper pluralities of mereological atoms. Finally, I will present a novel reading of the ‘one of’ relation that not only avoids the problems presented by Yi Composition as identity. Oxford University Press, Oxford, pp 169–191, 2014) and Calosi :429–443, 2016b, Am Philos Q 55:281–292, 2018) but can also help ACAI-theorists to make sense of the idea that a composite entity is both one and many. (shrink)

According to ‘Strong Composition as Identity’, if an entity is composed of a plurality of entities, it is identical to them. As it has been argued in the literature, SCAI appears to give rise to some serious problems which seem to suggest that SCAI-theorists should take their plural quantifier to be governed by some ‘weak’ plural comprehension principle and, thus, ‘exclude’ some kinds of pluralities from their plural ontology. The aim of this paper is to argue that, contrary to what (...) may appear at first sight, the assumption of a weak plural comprehension principle is perfectly compatible with plural logic and the common uses of plural quantification. As I aim to show, SCAI-theorists can simply claim that their theory must be understood as formulated by means of the most ‘joint-carving’ plural quantifier, thus leaving open the possibility of other, less joint-carving, ‘unrestricted’ plural quantifiers. In the final part of the paper I will also suggest that SCAI-theorists should not only allow for singular quantification over pluralities of entities, but also for plural quantification over ‘super-pluralities’ of entities. (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 this paper I take second order-quantification to be a sui generis form of quantification, irreducible to first-order quantification, and I examine the implications of doing so for the debate over the existence of properties. Nicholas K. Jones has argued that adding sui generis second-order quantification to our ideology is enough to establish that properties exist. I argue that Jones does not settle the question of whether there are properties because—like other ontological questions—it is first-order. Then I examine three of (...) the main arguments for the existence of properties. I conclude that sui generis second-order quantification defeats the “one over many” argument and that, coupled with second-order predication, it also defeats the reference and quantification arguments. (shrink)

Philosophers disagree whether composition as identity entails mereological universalism. Bricker :264–294, 2016) has recently considered an argument which concludes that composition as identity supports universalism. The key step in this argument is the thesis that any objects are identical to some object, which Bricker justifies with the principle of the universality of identity. I will spell out this principle in more detail and argue that it has an unexpected consequence. If the universality of identity holds, then composition as identity not (...) only leads us to universalism, but also leads to the view that there are no mereological atoms. (shrink)

Composition as Identity claims that a composite object is identical to its parts taken collectively. This is often understood as reducing the identity of composite objects to the identity of their parts. The author argues that Composition as Identity is not such a reduction. His central claim is that an intensional notion of composition, which is sensitive to the arrangement of the composing objects, avoids criticisms based on an extensional understanding of composition. The key is to understand composition as an (...) intensional kind of identity relation, many-one identity. Eventually, the author suggests an arrangement condition for many-one identity that allows him to distinguish between composite objects, even if they have the same parts. (shrink)

In this paper we argue that physical theories, including quantum mechanics, refer to some kind of ‘objects’, even if only implicitly. We raise questions about the logico-mathematical apparatuses commonly employed in such theories, bringing to light some metaphysical presuppositions underlying such apparatuses. We point out to some incongruities in the discourse holding that quantum objects would be entities of some ‘new kind’ while still adhering to the logico-mathematical framework we use to deal with classical objects. The use of such apparatus (...) would hinder us from being in complete agreement with the ontological novelties the theories of quanta seem to advance. Thus, we join those who try to investigate a ‘logic of quantum mechanics’, but from a different point of view: looking for a formal foundation for a supposed new ontology. As a consequence of this move, we can revisit Einstein’s ideas on physical reality and propose that, by considering a new kind of object traditionally termed ‘non-individuals’, it is possible to sustain that they still obey some of Einstein’s conditions for ‘physical realities’, so that it will be possible to talk of a ‘principle of separability’ in a sense which is not in complete disagreement with quantum mechanics. So, Einstein’s departure from quantum mechanics might be softened at least concerning a form of his realism, which sees separated physical objects as distinct ‘physical realities’. (shrink)

Byeong-Uk Yi has argued that number words like ‘two’ primarily function as numerical predicates as in ‘Socrates and Hippias are two ’, and other grammatical uses of number words can be paraphrased in terms of the predicative use. This paper critically examines Yi’s paraphrase scheme and also some other alternative schemes, and argues that the adjectival use of number words as in ‘The Scots and the Irish are two peoples’ cannot be paraphrased in terms of the predicative use.

The state of affairs of some things falling under a predicate is supposedly a single entity that collects these things as its constituents. But whether we think of a state of affairs as a fact, a proposition or a possibility, problems will arise if we adopt a plural logic. For plural logic says that any plurality include themselves, so whenever there are some things, the state of affairs of their plural self-inclusion should be a single thing that collects them all. (...) This leads to paradoxes analogous to those that afflict naïve set theory. Here I suggest that they are the very same paradoxes, because sets can be reduced to states of affairs. However, to obtain a consistent theoretical reduction we must restrict the usual axiom scheme of Comprehension for plural logic to ‘stratified’ formulas, to avoid viciously circular definitions. I prove that with this modification to the background plural logic, the theory of states of affairs is consistent; moreover, it yields the axioms of the familiar set theory NFU. (shrink)

We say that each social group is identical to its members. The group just is them; they just are the group. This view of groups as pluralities has tended to be swiftly rejected by social metaphysicians, if considered at all, mainly on the basis of two objections. First, it is argued that groups can change in membership, while pluralities cannot. Second, it is argued that different groups can have exactly the same members, while different pluralities cannot. We rebut these objections, (...) and argue that our plural view is superior to alternative reductive proposals which would identify social groups with the sets or fusions of their members. Finally we deal with some further potential challenges for the view of groups as pluralities. Thus we aim to establish it as a serious contender in the metaphysics of groups. (shrink)

There has been much work on ontological dependence in recent literature. However, relatively little of it has been dedicated to the ways in which individual physical objects may depend on other distinct, non-overlapping objects. This paper gives several examples of such object-dependence and distinguishes between different types of it. The paper also introduces and refines the notion of an n-tet. N-tets (typically) occur when there are object-dependence relations between n objects. I claim that the identity (or, rather, what I call (...) the n-dentity) conditions for n-tets are not grounded in the individual identity conditions of each of the n objects, but instead are metaphysically basic. The paper then briefly discusses some ramifications of accepting object-dependence (and n-tets) on the philosophy of biology, ethics, and logic. (shrink)

There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and (...) showing that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language plurals, motivating a case against (Necinc) by developing a case that natural language plural terms are not de jure rigid designators. The paper concludes by developing a model theory for modal PFO-f which does not validate (Necinc). An Appendix discusses (Necinc) in relation to counterpart theory. Of course, it would be a mistake to think that the rules for "multiple pointing" follow automatically from the rules for pointing proper. Max Black—The Elusiveness of Sets In some influential articles during the 1980s George Boolos proposed an interpretation of monadic second-order logic in terms of plural quantification [4, 5]. One objection to this proposal, pressed by Williamson [22, 456-7], focuses on the modal behaviour of plural variables, arguing that the proposed interpretation yields the wrong results in respect of the modal status of atomic predications. In the present paper I will present this objection and argue against it. In the course of developing the argument, I will have cause to consider the under-investigated question of how a logic for plurals should be extended to incorporate modal operators. (shrink)

I discuss Aristotle’s opening argument against Platonic Forms in _Metaphysics_ A.9, ‘the Razor’, which criticizes the introduction of Forms on the basis of an analogy with a hypothetical case of counting things. I argue for a new interpretation of this argument, and show that it involves two interesting objections against the introduction of Forms as formal causes: one concerns the completeness and the other the adequacy of such an explanatory project.

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that (...) propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise. (shrink)

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...) main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

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)

The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of pluralities for Boolos’ (...) plural reading of second-order quantifiers, for the notion of plurality is much more general, not only of that set, but also of class. In fact, by showing that a plurality is equivalent to sub-sets of a power set, the notion of plurality comes to suffer a loss of generality. Despite of this equivalence result, I maintain that Boolos’ formal semantics does not committ second-order languages to second-order entities, contrary to standard semantics. Further, such an equivalence result provides a rationale for many criticisms to Boolos’ formal semantics, in particular those by Resnik and Parsons against its alleged ontological innocence and on its Platonistic presupposition. The key set-theoretic notion involved in the equivalence proof is that of many-valued function. But, first, I will provide a clarification of the philosophical context and theoretical grounds of the genesis of Boolos’ formal semantics. (shrink)

We discuss abstraction principles in the context of modal and temporal logic. It is argued that abstractionism conflicts with both serious presentism and serious actualism.

There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two (...) theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one’s mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis. (shrink)

This paper deals with Leibniz’s well-known reductio argument against the infinite number. I will show that while the argument is in itself valid, the assumption that Leibniz reduces to absurdity does not play a relevant role. The last paragraph of the paper reformulates the whole Leibnizian argument in plural terms to show that it is possible to derive the contradiction that Leibniz uses in his argument even in the absence of the premise that he refutes.

David Lewis defends the following "non-circular definition of personhood": "something is a continuant person if and only if it is a maximal R-interrelated aggregate of person-stages. That is: if and only if it is an aggregate of person-stages, each of which is R-related to all the rest (and to itself), and it is a proper part of no other such aggregate." I give a counterexample, involving a person who is a part of another, much larger person, with a separate mental (...) life. I then offer an easy repair, which preserves the virtues of Lewis's definition without introducing any new vices. (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)

In Mathematics is megethology. Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed (...) in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification. (shrink)