An encyclopedia entry which covers various revisionary conceptions of which macroscopic objects there are, and the puzzles and arguments that motivate these conceptions: sorites arguments, the argument from vagueness, the puzzles of material constitution, arguments against indeterminate identity, arguments from arbitrariness, debunking arguments, the overdetermination argument, and the problem of the many.

Are a material object, such as a statue, and its constituting matter, the clay, parts of one another? One wouldn't have thought so, and yet a number of philosophers have argued that they are. I review the arguments for this surprising claim showing how they all fail. I then consider two arguments against the view concluding that there are both pre-theoretical and theoretical considerations for denying that the statue and the clay are mutual parts.

One of the central debates in contemporary metaphysics has been the debate between endurantism and perdurantism about persistence. In this paper I argue that much of this debate has been misconstrued: most of the arguments in the debate crucially rely on theses which are strictly orthogonal to the endurantism/perdurantism debate. To show this, I note that the arguments in the endurantism/perdurantism debate typically take the following form: one presents a challenge that endurantists allegedly have some trouble addressing, and to which (...) perdurantism apparently has a straightforward response. I argue, however, that in each case, there are versions of endurantism that can offer precisely the same response to the challenge, and thus the ability to provide this particular solution does not directly tell in favour of one the two views. In §1, I elaborate two views which will be particularly prominent in the discussion: liberal endurantism and restrictive perdurantism. In §2–6 I discuss in turn the central pro-perdurantism arguments: the argument from anthropocentricism, the argument from vagueness, the argument from recombination, the argument from temporary intrinsics, and the argument from coincidence. In §7–8, I discuss the main pro-endurantism arguments: the arguments from motion, and the argument from permanent coincidence. Finally, in §9, I discuss what conclusion can be drawn from this discussion. (shrink)

Mereological principles are often controversial; perhaps the most stark contrast is between those who claim that Weak Supplementation is analytic—constitutive of our notion of proper parthood—and those who argue that the principle is simply false, and subject to many counterexamples. The aim of this paper is to diagnose the source of this dispute. I’ll suggest that the dispute has arisen by participants failing to be sensitive to two different conceptions of proper parthood: the outstripping conception and the non-identity conception. I’ll (...) argue that the outstripping conception, can deliver the analyticity of Weak Supplementation on at least one sense of ‘analyticity’. I’ll also suggest that the non-identity conception cannot do so independently of considerations to do with mereological extensionality. (shrink)

Those who accept the necessity of mereological universalism face what has come to be known as the ‘junk argument’ due to Bohn [2009], which proceeds from the incompatibility of junk with universalism and the possibility of junk, to conclude that mereological universalism isn't metaphysically necessary. Most attention has focused on ; however, recent authors have cast doubt on . This paper undertakes a defence of premise against three main objections. The first is a new objection to the effect that Bohn's (...) defence of that premise presupposes far too much. I show that one can defend premise from a much weaker set of assumptions. The second objection, due to Contessa [2012], is that those who accept unrestricted composition should only accept the existence of binary sums rather than infinitary fusions. I argue that this conception of unrestricted composition is problematic: it is in conflict with an intuitive remainder principle. The final objection is .. (shrink)

Ned Markosian has recently defended a new theory of composition, which he calls regionalism : some material objects xx compose something if and only if there is a material object located at the fusion of the locations of xx. Markosian argues that regionalism follows from what he calls the subregion theory of parthood. Korman and Carmichael agree. We provide countermodels to show that regionalism does not follow from, even together with fourteen potentially implicit background principles. We then show that regionalism (...) does follow from five of those background principles together with and two additional principles connecting parthood and location, which we call and. While the additional principles are not uncontroversial, our conjecture is that many will find them attractive. We conclude by mentioning that fills a previously unnoticed gap in the formal theory of location presented in Parsons. (shrink)

David Lewis famously endorsed Unrestricted Composition. His defense of such a controversial principle builds on the alleged innocence of mereology. This innocence defense has come under different attacks in the last decades. In this paper I pursue another line of defense, that stems from some early remarks by van Inwagen. I argue that Unrestricted Composition leads to a better metaphysics. In particular I provide new arguments for the following claims: Unrestricted Composition entails extensionality of composition, functionality of location and four-dimensionalism (...) in the metaphysics of persistence. Its endorsement yields an impressively coherent and powerful metaphysical picture. This picture shows a universe that might not be innocent but it is certainly elegant. (shrink)

David Lewis famously endorsed Unrestricted Composition. His defense of such a controversial principle builds on the alleged innocence of mereology. This innocence defense has come under different attacks in the last decades. In this paper I pursue another line of defense, that stems from some early remarks by van Inwagen. I argue that Unrestricted Composition leads to a better metaphysics. In particular I provide new arguments for the following claims: Unrestricted Composition entails extensionality of composition, functionality of location and four-dimensionalism (...) in the metaphysics of persistence. Its endorsement yields an impressively coherent and powerful metaphysical picture. This picture shows a universe that might not be innocent but it is certainly elegant. (shrink)

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts without proper parts. Typically, this thesis is characterized by an axiom stating that everything has atomic parts. The present paper argues that the success of this standard characterization depends on how the notions of sum and composition are defined. In particular, we put forward a novel definition of mereological sum that: (i) is not equivalent to existing definitions in the literature, if no strong decomposition principle (...) is assumed; (ii) can be used to argue that the standard characterization of atomism fails, because having atomic parts is not sufficient to be a sum of atoms; and (iii) provides a purely mereological distinction between structured and unstructured wholes, contributing to the ongoing debate on this crucial topic. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Are submergence and submergent properties metaphysically possible? This is a substantive question that has been either utterly neglected or quickly answered in the negative. This neglect is not only significant in itself; the possibility of submergence plays a crucial role in hotly debated topics in metaphysics, for example, the debate over Monism and Pluralism. This paper is intended to prompt a discussion about metaphysical submergence. In particular I will provide examples of submergent properties, argue that these are metaphysically possible and (...) finally propose a pluralist argument from submergence. (shrink)

Some philosophers say that a whole is “nothing over and above” its parts. Most also take general extensilonal mereology to be treating wholes as “nothing over and above” their parts. It is not always clear, however, what exactly is meant by the phrase “nothing over and above.” Nor is it obvious why the phrase is associated with mereology, and what purpose it serves there. In the words of Peter Van Inwagen : “This slippery phrase has had a lot of employment (...) in philosophy, but what it means is never explained by its employers.” This paper sheds light on the various senses in which one might hold that a whole is “nothing over and above” its parts, and on how these senses are related both to each other and to mereology. (shrink)

Perichoresis, or “mutual indwelling,” is a crucial concept in Trinitarian theology. But the philosophical underpinnings of the concept are puzzling. According to ordinary conceptions of “indwelling” or “being in,” it is incoherent to think that two entities could be in each other. In this paper, I propose a mereological way of understanding “being in,” by analogy with standard examples in contemporary metaphysics. I argue that this proposal does not conflict with the doctrine of divine simplicity, but instead affirms it. I (...) conclude by discussing how mutual indwelling relates to the concepts of unity and identity. (shrink)

In this paper, we present an extensional system of mereology suitable to account for the intuitive distinction between heaplike and non-heaplike entities. Since the need to capture this distinction has been a key motivation for non-extensional mereologies, we first assess the main non-extensional systems advanced in the last years and highlight some mereological and metaphysical difficulties they involve. We then advance a novel program, according to which the distinction between heaplike and non-heaplike entities can be accounted for by bringing together (...) the parthood relation characterized by classical extensional mereology and an Aristotelian extensional notion of potential parthood. Thus, while rejecting the thesis of mereological monism, our proposal is consistent with the thesis of mereological extensionalism. We show that within this framework it is possible to characterize the above-mentioned distinction, to define the relation of material constitution, and to capture three fundamental standpoints in metaphysics. (shrink)

In this paper, using a propositional modal language extended with the window modality, we capture the first-order properties of various mereological theories. In this setting,$\Box \varphi $readsall the parts(of the current object)are$\varphi $, interpreted on the models with awhole-partbinary relation under various constraints. We show that all the usual mereological theories can be captured by modal formulas in our language via frame correspondence. We also correct a mistake in the existing completeness proof for a basic system of mereology by providing (...) a new construction of the canonical model. (shrink)

In the last several years, paraconsistent mereology has begun to be developed and applied to a range of philosophical issues, from puzzles about boundaries, to the Meinongian ‘problem of nothingness’, to the metaphysics of unity. Because these formal systems are fresh out of the package, as it were, there will inevitably be some wrinkles that need ironing out. In this note, I’ll point out a problem with the system in Priest (2014a, 2014b), and suggest a natural fix.

This paper presents three claims concerning boundaries, dependence and parthood. The claims are intuitively plausible, but cannot, at face value, all be true on pain of contradiction. Each of the three claims is shown to be more plausible than its converse and some solutions to the puzzle are presented.

The literature suggests two main answers to the question of what it is for a material object to be located at a region of spacetime. Both have a number of virtues. However, both suffer from well-known problems. According to one answer, location is a primitive relation with no informative metaphysical analysis. But this makes a number of necessary truths seem mysterious and leaves them unexplained. According to the other answer, to be located at a region is just to be identical (...) to that region. But this is inconsistent with a number of independently plausible theses about material objects and their locations. In this paper, I explore a new theory of location and argue that it has the virtues of these familiar theories but not their vices. I then explore some further connections the new theory has with some contemporary issues in metaphysics. (shrink)

This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...) of the argument. (shrink)

I reply to Hawthorne and Uzquiano’s arguments for the incompatibility between mereological universalism and plenitudinous co-location. I argue that a mereology in which antisymmetry for parthood fails is independently motivated, and allows for both universalism and plenitudinous co-location. There can be as many angels in a place as there are cardinalities.

In the literature on mereology it is often accepted that mereological universalism entails extensionalism. More precisely, many accept that, if parthood is assumed to be a partial order, the thesis that every plurality of entities has a mereological fusion entails the thesis that different composite entities have different proper parts. Central to this idea is the principle known as ‘Weak Supplementation’ which many take to impose an important constraint on the relation of proper parthood. In this paper I argue that (...) this claim is false as the principle that I will call ‘Minimal Supplementation’ appears to be capable of doing all the work done by Weak Supplementation but without entailing extensionalism if conjoined with universalism and core mereology. (shrink)

One of the most influential arguments in favour of perdurantism is the Argument from Vagueness. The argument proceeds in three stages: The first aims to establish atemporal universalism. The second presents a parallel argument in favour of universalism in the context of temporalized parthood. The third argues that diachronic universalism entails perdurantism. I offer a novel objection to the argument. I show that on the correct way of formulating diachronic universalism the principle does not entail perdurantism. On the other hand, (...) if diachronic universalism is formulated as Sider proposes, the argument fails to establish his principle, and thus perdurantism. (shrink)

This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars.

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation, which is super-rigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a two-dimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...) and their metaphysical possibility or verification. I then generalize the approach to haecceitistic properties, and examine the Julius Caesar problem as a test case. (shrink)

According to Whitehead’s rectified principle, two individuals are connected just in case there is something self-connected which overlaps both of them, and every part of which overlaps one of them. Roberto Casati and Achille Varzi have offered a counterexample to the principle, consisting of an individual which has no self-connected parts. But since atoms are self-connected, Casati and Varzi’s counterexample presupposes the possibility of gunk or, in other words, things which have no atoms as parts. So one may still wonder (...) whether Whitehead’s rectified principle follows from the assumption of atomism. This paper presents an atomic countermodel to show the answer is no. (shrink)

Compliments have received only cursory attention from speech act theorists and are usually characterised as run-of-the-mill illocutionary acts. Yet both intentionalist and conventionalist theories of illocutionary force struggle to accommodate ordinary language uses of ‘compliment’. I argue that this is because there are in fact two kinds of compliment: illocutionary compliments and perlocutionary compliments. This account illuminates the practice of complimenting, as well as its converse, insulting, and illustrates the complex relationship between illocutionary force and perlocutionary effect.

A.J. Cotnoir has argued that we should distinguish between two notions of proper parthood: outstripped part and non-identical part. Outstripped parthood is an asymmetric relation, but non-identical parthood is not. We argue, first, that the intuitions Cotnoir uses to motivate these notions do not always give the right verdict; and, second, that systematic reasons for distinguishing these two notions of parthood have further counter-intuitive consequences. This means the distinction between two notions of proper parthood currently lacks adequate motivation.

Late Lowe’s metaphysics of material objects is an interesting multi-thingist theory that still attracts interest from various authors. The core idea is that ifxmaterially constitutesy, thexis a proper part ofy. I discuss some mereological issues that arise from the approach and propose a revision of the mereology associated. Particularly, I examine the tenability of a number of supplementation principles and conclude that just one may serve the theory adequately. Still, the endorsement of such a principle does not come for free. (...) Successively, I address the derivability of an important extensionality theorem and conclude that the theorem must be taken as an axiom in the mereology at stake. Lastly, I discuss two notable definitions of mereological fusions to assess which one best suits the present theory. The result is that authors sharing Lowe’s multi-thingist conception of material objects can still enjoy a moderately strong mereology. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)