This collection of essays is the first of its kind to focus on the relationship between composition and identity. Twelve original articles--written by internationally renowned scholars and rising stars in the field--argue for and against the controversial doctrine that composition is identity.--Provided by publisher.

I examine the link between extensionality principles of classical mereology and the anti‐symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti‐symmetry. I examine the notions of proper parthood, weak supplementation and non‐well‐foundedness. By rejecting anti‐symmetry, the anti‐extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non‐extensional mereology in which anti‐symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non‐anti‐symmetric mereology recaptures all of the structure (...) of classical mereology. (shrink)

Does a commitment to mereological universalism automatically bring along a commitment to the controversial doctrine of mereological extensionalism—the view that objects with the same proper parts are identical? A recent argument suggests the answer is ‘yes’. This paper attempts a systematic response to the argument, considering nearly every available line of reply. It argues that only one approach—the mutual parts view—can yield a viable mereology where universalism does not entail extensionalism.

This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to (...) classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete. (shrink)

The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, (...) the paper considers an alternative approach that focuses the blame on antisymmetry but allows us to keep natural supplementation axioms. Third, we look at counterexamples to the idempotency of composition and the associated ‘parts just once’ principle. We explore options for developing weaker mereologies that avoid such commitments. (shrink)

Mereological nihilists are faced with a difficult challenge: explaining ordinary talk about material objects. Popular paraphrase strategies involve plurals, arrangements of particles, or fictions. In this paper, a new paraphrase strategy is put forward that has distinct advantages over its rivals: it is compatible with gunk and emergent properties of macro-objects. The only assumption is a commitment to a liberal view of the nature of simples; the nihilist must be willing to accept the possibility of heterogeneous extended simples. The author (...) suggests reinterpreting the parthood and composition relations as modal. According to this paraphrase, composition is a kind of counterpart relation. The author shows that one can accept that mereological nihilism is metaphysically necessary, while endorsing all the claims of classical mereology. As a result, the nihilists are in exactly the same position as the classical mereologist when it comes to explaining talk about ordinary objects, but without the additional ontology. (shrink)

Contemporary metaphysicians have been drawn to a certain attractive picture of the structure of the world. This picture consists in classical mereology, the priority of parts over wholes, and the well-foundedness of metaphysical priority. In this short note, I show that this combination of theses entails superatomism, which is a significant strengthening of mereological atomism. This commitment has been missed in the literature due to certain sorts of models of mereology being overlooked. But the entailment is an important one: we (...) must either accept superatomism or reject one (or other) of the most widespread theses of contemporary metaphysics. (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)

Christine Tappolet posed a problem for alethic pluralism: either deny the truth of conjunctions whose conjuncts are from distinct domains of inquiry, or posit a generic global truth property thus making other truth properties redundant. Douglas Edwards has attempted to solve the problem by avoiding the horns of Tappolet's dilemma. After first noting an unappreciated consequence of Edwards's view regarding a proliferation of truth properties, I show that Edwards's proposal fails to avoid Tappolet's original dilemma. His response is not successful, (...) as it lets in a generic truth property through the ‘back door’. I conclude by briefly offering a new solution to the problem, and an alternative diagnosis of Tappolet's dilemma.1. Tappolet's dilemmaThe alethic pluralist ; Sher ; Wright ) contends that propositions from different domains can be true in different ways. Mixed conjunctions have conjuncts from different domains; consider for example, ‘1+1=2 and murder is wrong’. A pressing question for the pluralist: if each conjunct is true in a distinct way, in what way is the conjunction true? Tappolet argues, " [M]ixed conjunctions need to be true in a further way. … But then each conjunct has to be true in the same way. This is what follows from the truism that a conjunction is true if and only if its conjuncts are true. Hence the question arises again why this further way of being true is not the only one we need. " Edwards puts Tappolet's contention as a dilemma: either admit a generic truth property that can apply to all propositions, regardless of domain or deny that mixed conjunctions can be true. It is prima facie plausible that mixed conjunctions can be true. Moreover, admitting a generic truth property would seemingly undermine alethic pluralism by making other truth properties redundant.2. Edwards's solutionEdwards's solution attempts …. (shrink)

Ontological pluralism holds that there are different ways of being. Truth pluralism holds that there are different ways of being true. Both views have received growing attention in recent literature, but so far there has been very little discussion of the connections between the views. The authors suggest that motivations typically given for truth pluralism have analogue motivations for ontological pluralism; they argue that while neither view entails the other, those who hold one view and wish to hold the other (...) will find natural routes by which to do so. The authors additionally identify some disanalogies between the views, by considering whether certain “mixed” problems commonly pressed against truth pluralism have analogues for ontological pluralism. (shrink)

We present a new axiomatization of classical mereology in which the three components of the theory—ordering, composition, and decomposition prin-ciples—are neatly separated. The equivalence of our axiom system with other, more familiar systems is established by purely deductive methods, along with additional results on the relative strengths of the composition and decomposition axioms of each theory.

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 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.

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.

Do powers have parts? Mereological thinking is typically guided by two different metaphors: building versus carving. The building picture treats wholes as constructed from fundamental bits; the carving treats wholes as the result of carving some interconnected space. After considering some suggestions for how to view powers as built from other components, this chapter opts for the carving picture and suggests that a mereology of powers can be generated by carving the underlying space of an interconnected web of fundamental powers. (...) The space of powers is a network of manifestation/triggering connections that can be modelled graph-theoretically where the identity of a fundamental power is importantly tied up with its position in the overall structure. This chapter considers the idea that powers are completely identified by their position in the structure (as pandispositionalists have thought), which then places limits on the sorts of structures that powers theorists can help themselves to. This chapter also considers another novel suggestion on the identity of powers borrowed from non-well-founded set theory. It shows how to identify principles governing ‘carving’ the web into groups of closely connected powers, such that one group can naturally be called ‘part’ of another group, and explore the resulting mereology. (shrink)

Jenkins (2007) charges that the language advanced in Beall (2007) is either expressively impoverished, or inconsistent. We argue that Jenkins’ objections are based on unreasonably strong constraints on formal theories of truth. Our primary concern is not to defend the ‘paranormal’ framework advanced in Beall, but to respond to a common – and implausible – ‘revenge’-style charge directed at a certain class of formal theories of truth and paradox.

In a series of papers, 137–158; 1994, Midwest Studies in Philosophy, 23, 61–74, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in. In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points (...) in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the second-order quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine’s principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine’s various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki’s main objection to Fine’s theory. In the appendix we present proofs of the inexpressibility results of Section 6. (shrink)

This paper provides a critical examination of three related attempts to defend Composition as Identity (CI), namely the thesis that if some things compose something, then they are it. First, it will be argued against Donald Baxter’s view of composition as ‘loose identity’ that by construing composition as strictly a many-many relation, the view trivializes CI, and cannot be an option for the advocate of CI who takes composition as a genuine many-one relation. Second, it is argued against Baxter’s modified (...) view of composition as ‘cross-count identity’ that the ‘are’ in ‘they are it’ cannot be viewed as expressing cross-count identity. Lastly, it is argued against Aaron Cotnoir’s view of composition as ‘general identity’ that it amounts to resorting back to Baxter’s old view of composition as a many-many relation. (shrink)

This is a short response to Aaron Cotnoir's 'Composition as General Identity', in which I suggest some further applications of his ideas, and try to press the question of why we should think of his 'general identity relation' as a genuine identity relation.

Alethic pluralism holds that there are many ways of being true. Such a view has been challenged to make sense of the standard account of logical validity as necessary truth preservation. In this paper, the recent solution elaborated by Aaron Cotnoir, based on an algebraic approach, is shown to be untenable. Some reflections about the relation of many-valued logics with truth pluralism are also discussed.

Aaron Cotnoir does all sorts of interesting things in his contribution to this volume. He makes a helpful distinction between syntactic and semantic objections to the thesis that composition is identity, and outlines some empirical points relevant to the syntactic issue. But the centrepiece is his development of a formal framework for addressing the semantic objections.

How do we know right from wrong? Do we even have moral knowledge? Moral epistemology studies these and related questions about our understanding of virtue and vice. It is one of philosophy’s perennial problems, reaching back to Plato, Aristotle, Aquinas, Locke, Hume and Kant, and has recently been the subject of intense debate as a result of findings in developmental and social psychology. Throughout the book Zimmerman argues that our belief in moral knowledge can survive sceptical challenges. He also draws (...) on a rich range of examples from Plato’s Meno and Dickens’ David Copperfield to Bernard Madoff and Saddam Hussein. (shrink)

Is a whole something more than the sum of its parts? Are there things composed of the same parts? If you divide an object into parts, and divide those parts into smaller parts, will this process ever come to an end? Can something lose parts or gain new ones without ceasing to be the thing it is? Does any multitude of things (including disparate things such as you, this book, and the tail of a cat) compose a whole of some (...) sort? Questions such as these have occupied us for at least as long as philosophy has existed. They define the field that has come to be known as mereology-the study of all relations of part to whole and of part to part within a whole-and have deep and far-reaching ramifications in metaphysics as well as in logic, the foundations of mathematics, the philosophy of language, the philosophy of science, and beyond. In Mereology, A. J. Cotnoir and Achille C. Varzi have compiled decades of advanced research into a comprehensive, up-to-date, and formally rigorous picture. The early chapters cover the more classical aspects of mereology; the rest of the book deals with variants and extensions. Whether you are an established professional philosopher, an interested student, or a newcomer, inside you will find all the tools you need to join this ever-evolving field of inquiry and theorize about all things mereological. (shrink)

There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their metaphysical (...) nonfundamentality. I conclude by sketching how Du Châtelet’s conception of mathematical indispensability differs interestingly from many contemporary approaches. (shrink)

Merold Westphal's book is a wonderful introduction to the history of philosophy.

It is widely held that, in his pre-Critical works, Kant endorsed a necessitation account of laws of nature, where laws are grounded in essences or causal powers. Against this, I argue that the early Kant endorsed the priority of laws in explaining and unifying the natural world, as well as their irreducible role in in grounding natural necessity. Laws are a key constituent of Kant’s explanatory naturalism, rather than undermining it. By laying out neglected distinctions Kant draws among types of (...) natural law, grounding relations, and ontological levels, I show that his early works present a coherent and sophisticated laws-first account of the natural order. (shrink)

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against (...) the divine attributes. (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)

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 (together with a specific set of definitions for other mereological notions), 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)

Traditional monotheism has long faced logical puzzles. We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed logic but an appendix is offered as a brief review.

Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of (...) empty parts, in delivering a balanced and bounded metaphysics of naive space. (shrink)

What is the proper role of logic in analytic theology? This question is thrown into sharp relief when a basic logical principle is questioned, as in Beall’s ‘Christ – A Contradiction.’ Analytic philosophers of logic have debated between exceptionalism and anti-exceptionalism, with the tide shifting towards anti-exceptionalism in recent years. By contrast, analytic theologians have largely been exceptionalists. The aim of this paper is to argue for an anti-exceptionalist view, specifically treating logic as a modelling tool. Along the way I (...) critically engage with Beall on the role of logic in theology, maintaining that theological inquiry is in some ways disanalogous with other theoretical enterprises. (shrink)

Polarization is a topic of intense interest among social scientists, but there is significant disagreement regarding the character of the phenomenon and little understanding of underlying mechanics. A first problem, we argue, is that polarization appears in the literature as not one concept but many. In the first part of the article, we distinguish nine phenomena that may be considered polarization, with suggestions of appropriate measures for each. In the second part of the article, we apply this analysis to evaluate (...) the types of polarization generated by the three major families of computational models proposing specific mechanisms of opinion polarization. (shrink)

Polarization is a topic of intense interest among social scientists, but there is significant disagreement regarding the character of the phenomenon and little understanding of underlying mechanics. A first problem, we argue, is that polarization appears in the literature as not one concept but many. In the first part of the article, we distinguish nine phenomena that may be considered polarization, with suggestions of appropriate measures for each. In the second part of the article, we apply this analysis to evaluate (...) the types of polarization generated by the three major families of computational models proposing specific mechanisms of opinion polarization. (shrink)

The aim of this paper is to bring recent work on metaphysical grounding to bear on the phenomenon of social construction. It is argued that grounding can be used to analyze social construction and that the grounding framework is helpful for articulating various claims and commitments of social constructionists, especially about social identities, e.g., gender and race. The paper also responds to a number of objections that have been leveled against the application of grounding to social construction from Elizabeth Barnes, (...) Mari Mikkola, and Jessica Wilson. (shrink)

Obligations to reduce one’s green house gas emissions appear to be difficult to justify prior to large-scale collective action because an individual’s emissions have virtually no impact on the environmental problem. However, I show that individuals’ emissions choices raise the question of whether or not they can be justified as fair use of what remains of a safe global emissions budget. This is true both before and after major mitigation efforts are in place. Nevertheless, it remains difficult to establish an (...) obligation to reduce personal emissions because it appears unlikely that governments will in fact maintain safe emissions budgets. The result, I claim, is that under current conditions we lack outcome, fairness, promotional, virtue or duty based grounds for seeing personal emissions reductions as morally obligatory. (shrink)

Hannah Arendt's essays about the 1957 crisis over efforts of a group of youth, the “Little Rock Nine,” to desegregate a high school in Little Rock, Arkansas, reveal a tension in her vision of the “public.” In this article Aaron Schutz and Marie Sandy look closely at the experiences of the youth desegregating the school, especially those of Elizabeth Eckford, drawing upon them to trace a continuum of forms of public engagement in Arendt's work. This ranges from arenas of (...) “deliberative friendship,” where unique individuals collaborate on common efforts, to a more conflictual “public stage,” where groups act in solidarity to change aspects of the public world. While Arendt famously asserted in her essay “The Crisis in Education” that political capacities should not be taught in schools, it makes more sense to see this argument as focused on what she sometimes called the conflictual “public stage,” reflecting the experience of the Little Rock Nine. In contrast, Schutz and Sandy argue that Arendt's own work implies that “deliberative friendship,” as described in her essay “Philosophy and Politics” and elsewhere, should be part of everyday practices in classrooms and schools. (shrink)

One of the most profound interactions that can occur between people, apologies have the power to heal humiliations, free the mind from deep-seated guilt, remove the desire for vengeance, and ultimately restore broken relationships. With On Apology, Aaron Lazare offers an eye-opening analysis of this vital interaction, illuminating an often hidden corner of the human heart. He discusses the importance of shame, guilt, and humiliation, the initial reluctance to apologize, the simplicity of the act of apologizing, the spontaneous generosity (...) and forgiveness on the part of the offended, the transfer of power and respect between two parties, and much more. Readers will not only find a wealth of insight that they can apply to their own lives, but also a deeper understanding of national and international conflicts and how we might resolve them. The act of apologizing is quite simply immensely fulfilling. On Apology opens a window onto this common occurrence to reveal the feelings and actions at the heart of this profound interaction. (shrink)

For Émilie Du Châtelet, I argue, a central role of the principle of sufficient reason is to discriminate between better and worse explanations. Her principle of sufficient reason does not play this role for just any conceivable intellect: it specifically enables understanding for minds like ours. She develops this idea in terms of two criteria for the success of our explanations: “understanding how” and “understanding why.” These criteria can respectively be connected to the determinateness and contrastivity of explanations. The crucial (...) role Du Châtelet’s principle of sufficient reason plays in identifying good explanations is often overlooked in the literature, or else run together with questions about the justification and likelihood of explanations. An auxiliary goal of the article is to situate Du Châtelet’s principle of sufficient reason with respect to some of the general epistemological and metaphysical commitments of her Institutions de Physique, clarifying how it fits into the broader project of that work. (shrink)

Timothy Williamson has argued that a person S ’s total evidence is constituted solely by propositions that S knows. This theory of evidence entails that a false belief can not be a part of S ’s evidence base for a conclusion. I argue by counterexample that this thesis (E = K for now) forces an implausible separation between what it means for a belief to be justified and rational from one’s perspective and what it means to base one’s beliefs on (...) the evidence. Furthermore, I argue that E = K entails the implausible result that there are cases in which a well-evidenced belief necessarily can not serve as evidence for a further proposition. (shrink)

The expansion of extractive corporations’ overseas business operations has led to serious concerns regarding human rights–related impacts. As theseapprehensions grow, we see a countervailing rise in calls for government intervention and in levels of socially conscious shareholder advocacy. I focus on the latter as manifested in recent use of the shareholder proposal mechanism found in corporate law. Shareholder proposals, while under-theorized, provide a valuable lens through which to consider the argument that economic behaviour is embedded within social relations. In doing (...) so, I situate my analysis within Third World Approaches to International Law (TWAIL) scholarship. Elsewhere, I have supported the use of corporate law tools in advancing the international human rights enterprise and argued that investment activism can be an essential component of this advancement. This paper represents a reflexive pause. Using the case study of a recent proposal submitted to Goldcorp Inc., I seek to problematize the shareholder proposal as a human rights advocacy tool and to examine it as a site of contestation. (shrink)