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)

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.

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.

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)

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 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)

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.

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.

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.

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.

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)

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)

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

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)

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)

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)

Adam Smith sought to explain the persistence of slavery as an institution in Wealth of Nations and Lectures on Jurispridence. In order to accomplish this he also drew on arguments he had developed in the Theory of Moral Sentiments. The result was a sophisticated explanation which bridged economic, psychological, and moral considerations. After presenting Smith’s explanation I will consider a discussion of the moral wrong of slavery in Ottobah Cugoano, the author of the incisive criticism of the slave trade Thoughts (...) and Sentiments on the Evil of Slavery (1787). I will suggest that Cugoano’s account of what is morally wrong in slavery shows an important lacuna in Smith‘s views. (shrink)

The central focus of Peirce’s work is the development of self-control through engaging in a critical, reflective practice of habit development. This book details that development from a philosophical, pragmatic perspective.

Prior research on the influence of various ways of framing anthropogenic climate change do not account for the organized ACC denial in the U.S. media and popular culture, and thus may overestimate these frames' influence in the general public. We conducted an experiment to examine how Americans' ACC views are influenced by four promising frames for urging action on ACC —when these frames appear with an ACC denial counter-frame. This is the first direct test of how exposure to an ACC (...) denial message influences Americans' ACC views. Overall, these four positive frames have little to no effect on ACC beliefs. But exposure to an ACC denial counter-frame does significantly reduce respondents' belief in the reality of ACC, belief about the veracity of climate science, awareness of the consequences of ACC, and support for aggressively attempting to reduce our nation's GHG emissions in the near future. Furthermore, as expected by the Anti-Reflexivity Thesis, exposure to the ACC denial counter-frame has a disproportionate influence on the ACC views of conservatives, effectively activating conservatives' underlying propensity for anti-reflexivity. (shrink)

Bayesian Conditionalization is a widely used proposal for how to update one’s beliefs upon the receipt of new evidence. This is in part because of its attention to the totality of one’s evidence, which often includes facts about what one’s new evidence is and how one has come to have it. However, an increasingly popular position in epistemology holds that one may gain new evidence, construed as knowledge, without being in a position to know that one has gained this evidence. (...) These are cases of KK-Failure, cases where one knows p but is not in a position to know that one knows p. This paper assumes that certain KK-Failures are possible and argues that Conditionalization goes wrong in those cases. (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)

I reconstruct J. H. Lambert’s views on how practical grounds relate to epistemic features, such as certainty. I argue, first, that Lambert’s account of moral certainty does not involve any distinctively practical influence on theoretical belief. However, it does present an interesting form of fallibilism about justification as well as a denial of a tight link between knowledge and action. Second, I argue that for Lambert, the persistence principle that underwrites induction is supported by practical reasons to believe; this indicates (...) that Lambert is a moderate pragmatist about reasons for theoretical belief. (shrink)

The thesis that aesthetic testimony cannot provide aesthetic justification or knowledge is widely accepted--even by realists about aesthetic properties and values. This Kantian position is mistaken. Some testimony about beauty and artistic value can provide a degree of aesthetic justification and, perhaps, even knowledge. That is, there are cases in which one can be justified in making an aesthetic judgment purely on the basis of someone else's testimony. But widespread aesthetic unreliability creates a problem for much aesthetic testimony. Hence, most (...) testimony about art does not have much epistemic value. The situation is somewhat different with respect to aesthetic testimony about nature, proofs, and theories. (shrink)

ABSTRACT This article distinguishes nine senses of polarization and provides formal measures for each one to refine the methodology used to describe polarization in distributions of attitudes. Each distinct concept is explained through a definition, formal measures, examples, and references. We then apply these measures to GSS data regarding political views, opinions on abortion, and religiosity—topics described as revealing social polarization. Previous breakdowns of polarization include domain-specific assumptions and focus on a subset of the distribution’s features. This has conflated multiple, (...) independent features of attitude distributions. The current work aims to extract the distinct senses of polarization and demonstrate that by becoming clearer on these distinctions we can better focus our efforts on substantive issues in social phenomena. (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.