A. J. Cotnoir

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.

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.

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.

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.

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.

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.

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.

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

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

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 …

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

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

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.

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 ..

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.

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.