Mereology

Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of quantum theory.

If possible worlds are conjunctions of states of affairs, as in David Armstrong’s combinatorial theory, then is the empty world to be thought of as the null conjunction of states of affairs? The proposal seems plausible, and has received support from David Efird, Tom Stoneham, and Armstrong himself. However, in this paper, it is argued that the proposal faces a trilemma: either it leads to the absurd conclusion that the actual world is empty; or it reduces to a familiar representation (...) of the empty world in which the concept of a null conjunction plays no role; or it needs to make room for the null individual of certain non-classical mereologies. (shrink)

There are two links that stand in the foreground of Deleuze’s treatment of Epicurus and Lucretius: the themes of immanent naturalism and of the externality of ontological relations. However, the links are problematised in Difference and Repetition, which presents an important critique of the concept of the atom. I will argue that this critique reveals the limits of the intellectual affinity between ancient atomism and Deleuzian metaphysics; in particular, that Deleuze’s notions of relationality and spatium respond to problems raised by (...) the relations between atoms and by the not-being of the atomists’ vacuum. In this sense, Deleuze’s treatment of atomism is significant because it makes clear Deleuze’s aim in shifting the mereological vocabulary from points to lines; it shows what, in Deleuze’s sense, it means to unfound and sets down the conditions for a successful Deleuzian critique of essentialist varieties of the metaphysics of structure. (shrink)

This paper extends the axiomatic treatment of intuitionistic mereology introduced in Maffezioli and Varzi (_Synthese, 198_(S18), 4277–4302 2021 ) by examining the behavior of constructive notions of overlap and disjointness. We consider both (i) various ways of defining such notions in terms of other intuitionistic mereological primitives, and (ii) the possibility of treating them as mereological primitives of their own.

The author , after Bergson , provides a formal deduction which defends Bergson ’s claim that “ the character of movements which are externally identical are internally different “ . The author is responding to Diana Coole and Samantha Frost ’s “ Introducing the New Materialisms ” , wherein neither Coole nor Frost showed a knowledge of Bergson or his existence whatsoever despite seemingly having to have read Deleuze and Deleuze ’s contemporaries … -/- The author also presents a novel (...) concept in mereology . -/- Available upon request . (shrink)

David Lewis in the short monograph Parts of Classes (PC) undertakes a fundamental re‐examination of the relationship between mereology, the general theory of parts, and set theory, the general theory of collections. Given Lewis's theses, to be an element of a set or member of class is just to have a singleton that is a part thereof. Lewis in PC adds a claim of kind of ontological innocence, comparable to that of first‐order logic, for mereology. The only substantive assumption of (...) plethynticology is that for any condition there are some things such that they are precisely the things for which the conditions hold. All the alternatives, making do with a single domain of individuals, have in common that they involve the axiom of choice. Restated in Hazen's terminology rather than Frege's, the fallback assumption is that there are no more small species than individuals. (shrink)

Spinoza seems to argue both that “God or Nature” is mereologically simple, and that this being is mereologically complex insofar as it is composed of parts. This chapter proposes on Spinoza's behalf a resolution of this antinomy. This resolution focuses on Spinoza's mereology of the material world. It offers an alternative interpretation according to which Spinoza adheres both to the indivisibility of extended substance and to the reality of the finite modal parts that compose an infinite modal whole. In the (...) Oldenburg Letter, Spinoza claims that “concerning whole and parts, the chapter considers things as parts of some whole to the extent that the nature of the one so adapts itself to the nature of the other so that they agree with one another as far as possible”. The chapter argues that a similar assumption underlies Peterson's argument against the reality in Spinoza of divisible spatial quantity. (shrink)

Review of Cotnoir and Varzi's _Mereology_.

This volume offers a fresh exploration of the parts-whole relations within a power and among powers. While the metaphysics of powers has been extensively examined in the literature, powers have yet to be studied from the perspective of their mereology. Powers are often assumed to be atomic; and yet what they can do--and what can happen to them--is complex. But if powers are simple, how can they have complex manifestations? Can powers have parts? According to which rules of composition do (...) powers compose into powers? Given the centrality of powers in current scientific as well as philosophical thought, recognizing and understanding the ontological differences between atomic and mereologically complex powers is important, for both philosophy and science. The first section of this book explores how powers divide; the second section how powers compose. The final section showcases some specific study cases in the domains of quantum mechanics and psychology. Powers, Parts and Wholes will be of interest to professional philosophers and graduate students working in metaphysics, philosophy of science and logic. (shrink)

Most ordinary objects - cats, humans, mountains, ships, tables, etc. - have indeterminate mereological boundaries. If the theory of mereology is meant to include ordinary objects at all, we need it to have some space for mereological indeterminacy. In this paper, we present a novel degree-theoretic semantics - Boolean semantics - and argue that it is the best degree-theoretic semantics for modeling mereological indeterminacy, for three main reasons: (a) it allows for incomparable degrees of parthood, (b) it enforces classical logic, (...) and (c) it is compatible with all the axioms of classical mereology. Using Boolean semantics, we will also investigate the connection between vagueness in parthood and vagueness in existence/identity. We show that, contrary to what many have argued, the connection takes neither the form of entailment nor the form of exclusion. (shrink)

Under what conditions are material objects, such as particles, parts of a whole object? This is the composition question and is a longstanding open question in philosophy. Existing attempts to specify a non-trivial restriction on composition tend to be vague and face serious counterexamples. Consequently, two extreme answers have become mainstream: composition (the forming of a whole by its parts) happens under no or all conditions. In this paper, we provide a self-contained introduction to the integrated information theory of consciousness (...) (IIT). We show that IIT specifies a non-trivial restriction on composition: composition happens when integrated information is maximized. We compare the IIT-restriction to existing proposals and argue that the IIT-restriction has significant advantages, especially in response to the problems of vagueness and counterexamples. An appendix provides an introduction to calculating parts and wholes with a simple system. (shrink)

Die Mereologie ist eine noch relativ junge philosophische Disziplin an der Grenze zwischen Logik und Philosophie. Sie untersucht in systematischer Weise auf der Grundlage geeigneter logischer Systeme die Beziehungen zwischen Teil (griech. "meros") und Ganzem. Von besonderem philosophischem Interesse ist die Frage, inwieweit sich mereologische Strukturen zur Klärung und Lösung verschiedenster Probleme vor allem der Ontologie und Erkenntnistheorie einsetzen lassen. Folgende Problemfelder sind dabei von Bedeutung: -/- (1) Was tragen mereologische Systeme zur Durchführung ontologischer Programme bei, die ohne die Annahme (...) abstrakter Gegenstände auskommen wollen? (2) In welcher Weise erlauben mereologische Mittel eine Beschreibung und Analyse von Wirklichkeitsstrukturen? (3) Lassen sich mit Hilfe mereologischer Mittel ausgehend von Einzelbeobachtungen Begriffe und Strukturen von Geometrie und Topologie gewinnen? Erklärt und garantiert eine solche Grundlegung die Anwendbarkeit von Geometrie und Topologie auf die Erfahrungswelt? (4) Welche Möglichkeiten bietet die Mereologie für eine Begründung der Mathematik? Ist eine mereologische Grundlegung der Mengenlehre möglich, die Mengen als abstrakte Gegenstände entbehrlich macht? -/- Die Forschungsbeiträge hinsichtlich dieser Problemkreise zeigen ein facettenreiches, uneinheitliches und vielfach unzusammenhängendes Bild. Die Arbeit verfolgt deshalb vorrangig zwei Ziele: die Systematisierung und Vereinheitlichung der unterschiedlichen mereologischen Systeme und die Prüfung der philosophischen Relevanz und Problemlösungskraft der verschiedenen Ansätze. (shrink)

Se presenta una teoría axiomática sobre entidades compuestas generales. Por entidad compuesta se hace referencia a cualquier ser hecho de partes. Usando esta formalización, es posible llegar a algunas conclusiones metafísicas valiosas, como la no equivalencia entre los conceptos de entidad compuesta y conjunto matemático. Asimismo, se analizan y desacreditan algunas formas de platonismo matemático. Se proponen algunos ejercicios para ayudar al lector a aprender la notación simbólica.

Disjointism is the view that co-located objects do not share any parts. A human-shaped statue is composed from a torso, head and limbs; the co-located lumpof clay is only composed from chunks of clay. This essay discusses the tenability of this relatively neglected view, focusing on two objections. The first objection is that disjointism implies co-located copies of microphysical particles. I argue that it doesn’t imply this and that there are more plausible disjointist views of tiny parts available. The second (...) objection is that disjointism is at a loss to explain how material objects can be co-located and why the weights of co-located objects don’t add up. The standard pluralist account appeals to the fact that co-located objects stand in mereological relations and this account is not available to the disjointist. I sketch an alternative account that appeals to a notion of ‘material identity’: the statue is taken to be the same matter as the lump of clay. The resort to a new theoretical primitive may seem to invite a quick rejection on grounds of unnecessary theoretical complexity but I argue that an abductive comparison with rival forms of pluralism shows that such a rejection is misguided. (shrink)

In his Confessions, Augustine says that he achieved great intellectual insight from what he cryptically calls the “books of the Platonists.” Prior to reading these books, he was a corporealist and was unable to conceive of incorporeal beings. Because of the insurmountable philosophical problems corporealism caused for the Christian belief he was seeking, Augustine claims that this was the greatest intellectual barrier he faced in converting to Christianity. As such, the specific contents and effects of these Platonist books are of (...) great biographical and philosophical interest. Heretofore, the explanation of the contents and effects of these books has not been forthcoming. This essay aims to supply it. I argue that Augustine learned the mereological distinction between pertensive and entensive presence in the books of the Platonists. This distinction is required for properly conceiving of incorporeal beings. In support of this thesis, I show that Augustine himself says that he learned this very distinction, that the distinction is present in Platonist texts that scholars agree were among “the books of the Platonists,” that the distinction is present in one of Augustine’s earliest works, and that this distinction is uniquely capable of resolving the philosophical difficulties he faced as a corporealist. (shrink)

The human lives in two universes. One inside. The other outside. One completely abstract. The other concrete. Telling all of us something important about Nature and ‘reality.’.

Consider the following pair of theses: all fundamental physical objects are spatiotemporal and all non-fundamental physical objects are ultimately composed of fundamental objects. Work on the physics of quantum gravity suggests that spacetime is a non-fundamental, emergent phenomenon and thus that thesis is false. The fundamentals are non-spatiotemporal in nature. This paper will argue against on the grounds that non-fundamental spatiotemporal objects cannot be composed of fundamental non-spatiotemporal objects. So, assuming that spacetime is emergent, new metaphysical resources are needed to (...) explain the relationship between the fundamental objects posited by quantum gravity and spacetime. (shrink)

Overview of themes and context -- Reading the text -- Reception and influence -- Further reading.

This article deals with the doctrine of providence in Thomas Aquinas based on the thinking of the French philosopher Christian Godin: divine providence would provide an understanding of the “totality” (totalité) that concerns not only the entire universe but also each individual. Aquinas gives an Aristotelian explanation of chance, luck and contingency from the divine perspective. Omniscience, omnipotence and divine providence, however, do not contradict the existence of either true contingency in the natural world or freedom but, on the contrary, (...) they support them. In short, the two peculiarities of the doctrine of providence in St. Thomas here exposed are: first, that God’s will is the ultimate foundation of all contingency (and not merely the deficiency of secondary causes); second, that the divine causality cannot be reduced to any of the two groups of created causes (necessary or contingent) but it is only known to us by analogy. (shrink)