** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and non-relativistic quantum theory. ** A large part of this dissertation is devoted to understanding different aspects of four different kinds of correlations: local, partially-local, no-signaling and quantum mechanical correlations. Novel characteristics of these correlations have been used to study how they are related and how they can (...) be discerned via Bell-type inequalities that give non-trivial bounds on the strength of the correlations. ** The study of quantum correlations has also prompted us to study a) the multi-partite qubit state space with respect to its entanglement and separability characteristics, and b) the differing strength of the correlations in separable and entangled qubit states. Results include a novel classification of multipartite (partial) separability and entanglement, strong constraints on the monogamy of entanglement and of non-local correlations, and many new entanglement detection criteria that are directly experimentally accessible. ** Because of the generality of the investigation these results also have strong foundational as well as philosophical repercussions for the different sorts of physical theories as a whole; notably for the viability of hidden variable theories for quantum mechanics, for the possibility of doing experimental metaphysics, for the question of holism in physical theories, and for the classical vs. quantum dichotomy. (shrink)

This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such (...) as 'whole', 'together', and 'alone', nominal and adverbial quanitfiers ranging over parts, and expressions of completion such as 'completely' and 'partly'. (shrink)

One source of tension within and between modern nation states derives from conflict between individual and cultural rights. Modern democracies have been built on ideas of individual liberty whose extensions to the rights of culturally distinctive groups to survival and acceptance can create normative and political conflict. Such tensions raise questions about the role of the state, the underlying theory legitimising liberal states, and the social aims of education. Philosophical aspects of such conflicts are explored in Kevin McDonough and Walter (...) Feinberg’s excellent volume, Citizenship and Education in Liberal-Democratic Societies: Teaching for Cosmopolitan Values and Collective Identities. The philosophical issues hinge on how individuals and groups are conceived, as well as how liberty and loyalty are understood. Most of the essays address these concepts in pragmatic rather than essentialist ways, suggesting that how these issues are conceived is itself an important part of the problem, or its resolution. I conclude by suggesting that all of these doctrines are faiths, the problem being to create conditions so that they, or their elements, can be accepted or rejected reasonably in the light of their social consequences. (shrink)

It is often held that according to Aristotle the city is a natural organism. One major reason for this organic interpretation is no doubt that Aristotle describes the relationship between the individual and the city as a part-whole relationship, seemingly the same relationship that holds between the parts of a natural organism and the organism itself. Moreover, some scholars (most notably Jonathan Barnes) believe this view of the city led Aristotle to accept an implicit totalitarianism. I argue, however, (...) that an investigation of the various ways Aristotle describes parts and wholes reveals that for Aristotle the city has a unity (and thus a nature) quite different from that of a natural organism. (shrink)

I want to try to elucidate passages like the following which are not only to be found frequently in Bradley’s writings, but which articulate a position central to his metaphysics.

Pace Dummett, the issue between molecularism and holism does not turn on whether a meaning theory is compositional, but on how successful communication is conceived. Given a notion of partial understanding, molecularism escapes the two most prevalent objections against holism (learnability and communication). Holism, too, can escape these objections, provided we also grant the holist a notion of partial understanding and suitably amend our conception of successful communication.

Starting in June 2012, a series of articles in the journal Nature and in the online journals of the Public Library of Science made public the first results of a massive, international collaborative scientific endeavor known as the “Human Microbiome Project” . This project, which is attempting to categorize the vast number of microbiological species and organisms that live in and on the “healthy” human body, raises important questions about what it means to be a whole individual organism, especially (...) if that individual involves a community of some hundreds of trillions of others. In this article, we will explore a handful of political, ethical, and philosophical issues that this new research raises .. (shrink)

Philosophical questions concerning parts and wholes have received a tremendous amount of the attention of contemporary analytic metaphysicians. In what follows, I discuss some of the central questions. The questions to be discussed are: how general is parthood? Are there different kinds of parthood or ways to be a part? Can two things be composed of the same parts? When does composition occur? Can material objects gain or lose parts? What is the logical form of the parthood (...) relation enjoyed by material objects? (shrink)

The Odd Universe Argument aims to show that from four intuitive assumptions about parts and wholes, we can conclude a priori that there is an odd number of things in the universe. This Element is an opinionated survey of philosophical issues involving parthood, composition, identity, and counting, guided by an investigation into where this argument has gone awry. We first walk through some general methodology, basic mereology, and plural logic. Next, we explore questions about the nature of composition and (...) decomposition. Does composition always occur? Never? Sometimes? Is the universe, at rock bottom, just many partless bits (simples)? Or do the parts have parts all the way down (gunk)? We then turn to arguments for and against the thesis that composition is identity, with a healthy bias in its favor. We conclude with a return to the odd universe argument, and my thoughts on how best to solve it. -/- *Free to download June 7 to June 21, 2023. (shrink)

Composed of essays and transcripts of discussions, this is an informative survey of problems involving the concepts of part and whole. Well-known scholars in a wide range of fields, from physics to literature, are the contributors: E. Purcell, physics; S. Kuznets, economics; S. Ramo, systems engineering; the late C. Kluckhohn, anthropology; E. Nagel, philosophy; R. Jakobson, linguistics; and I. A. Richards, poetry.--A. E. F.

A paper exploring what we can learn about part/whole by focusing on the differences in the existence conditions of fusions and ordinary things, rather than the differences in their persistence conditions.

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)

Purpose: The purpose of the paper is to provide a constructivist account of the "self as subject" that avoids the need for any metaphysical assumptions. Findings: The thesis developed in this paper is that the human "psychological individual," "self" or "subject" is an emergent within the nexus of human social interaction. With respect to psychological and social wholes (composites) there is no distinction between the form of the elements and the form of the composites they constitute i.e., all elements have (...) the form of composites. Further, recursively, composites may serve as elements within higher order composites. Implications for a rational theory of ethics are discussed. Original Value: The thesis contributes in a fundamental way to the research programme of radical constructivism by demonstrating that metaphysical assumptions about the nature of the "subject" are not an a priori necessity. Although the thesis in itself is not original, the paper offers a useful synthesis of ideas from a number of key thinkers in the disciplines of cybernetics, biology, psychology and philosophy. (shrink)

This text, which is part of a project, ‘Toward a Politics and Poetics of Singularity’, explores the implications of a phrase used more or less simultaneously, although independently, by Walter Benjamin and Sigmund Freud, ‘the single trait’. In his 1962 lectures on the problem of identification, Jacques Lacan focused on this phrase in Freud in order to exemplify the difference between the subject and the signifier. The use of the phrase by Benjamin in his essay on ‘Destiny and Character’ inflects (...) the discussion toward questions of ‘comedy’ and ‘tragedy’, and thereby links the singularity of the signifying process to literary and theatrical forms. (shrink)

It is well-known that in the fifth of his Cartesian Meditations, Husserl puts forth a theory of intersubjectivity. Most commentators of Husserl have read his Cartesian Meditations as presenting a theory of intersubjectivity whose basis is empathy, in the form of a process of constituting the sense of “other” in one’s own experience, as the primary origin of the intersubjective layer of experience. In this paper, I claim that the structure of intersubjectivity as Husserl presents it in the Cartesian Meditations (...) is articulated as being governed by a logic of parts and wholes rather than that of a phenomenology of empathy, and that the articulation of this logic demonstrates that the transcendental ego is intrinsically intersubjective. My main philosophical claim in this regard is that the way Husserl’s account of transcendental empathy unfolds in the Cartesian Meditations implies a prior fundamental mereological structure of which the individual transcendental ego is only a part. That is, the transcendental ego has an eidetic a-priori intersubjective structure, in the sense of being a moment of an intersubjectively structured transcendental whole. In this sense, rather than being a singulare tantum, it is more fitting to say that transcendental subjectivity is actually a plurale tantum. (shrink)

In this paper I reconstruct and discuss Antonio Rubio (1546-1615)’s theory of the composition of the continuum, as set out in his Tractatus de compositione continui, a part of his influential commentary on Aristotle’s Physics, published in 1605 but rewritten in 1606. Here I attempt especially to show that Rubio’s is a significant case of Scholastic overlapping between Aristotle’s theory of infinitely divisible parts and indivisibilism or ‘Zenonism’, i.e. the theory that allows for indivisibles, extensionless points, lines, and surfaces, (...) which are supposed to take part in the composition of the continuum. Even if such a syncretic tendency was, in many different ways, already developing in the medieval period and then at the end of the sixteenth century, Rubio’s position is indeed peculiar. He maintains that indivisibles are real and actual, infinite in act, really distinct from each other, and that, although they indwell in substance, indivisibles do not contribute directly to the constitution of the continuum. In this reconstruction I emphasize notably Rubio’s usage of mereological notions like those of part, whole, completeness and incompleteness. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Plato on Parts and Wholes: The Metaphysics of StructureNicholas SmithVerity Harte. Plato on Parts and Wholes: The Metaphysics of Structure. Oxford: Clarendon Press of Oxford University Press, 2002. Pp. x + 311. Cloth, $45.00.In this book, Verity Harte seeks to provide an account of Plato's view of mereology. According to Harte, Plato presents two distinct models about the relation of part to whole, but actually (...) only ever accepts one of these two models. Plato presents one model in the Parmenides, Theaetetus, and one passage in the Sophist. In this model, which Harte compares to a conception of part and whole recently advanced by David Lewis, the whole is simply identical to its collective parts and Plato attends to this model only to call attention to its problems. Harte explicates Plato's presentation of this model in the last section of Chapter 1 and in Chapter 2 of her book. The second model—the only one Plato actually accepts, according to Harte—Plato initially outlines in the Parmenides, but then explicates in finer detail in the Sophist, Philebus, and Timaeus. In this conception, wholes are now understood as "structures, the identity of whose parts is determined only in the context of the whole they compose" (3). Harte presents her evidence for Plato's endorsement of this model in Chapters 3 and 4, and then draws conclusions in Chapter 5.The book has several significant virtues, including especially clarity of exposition, and care and thoroughness in the review of the relevant texts from Plato's later dialogues. But this same care and attention to detail does not at all extend to any of Plato's discussions of part and whole in earlier works, and Harte's peremptory refusal to consider the relevant passages in these other works is puzzling, at best.Indeed, Harte bothers to identify only two such passages from earlier works, and then only to explain why they and other passages like them do not merit further attention: the Republic's famous division of the soul into three parts in Book IV and the consideration of virtue as a whole and the several virtues as parts of that whole in the Protagoras. Harte acknowledges that Plato explicitly supplies, in the Protagoras discussion, two different sorts of relations of part and whole, in distinguishing the way in which parts of gold form a larger whole, and the way the parts of the face are related to the whole face (349d4-8), but seems oblivious to the clear implication that—at least when he wrote the Protagoras, and contrary to Harte's primary thesis—Plato recognized more than one way in which wholes could be composed of parts. But Harte dismisses the significance of both discussions by noting, first, that the "principle of opposition" given in the Republic by which Plato divides the soul provides "at most, a sufficient, and not necessary, condition on something having parts" and concludes that it thus "cannot be used to establish general claims about parts" (2). Harte never mentions that this same view of the partitioned soul seems to reappear in the Phaedrus and Timaeus—a dialogue in which the allegedly preferred conception of mereology is presented—and also passes over the Republic's representation of the tripartition of the kallipolis, and Plato's conception of the citizen as a part of a state. As for the Protagoras's discussion of the relationships between the virtues, Harte says only that "there is here no discussion of the nature of parts or of the relation between parts and whole" (2). She concludes that "in both works the focus of discussion is the examples themselves (the soul, the virtues) and not wholes of parts as such" (2). Harte fails to notice, however, that the arrangement of virtues into parts and wholes may also be found in the Laches (190a1-199e7), [End Page 333] Meno (78d7-e2), and especially the Euthyphro (12c2-d2), in which the relation of piety to justice as part to whole is likened to the relationships between reverence and fear and odd numbers and numbers, which are plainly not examples of part-whole relationships between virtues.Harte is well... (shrink)

What is the relation between a whole and its parts? The metaphysics of structure and composition is much discussed in modern philosophy; now Verity Harte provides the first sustained examination of Plato's rich but neglected discussion of the topic, and shows how it can illuminate current debates. This book is an invaluable resource both for scholars of Plato and for modern metaphysicians.

Parts and wholes come in an infinite variety, but in each instance something, namely relations, joins the parts together to make them into a whole rather than an Aristotelian "heap." The ontological status of relations is the subject of this dissertation. ;The question of whether relations are real presupposes some method of determining what is real. A modified version of Whitehead's ontological principle, or the idea that only real things can have effects on other things, serves as (...) the test of the reality. If any effects result from a whole but not from a collection of parts, then a whole differs from its parts and relations are real. Such effects can manifest themselves in two ways: parts themselves may somehow be affected by being joined into a whole or some new property may emerge with a whole that cannot be attributed to the parts taken separately. If one discovers either type of effect, then relations are real. ;The first section of the dissertation is an historical examination on the question of the reality of the relations. In the first chapter, the positions of Hume, Parmenides and Whitehead are considered but ultimately rejected. The second chapter examines the positions of Aristotle and Wittgenstein, thinkers for whom relations are in some cases real, while the third examines Plato's idea on relations. ;In the fourth chapter, a distinction between two types of relations is drawn. The difference between these relations is found in whether or not the parts joined are affected by being in a whole. Static relations are those which join parts into a whole without affecting those parts, while parts joined by dynamic relations are affected by being in a whole. Both static and dynamic wholes possess emergent properties which come into being only when parts are joined into wholes. ;The second section focuses on the consequences of the reality of relations in philosophy, specifically in ethics, logic and the philosophy of space and time. (shrink)

A brief introductory note to the special issue of the Journal of Philosophy on "Parts and Wholes", setting the background for the seven papers included in the rest of the issue (by K. Fine, H. Hudson, M. Johnston, K. Koslicki, C. Normore, P. M. Simons, and P. van Inwagen).

This volume is the first systematic and thorough attempt to investigate the relation and the possible applications of mereology to contemporary science. It gathers contributions from leading scholars in the field and covers a wide range of scientific theories and practices such as physics, mathematics, chemistry, biology, computer science and engineering. Throughout the volume, a variety of foundational issues are investigated both from the formal and the empirical point of view. The first section looks at the topic as it applies (...) to physics. The section addresses questions of persistence and composition within quantum and relativistic physics and concludes by scrutinizing the possibility to capture continuity of motion as described by our best physical theories within gunky space times. The second part tackles mathematics and shows how to provide a foundation for point-free geometry of space switching to fuzzy-logic. The relation between mereological sums and set-theoretic suprema is investigated and issues about different mereological perspectives such as classical and natural Mereology are thoroughly discussed. The third section in the volume looks at natural science. Several questions from biology, medicine and chemistry are investigated. From the perspective of biology, there is an attempt to provide axioms for inferring statements about part hood between two biological entities from statements about their spatial relation. From the perspective of chemistry, it is argued that classical mereological frameworks are not adequate to capture the practices of chemistry in that they consider neither temporal nor modal parameters. The final part introduces computer science and engineering. A new formal mereological framework in which an indeterminate relation of part hood is taken as a primitive notion is constructed and then applied to a wide variety of disciplines from robotics to knowledge engineering. A formal framework for discrete mereotopology and its applications is developed and finally, the importance of mereology for the relatively new science of domain engineering is also discussed. (shrink)