We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology (...) as a general theory subsuming mereology. Some more speculative strategies and directions for further research are also considered. (shrink)

A clever argument purports to show that we can directly perceive the emotions of others: (1) some emotional expressions are parts of the emotions they express; (2) perceiving a part of something is sufficient for perceiving the whole; (3) therefore, perceiving some emotional expressions is sufficient for perceiving the emotions they express. My aim in this paper is to assess the extent to which contemporary psychological theories of emotion support the first premise of this argument.

A taxonomy of part‐whole or meronymic relations is developed to explain the ordinary English‐speaker's use of the term “part of” and its cognates. The resulting classification yields six types of meronymic relations: 1. component‐integral object (pedal‐bike), 2. member‐collection (ship‐fleet), 3. portion‐mass (slice‐pie), 4. stuff‐object (steel‐car), 5. feature‐activity (paying‐shopping), and 6. place‐area (Everglades‐Florida). Meronymic relations ore further distinguished from other inclusion relations, such as spatial inclusion, and class inclusion, and from several other semantic relations: attribution, attachment, and ownership. (...) This taxonomy is then used to explain cases of apparent intransitivity in merological syllogisms, and standard form syllogisms whose premises express different inclusion relations. The data suggest that intransitivities arise due to equivocations between different types of semantic relations. These results are then explained by means of the relation element theory which accounts for the character and behavior of semantic relations in terms of more primitive relational elements. The inferential phenomena observed are then explained by means of a single principle of element matching. (shrink)

Gordon P. Barnes has recently argued that presence by power is inadequate as an explanation of the way elements are present in complex bodies, and that it would be better to explain the elements’ presence by claiming that simpler substances—carbon atoms, for example—are actually and substantially present in living things. In order to address his arguments, this paper begins by briefly presenting St. Thomas’s understanding of presence by power, and then argues that Barnes’s proposal—that there is a multiplicity of substantial (...) forms in one matter—is unsatisfactory. First, the paper explains why the scientific facts do not require a plurality of substantial forms. Second, it shows how Barnes’s theory does not adequately explain living things. Third, it argues against Barnes’s claim that St. Thomas’s explanation is insufficient because it denies "the universal causality of nature.". (shrink)

Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories (...) of set size are wrong, but that they must be either very weak and narrow or largely arbitrary and misleading. (shrink)

This chapter reconstructs the account of the organization of unified definite manifolds that Husserl developed in his early logic of parts and wholes. I argue that Husserl’s conception of necessity gets fixed through the logic of fitness that is operative in his account of unified definite manifolds that are organized by symmetrical part/whole relations. Husserl’s logical account of necessity finds its ultimate justification in his theory of intentionality and is operative in his phenomenological methodology generally. Through this (...) conception of necessity of the way in which manifolds are unified and organized, Husserl radicalized and exploded the Kantian conception of the material a priori and distinguished among several kinds of a priori, e.g., the correlational a priori, a priori bound to the empirical, and pure material a priori. Husserl’s phenomenological account of the material a priori further clarifies the important differences with Kant’s approach to the problem of necessity. (shrink)

A taxonomy of part‐whole or meronymic relations is developed to explain the ordinary English‐speaker's use of the term “part of” and its cognates. The resulting classification yields six types of meronymic relations: 1. component‐integral object (pedal‐bike), 2. member‐collection (ship‐fleet), 3. portion‐mass (slice‐pie), 4. stuff‐object (steel‐car), 5. feature‐activity (paying‐shopping), and 6. place‐area (Everglades‐Florida). Meronymic relations ore further distinguished from other inclusion relations, such as spatial inclusion, and class inclusion, and from several other semantic relations: attribution, attachment, and ownership. (...) This taxonomy is then used to explain cases of apparent intransitivity in merological syllogisms, and standard form syllogisms whose premises express different inclusion relations. The data suggest that intransitivities arise due to equivocations between different types of semantic relations. These results are then explained by means of the relation element theory which accounts for the character and behavior of semantic relations in terms of more primitive relational elements. The inferential phenomena observed are then explained by means of a single principle of element matching. (shrink)

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

In the visual representation of ontologies, in particular of part-whole relationships, it is customary to use graph theory as the representational background. We claim here that the standard graph-based approach has a number of limitations, and we propose instead a new representation of part-whole structures for ontologies, and describe the results of experiments designed to show the effectiveness of this new proposal especially as concerns reduction of visual complexity. The proposal is developed to serve visualization (...) of ontologies conformant to the Basic Formal Ontology. But it can be used also for more general applications, particularly in the biomedical domain. (shrink)

One of the unresolved issues in Aristotle’s hylomorphism is the part-whole puzzle. Some scholars suppose that in Metaphysics Z 17, 1041b11-33 he endorses non-mereological hylomorphism. This kind of interpretation, however, has been challenged by K. Koslicki who argues that if the evidence in Metaphysics Z 17 is combined with some related textual and conceptual considerations, then a convincing case can be made for a mereological construal of Aristotelian hylomorphism. This paper does four things. First, it scrutinizes these opposing (...) approaches to Aristotle’s theory. Second, it suggests that to adjudicate the dispute at hand one ought to determine how Aristotle deals with what has come to be known as ‘Ackrill’s problem’. It is proposed that if we consider Aristotle’s theory in light of some distinctions drawn in contemporary discussions of hylomorphism, then it transpires that he does have a solution to Ackrill’s problem. Third, it is shown that his solution to this problem suggests a particular way of settling the debate over the part-whole puzzle. And finally, it is argued that the suggested reconstruction of Aristotelian hylomorphism is consistent with the textual evidence in Metaphysics Z 17 and its associated texts. (shrink)

I use Carl Gillett’s much heralded dimensioned theory of realization as a platform to develop a plausible part–whole theory. I begin with some basic desiderata for a theory of realization that its key terms should be defined and that it should be explanatory. I then argue that Gillett’s original theory violates these conditions because its explanatory force rests upon an unspecified “in virtue of” relation. I then examine Gillett’s later version that appeals instead to (...) theoretical terms tied to “mechanisms.” Yet I argue that it too violates the desiderata, since it defines realization for mechanisms in terms of two undefined ideas whose explanatory credentials have not been established—“implementation” and “grounds.” Thus I drop those ideas in favor of an explicit constraint that the parts and properties provide a mechanistic explanation. I also distinguish a special mechanistic theory from a preferred general theory that incorporates other kinds of part–whole explanations that target causal powers or capacities. The result is a theory that has the explanatory virtues of mechanistic theories as well as a broader scope desired by Gillett. I also compare the result to a similar idea from Robert Cummins that has been neglected in recent discussions of realization, namely, his general property analysis rather than his functional analysis. Finally, I defend the preferred general theory against possible objections that attempt to show a conflict between metaphysical demands on a theory of realization versus facts about good scientific explanation. (shrink)

The purpose of the paper is demonstrate the thesis that Ingarden's ontological system allows a better understanding of the “part-whole” problem then previous theories. Especially, if we take into account the existential ontology of Ingarden, which refers to Husserl “part-whole” theory, we can see that development of terms made by Ingarden sheds new light on old problems. In this context, particularly important is to distinguish between two existential moments: contingancy/inseparatness, because thanks to them we can (...) talk about many different types of relationships and hence many types of objects. (shrink)

In this paper, I suggest a way of resolving the whole-part dilemma suggested in the Parmenides. Specifically, I argue that grabbing the second horn of the dilemma does not pose a significant challenge. To argue for this, I consider two theses about Forms, namely, the oneness and indivisibility theses. More specifically, I argue that the second horn does not violate the oneness thesis if we treat composition as identity and that the indivisibility thesis ought to be reinterpreted given (...) Plato’s later dialogues. By doing so, I suggest a com-positional understanding of Plato’s theory of Forms, which can resolve the whole-part dilemma. (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)

The very formal structure of quantum mechanics implies the loss of individuality of physical systems and it requires to look at the Universe as an unbroken whole. The main reason for which, within such a theory, one must renounce to a clear identification of the parts and the whole is the superposition principle which stays at the basis of the theory. It implies, as well known, the phenomenon of entanglement which, in the most extreme case, entails (...) that the constituents of a composite system do not possess any objective property; only the system as a whole, when it is isolated, has some properties. Another source of difficulties derives from the symmetry requests that the theory imposes in the case of systems containing identical constituents. We discuss these points in detail and we outline recent proposals yielding a consistent solution to the problems arising from the entanglement between a microsystem and a macrosystem which unavoidably occurs in a measurement process. In particular we take into account the so called “collapse” theories which embody a mechanism forbidding, at an appropriate level, the persistence of superpositions and, as a consequence, lead, in general, to the emergence of precise individual properties for macroscopic systems. We then pass to a critical analysis of the difficulties related to the identity of the constituents. We stress that various misunderstandings characterize the treatment of this problem and we make fully clear how one has to deal with the very concept of entangled systems when identical constituents are involved. The ensuing picture should make clear to which extent one can still consistently ground the distinction between the parts and the whole in a genuinely quantum context. (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)

This paper presents a theory of situated part structures involving the notion of an integrated and not just a part-of relation. The theory is applied in particular to the semantics of the modifiers 'whole' and 'individual', as in 'the whole collection' and 'the individual students'. The adnominal modifiers 'whole' and 'individual' have been entirely been ignored in the linguistic and philosophical literature, even though they pose significant challenges for standard views of reference, of (...) the semantics of referential NPs, and for ontology (the exception being medieval philosophy of language where 'whole' has received significant attention). 'Whole' strikingly displays two opposite readings: 'The whole collection is expensive' can mean - 'as a whole' or 'every part'. The paper proposes that the two readings be traced to two different conceptions of part structures of objects: one according to which the parts of an objects are just the material parts and another, Aristotelian conception according to which the parts of an object include properties of form. (shrink)

In this essay we aim to present some considerations regarding a minimal but concrete notion of agency and goal-directed behavior that are useful for characterizing biological systems at different scales. These considerations are a particular perspective, bringing together concepts from dynamical systems, combinatorial problem-solving, and connectionist learning with an emphasis on the relationship between parts and wholes. This perspective affords some ways to think about agents that are concrete and quantifiable, and relevant to some important biological issues. Instead of advocating (...) for a strict definition of minimally agential characteristics, we focus on how (even for a modest notion of agency) the agency of a system can be more than the sum of the agency of its parts. We quantify this in terms of the problem-solving competency of a system with respect to resolution of the frustrations between its parts. This requires goal-directed behavior in the sense of delayed gratification, i.e., taking dynamical trajectories that forego short-term gains (or sustain short-term stress or frustration) in favor of long-term gains. In order for this competency to belong to the system (rather than to its parts or given by its construction or design), it can involve distributed systemic knowledge that is acquired through experience, i.e., changes in the organization of the relationships among its parts (without presupposing a system-level reward function for such changes). This conception of agency helps us think about the ways in which cells, organisms, and perhaps other biological scales, can be agential (i.e., more agential than their parts) in a quantifiable sense, without denying that the behavior of the whole depends on the behaviors of the parts in their current organization. (shrink)

The concepts of a spatially continuous substance, of spatial dimension and of spatial boundary are here "analyzed out" of the concepts of individual thing, of constituent and of coincidence. The analysis is based upon the theory of spatial coincidence that was developed by Brentano. Its presuppositions are essentially these: (1) if there are spatial objects of any kind, then there are continuous spatial substances. (2) such substances are possibly such that they are not constituents of any individual thing; and (...) (3) they contain constituents (namely, boundaries) which are necessarily such that they are constituents of spatial substances. (shrink)

The centrality of the whole/part relation in mathematics is demonstrated through the presentation and analysis of examples from algebra, geometry, functional analysis,logic, topology and category theory.

The strongly innovative theory of whole-parts relations outlined by Husserl in his Third logical Investigation—to which he attributed a basic value for his entire phenomenology—has recently attracted a renewed interest. Although many important issues have been clarified (especially by Kit Fine) the subject seems still worth being revisited. To this aim Husserlian universes are introduced. These are lower bounded distributive lattices endowed with a unary operation of defect and a binary relation of isogeneity. Husserl's contents are identified with (...) nonzero elements of a Husserlian universe and the dependence relations among contents are defined and studied starting from the idea that the defect of xis what x needs in order to ‘exist’ i.e., in order to be ‘closed’ with respect to the closure operation defined as the sup of x and its defect. It turns out that there are (at least) eight dependence relations which are worth to be considered. Many other questions concerning the world of contents (among them the proofs of the famous Husserl's Sätze) may now be discussed and clarified. Then the theory of species and genera is developed. Ultimate species (for short: species) are identified with equivalence classes of contents modulo isogeneity, and species in general (for short: genera) are identified with arbitrary unions of species. On the basis of the relation obtaining among two contents when they are isogeneous to two contents the first of which is a part of the second it becomes possible to develop a rather satisfying interpretation of Husserl's theory of the dependencies among species and genera and of the material a priori laws. By strengthening the notion of Husserlian universe into the notion of rigid Husserlian universe, the theory of species and genera obtains a stronger version. Three models of the theory are exhibited. The first one, suggested by combinatorial-topological considerations, identifies contents with finite non-empty sets of natural numbers; the second one identifies contents with non-empty sets of formulas of a formal language; the third one (not totally ‘rigid’) identifies contents with positive integers. (shrink)

Reconstructability analysis (RA) decomposes wholes, namely data in the form either of set theoretic relations or multivariate probability distributions, into parts, namely relations or distributions involving subsets of variables. Data is modeled and compressed by variable-based decomposition, by more general state-based decomposition, or by the use of latent variables. Models, which specify the interdependencies among the variables, are selected to minimize error and complexity.

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)

Whenever the name Edmund Husserl appears in the context of nursing research, what correctly comes to mind is the phenomenological approach to qualitative methodology. Husserl is not only considered the founder of phenomenology, but his broad concept development also contributed to the demise of positivism and inspired fruitful approaches to the social sciences. In this spirit of inspiration, it must be expressed that Husserl's theory of wholes and parts, and particularly his differentiation of parts into ‘pieces’ and ‘moments’, is (...) very helpful in guiding the selection of research methods across the board in nursing science. The purpose of this paper is to highlight a frame of reference for nursing researchers to use in examining the essential nature of that which is being studied. This frame of reference is the Husserlian philosophy of ‘pieces’ and ‘moments’ in relation to the whole. ‘Pieces’ are independent parts of the whole that are subject to isolability in study, whereas ‘moments’ are nonindependent parts, which cannot be detached, presented, or studied apart from the whole. The intent is to propose this frame of reference as a philosophical base from which nursing researchers may better select among paradigms and methodological approaches in regard to the essential nature (‘pieces’ or ‘moments’) of that which they are researching. (shrink)

** 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)

Since the early 80s, metonymy has progressively gained central stage in linguistic investigations. The advent of cognitive linguistics marked a new turn in the study of this trope conceived, not as a deviation from semantic conventions (contra classical rhetorical theories), but as a phenomenon rooted in non-language-specific mechanisms of conceptualization and structuring of the world. Focusing on the particular case of whole-for-part (WP) metonymy, the general stand of this presentation will be to argue for the need to re-inject (...) properly semantic (descriptive and formal) considerations in the study of metonymy. It will be shown that semantic typologies of meronymic relations, as well as recent results in the semantics of partial predicates and colour predicates, can be jointly exploited to attain a better understanding of the mechanism of WP-metonymy. The resulting view will in particular connect such metonymies to mechanisms of reference and property attribution to functional parts for classificatory purposes. (shrink)

The present article provides a mereological analysis of Euclid’s planar geometry as presented in the first two books of his Elements. As a standard of comparison, a brief survey of the basic concepts of planar geometry formulated in a set-theoretic framework is given in Section 2. Section 3.2, then, develops the theories of incidence and order using a blend of mereology and convex geometry. Section 3.3 explains Euclid’s “megethology”, i.e., his theory of magnitudes. In Euclid’s system of geometry, megethology (...) takes over the role played by the theory of congruence in modern accounts of geometry. Mereology and megethology are connected by Euclid’s Axiom 5: “The whole is greater than the part.” Section 4 compares Euclid’s theory of polygonal area, based on his “Whole-Greater-Than-Part” principle, to the account provided by Hilbert in his Grundlagen der Geometrie. An hypothesis is set forth why modern treatments of geometry abandon Euclid’s Axiom 5. Finally, in Section 5, the adequacy of atomistic mereology as a framework for a formal reconstruction of Euclid’s system of geometry is discussed. (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)

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)

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 (...) class='Hi'>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)

The discovery of the importance of mereology follows and does not precede the formalisation of the theory. In particular, it was only after the construction of an axiomatic theory of the part-whole relation by the Polish logician Stanisław Leśniewski that any attempt was made to reinterpret some periods in the history of philosophy in the light of the theory of parts and wholes. Secondly, the push for formalisation - and the individuation of mereology as a (...) specific theoretical field - arise from several particular theories, first from biology and then from psychology. Mereological considerations were explicitly developed within the school of Brentano, by Brentano himself- starting from the problem of the unity of consciousness - and by his students, particularly Stumpl, Twardowski and the Gestaltists. The most complete result of this tradition is undoubtedly the third of Husserl's Logical Investigations, called "the single most important contribution to realist (Aristotelian) ontology in the modern period". (shrink)

In his book, The Principles of Mathematics , the young Bertrand Russell abandoned the common-sense notion that the whole must be greater than its part, and argued that wholes and their parts can be similar, e.g. where both are infinite series, the one being a sub-series of the other. He also rejected the popular view that the idea of an infinite number is self-contradictory, and that an infinite set or collection is an impossibility. In this paper, I intend (...) to re-examine Russell's wisdom in doing both these things, and see if it might not have made more sense, and caused his enterprise fewer problems, if he had simply stuck to our commonplace ideas. To this end, I shall also be considering his treatment of certain paradoxes that he claims can only be resolved by the abandonment of the above notions, as well as certain others which his theories appear to have generated. (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)

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.

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)

BackgroundThe nature of a woman’s orgasm has been a source of scientific, political, and cultural debate for over a century. Since the Victorian era, the pendulum has swung from the vagina to the clitoris, and to some extent back again, with the current debate stuck over whether internal sensory structures exist in the vagina that could account for orgasms based largely on their stimulation, or whether stimulation of the external glans clitoris is always necessary for orgasm.MethodWe review the history of (...) the clitoral versus vaginal orgasm debate as it has evolved with conflicting ideas and data from psychiatry and psychoanalysis, epidemiology, evolutionary theory, feminist political theory, physiology, and finally neuroscience.ResultsA new synthesis is presented that acknowledges the enormous potential women have to experience orgasms from one or more sources of sensory input, including the external clitoral glans, internal region around the “G-spot” that corresponds to the internal clitoral bulbs, the c... (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)