What are the conditions under which one biological object is a part of another biological object? This paper answers this question by developing a general, systematic account of biological parthood. I specify two criteria for biological parthood. Substantial Spatial Inclusionrequires biological parts to be spatially located inside or in the region that the natural boundary of t he biological whole occupies. Compositional Relevance captures the fact that a biological part engages in a biological process that must make a (...) necessary contribution to a condition that is minimally sufficient to one or more of the characteristic behaviors of the biological whole. Instead of emphasizing the diversity of part-whole relations in the biological world, this paper asks what biological part-whole relations have in common and what constrains their existence, in general. After presenting the two criteria for biological parthood I discuss in how far my account can cope with hard cases (e.g., redundant parts) and I reveal the merits and limits of monism. (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)

The subset realization view proposes to solve the causal exclusion problem of non‐reductive mental instances by taking the mental instance as a part of its physical realizer. Many philosophers have argued that such a part‐whole relation will undermine physicalist realization because parts are ontologically prior to their wholes and the subset view is thus flawed. I argue that the relation that the subset view should propose is different from the ordinary part‐whole relation. What they should propose is (...) another kind of part‐whole relation under which parts are posterior to wholes. So, the subset view is not flawed in the aforementioned aspect. But discussion of the new part‐whole relation reveals that the subset view is in lack of a crucial argument against the exclusion reasoning, thus cannot solve the exclusion problem. Adopting the principle of causal proportionality (a route subset realizationists sometimes take) will not help the subset view either. So, my conclusion is, the subset view is yet to find a way to solve the exclusion problem. (shrink)

Representing parthood relations in ORM has received little attention, despite its added-value of the semantics at the conceptual level. We introduce a high-level taxonomy of types of meronymic and mereological relations, use it to construct a decision procedure to determine which type of part- whole role is applicable, and incrementally add mandatory and uniqueness constraints. This enables the conceptual modeller to develop models that are closer to the real-world subject domain semantics, hence improve quality of the software.

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)

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 recurring problem in conceptual modelling and ontology development is the representation of part-whole relations, with a requirement to be able to distinguish between essential and mandatory parts. To solve this problem, we formally characterize the semantics of these shareability notions by resorting to the temporal conceptual model E RVT and its formalization in the description logic DLRUS.

Many types of part-whole relations have been proposed in the literature to aid the conceptual modeller to choose the most appropriate type, but many of those relations lack a formal specification to give clear and unambiguous semantics to them. To remedy this, a formal taxonomy of types of mereological and meronymic part-whole relations is presented that distinguishes between transitive and intransitive relations and the kind of entity types that are related. The demand to use (...) it effectively brings afore new requirements for automated reasoning over a hierarchy of relations. To ensure logically and ontologically correct inferencing over both the class and role hierarchy, the new reasoning service RBox compatibility for Description Logics reasoners is introduced. The proposed combination of formal semantics and the new reasoning service will improve the representation of the application domain when using part-whole relations in conceptual models and ontologies. (shrink)

Book synopsis: Donald Davidson is among the most influential philosophers of the 20th century. This volume includes some 30 essays which variously criticize, comment on and develop Davidson's philosophy as represented in his collected papers "Essays on Actions and Events", in addition to three further essays by Davidson himself. The essays divide into three sections, each opening with an editorial introduction and corresponding to the three major sections of "Actions and Events". The first section discusses the nature of rational explanation, (...) the relationships between reasons and actions, intentions and actions, will and irrationality, and the concepts of agency, freedom and weakness of the will. This section also contains an essay in which Davidson presents his views on self-deception. The second section considers the nature of events, causal relationships, and the logical form of action and singular causal statements. Finally, the volume looks at the relationship between the mental and the physical, the scientific status of psychological and psychophysical laws, and the relationship between laws and causal and rational explanations. (shrink)

In this paper I aim at showing that, in Aristotle’s view, spoken and written language differ in their material organisation, in particular in their respective part-whole relations. I argue that, according to Aristotle, written language is an additive system (i.e. a system whose parts exist and are produced prior to what they are parts of), whereas spoken language is a non-additive system (i.e. a system whose parts cannot exist and be produced prior to what they (...) are parts of), and that, in his view, spoken language, qua non-additive system, is analogous to organisms. Further, I outline two possible implications of this hypothesis. The first concerns the relevance of Aristotle’s conception of spoken language as a non-additive system to his account of human language’s power to signify. I set out some reasons for thinking that Aristotle endorses the view that the form of human language (i.e. its power to signify) is matter-involving. The second implication concerns the syllable analogy that Aristotle employs in Metaphysics Ζ 17. I argue that the syllable Aristotle refers to is a spoken one, and I develop some consequences of this hypothesis for the meaning of the analogy and, more generally, of the chapter. (shrink)

This article argues that the second part of the Parmenides (137-166) consists not only of the well-known logical structure that has been widely studied but also of a great variety of definitions of forms. My aim is to show how these definitions depend on a specific group of closely connected primary forms (i.e., same, different, part, whole). The definitions that Parmenides provides help Socrates overcome his failure in attempting to define forms in the first part of the dialogue.

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)

We address the question whether there is an explanation for the fact that as Fodor put it the micro-level “converges on stable macro-level properties”, and whether there are lessons from this explanation for other issues in the vicinity. We argue that stability in large systems can be understood in terms of statistical limit theorems. In the thermodynamic limit of infinite system size N → ∞ systems will have strictly stable macroscopic properties in the sense that transitions between different macroscopic phases (...) of matter (if there are any) will not occur in finite time. Indeed stability in this sense is a consequence of the absence of fluctuations, as (large) fluctuations would be required to induce such macroscopic transformations. These properties can be understood in terms of coarse-grained descriptions, and the statistical limit theorems for independent or weakly dependent random variable describing the behaviour averages and the statistics of fluctuations in the large system limit. We argue that RNG analyses applied to off-critical systems can provide a rationalization for the applicability of these limit theorems. Furthermore we discuss some related issues as, for example, the role of the infinite-system idealization. (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)

Part–whole causation is the thesis that some causes are part of their effects. PWC has been objected to because of its incompatibility with the criterion that causes not be spatially included within their effects and the criterion that causes and effects are ontologically distinct in some sense. This paper serves to undermine the sufficiency of these ways of objecting to PWC by showing that for each criterion either cause-effect relationships need not satisfy it or part–whole relationships can. A (...) case-study of the collapse of Bridge 9340 is employed to facilitate the discussion. (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.

One of the most exciting things about science is the access that it provides to phenomena remote from everyday experience. Through science we delve into the distant past, explore other cultures, peer across vast reaches of space, and assay the microscopic structure of the world. As our understanding extends in all these directions, philosophers and scientists often ask how the resulting branches of knowledge are related.

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)

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)

According to the subset view of realization, a property realizes another if the causal powers of the latter are a subset of those of the former. Against this view, some authors (in particular, Kevin Morris and Paul Audi) have argued that it has an untenable consequence that realizing properties are less fundamental than the properties they realize, because the subset view characterizes realized properties as parts (subsets) of their realizers whereas it is generally true that a part is prior (...) to its whole. This paper defends the subset view from this “part-whole” objection, by arguing that if we compare individual powers of realizer and realizee with particular attention to their manifestation conditions, it turns out that each power of a realizee is grounded in some power of its realizer. This grounding relation between powers, I shall argue, allows subset theorists to explain why a realizer is more fundamental than its realizee, even while having the latter as a part. (shrink)

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)

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)

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)

The paper argues that very different part-whole relations hold between different kinds of entities. While these relations share most of their formal properties, they need not share all of them. Nor need other mereological principles be true of all kinds of part–whole pairs. In particular, it is argued that the principle of unrestricted composition, that any two or more entities have a mereological sum, while true of sets and propositions, is false of things and events.

The approach adopted by Early Modern authors to the notions of ‘whole’ and ‘part’ (what is called, in contemporary metaphysics, “mereology”, from the Ancient Greek word μερος: ‘part’) constitutes a central feature of their respective systems. The issue of what constituted a whole became all the more crucial as the new, revolutionary approaches to matter and extension – which mark the unavoidably fuzzy beginning of what we define as “modernity” – demanded a novel (and in some cases, radical) (...) approach to the questions of what constitutes a whole and how parts are arranged and bound together. It is important to mention that diverse attitudes towards mereology characterised Early Modern philosophers orthogonally to their belonging to different camps, such as the traditional categories of ‘Rationalists’ and ‘Empiricists’. Some of these philosophers considered wholes to be ontologically and/or logically prior to their parts (an approach that we may call “organicist” or “holist”, applying an anachronistic but nonetheless appropriate label). Others considered wholes to be derivative, resulting from the union of their parts (an approach that could be named “mereological mechanism”). Therefore, a word about terminology is in order: in what follows, I will apply the label “holist/organicist” to refer to a philosopher who would favour the priority of wholes over parts. Vice versa, I shall label as a “mereological mechanist” any philosopher favouring the priority of parts over the wholes formed by those parts, regardless of such parts being exclusively material, or including spiritual/mental parts as well as material ones. (shrink)

This paper examines a specific kind of part-whole relations that exist in the molecular genetic domain. The central question is under which conditions a particular molecule, such as a DNA sequence, is a biological part of the human genome. I address this question by analyzing how biologists in fact partition the human genome into parts. This paper thus presents a case study in the metaphysics of biological practice. I develop a metaphysical account of genomic parthood by analyzing (...) the investigative and reasoning practices in the ENCODE (ENCyclopedia Of DNA Elements) project. My account reveals two conditions that determine whether a molecule is a part of the human genome (i.e., a genomic part). First, genomic parts must possess a causal role function in the genome as a whole, that is, their functions must contribute to the genome directing the overall functioning of the cell. Second, genomic parts must have a specific chemical structure and be actual segments of the DNA sequence of the genome. (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.

Understanding the organization of an organism by individuating meaningful parts and accounting for organismal properties by studying the interaction of bodily parts is a central practice in many areas of biology. While structures are obvious bodily parts and structure and function have often been seen as antagonistic principles in the study of organismal organization, my tenet is that structures and functions are on a par. I articulate a notion of function (functions as activities), according to which functions (...) are bodily parts just as structures are. Recognizing part-whole relations among an organism’s various structures and functions permits fruitful investigation and multilevel explanation of organismal properties and functioning, across both developmental and evolutionary time. I show how my perspective clarifies debates surrounding homology and evolutionary novelty that stem from an alleged structure-function dichotomy. My approach favors a pluralism about individuation, where the criteria of what counts as a meaningful bodily part depend on the particular epistemic aims pursued in a scientific context. (shrink)

I relate plural quantification, and predicate logic where predicates do not need a fixed number of argument places, to the part-whole relation. For more on these themes see later work by Boolos, Lewis, and Oliver & Smiley.

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).

Rudolf Leuckart's 1851 pamphlet Ueber den Polymorphismus der Individuen (On the polymorphism of individuals) stood at the heart of naturalists' discussions on biological individuals, parts and wholes in mid-nineteenth-century Britain and Europe. Our analysis, which accompanies the first translation of this pamphlet into English, situates Leuckart's contribution to these discussions in two ways. First, we present it as part of a complex conceptual knot involving not only individuality and the understanding of compound organisms, but also the alternation of generations, (...) the division of labor in nature, and the possibility of finding general laws of the organic world. Leuckart's pamphlet is important as a novel attempt to give order to the strands of this knot. It also solved a set of key biological problems in a way that avoided some of the drawbacks of an earlier teleological tradition. Second, we situate the pamphlet within a longer trajectory of inquiry into part-whole relations in biology from the mid-eighteenth century to the present. We argue that biological individuality, along with the problem-complexes with which it engaged, was as central a problem to naturalists before 1859 as evolution, and that Leuckart's contributions to it left a long legacy that persisted well into the twentieth century. As biologists' interests in part-whole relations are once again on the upswing, the longue durée of this problem merits renewed consideration. (shrink)

Part/whole is said in many ways: the leg is part of the table, the subset is part of the set, rectangularity is part of squareness, and so on. Do the various flavors of part/whole have anything in common? They may be partial orders, but so are lots of non-mereological relations. I propose an “upward difference transmission” principle: x is part of y if and only if x cannot change in specified respects while y stays the same in (...) those respects. (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.

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.

What is the relation between parts taken together and the whole that they compose? The recent literature appears to be dominated by two different answers to this question, which are normally thought of as being incompatible. According to the first, parts taken together are identical to the whole that they compose. According to the second, the whole is grounded in its parts. The aim of this paper is to make some theoretical room for the (...) view according to which parts ground the whole they compose while being, at the same time, identical to it. (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 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)

Classical mereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. There are various different definitions of fusion in the literature, and various axiomatizations for classical mereology. Though the equivalence of the definitions of fusion is provable from axiom sets, the definitions are not logically equivalent, and, hence, are not inter-changeable when laying down the axioms. We examine the relations between the main definitions of fusion and correct some technical errors (...) in prominent discussions of the axiomatization of mereology. We show the equivalence of four different ways to axiomatize classical mereology, using three different notions of fusion. We also clarify the connection between classical mereology and complete Boolean algebra by giving two "neutral" axiom sets which can be supplemented by one or the other of two simple axioms to yield the full theories; one of these uses a notion of "strong complement" that helps explicate the connections between the theories. (shrink)

Rudolf Leuckart’s 1851 pamphlet Ueber den Polymorphismus der Individuen stood at the heart of naturalists’ discussions on biological individuals, parts and wholes in mid-nineteenth-century Britain and Europe. Our analysis, which accompanies the first translation of this pamphlet into English, situates Leuckart’s contribution to these discussions in two ways. First, we present it as part of a complex conceptual knot involving not only individuality and the understanding of compound organisms, but also the alternation of generations, the division of labor in (...) nature, and the possibility of finding general laws of the organic world. Leuckart’s pamphlet is important as a novel attempt to give order to the strands of this knot. It also solved a set of key biological problems in a way that avoided some of the drawbacks of an earlier teleological tradition. Second, we situate the pamphlet within a longer trajectory of inquiry into part-whole relations in biology from the mid-eighteenth century to the present. We argue that biological individuality, along with the problem-complexes with which it engaged, was as central a problem to naturalists before 1859 as evolution, and that Leuckart’s contributions to it left a long legacy that persisted well into the twentieth century. As biologists’ interests in part-whole relations are once again on the upswing, the longue durée of this problem merits renewed consideration. (shrink)

Thinking about space is thinking about spatial things. The table is on the carpet; hence the carpet is under the table. The vase is in the box; hence the box is not in the vase. But what does it mean for an object to be somewhere? How are objects tied to the space they occupy? This book is concerned with these and other fundamental issues in the philosophy of spatial representation. Our starting point is an analysis of the interplay between (...) mereology (the study of part/whole relations), topology (the study of spatial continuity and compactness), and the theory of spatial location proper. This leads to a unified framework for spatial representation understood quite broadly as a theory of the representation of spatial entities. The framework is then tested against some classical metaphysical questions such as: Are parts essential to their wholes? Is spatial colocation a sufficient criterion of identity? What (if anything) distinguishes material objects from events and other spatial entities? The concluding chapters deal with applications to topics as diverse as the logical analysis of movement and the semantics of maps. (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)