Two cars are moving towards an intersection, one traveling east the other going north. The driver of the eastbound car runs the red light; his car and the northbound one collide at precisely noon. Call the ensuing accident High Noon. Had the driver of one of the cars braked a second earlier, their collision would have occurred later than it did (if it occurred at all). Would that slightly postdated collision, however, have been the start of High Noon?

Decompositional analysis is the process of constructing explanations of the characteristics of whole systems in terms of characteristics of parts of those whole systems. Cognitive psychology is an endeavour that develops explanations of the capacities of the human organism in terms of descriptions of the brain's functionally defined information-processing components. This paper details the nature of this explanatory strategy, known as functional analysis. Functional analysis is contrasted with two other varieties of decompositional analysis, namely, structural analysis and capacity analysis. After (...) an examination of these three varieties of analysis, there follows a consideration of a mistake to avoid when conducting decompositional analyses in psychology, and a possible limitation on their explanatory scope. (shrink)

This paper develops co-ordinated multiple-domain supervenience relations to model determination and dependence relations between complex entities and their constituents by appealing to R-related pairs and by making use of associated isomorphisms. Supervenience relations are devised for order-sensitive and repetition-sensitive mereologies, for mereological systems that make room for many-many composition relations, as well as for hierarchical mereologies that incorporate compositional and hylomorphic structure. Finally, mappings are provided for theories that consider wholes to be prior to their parts.

Formal ontology as it is presented in Husserl`s Third Logical Investigation can be interpreted as a fundamental tool to describe objects in a formal sense. It is presented one of the main sources: chapter five of Carl Stumpf`s Ûber den psycholoogischen Ursprung der Raumovorstellung (1873), and then it is described how Husserlian Formal Ontology is applied in Fifth Logical Investigation. Finally, it is applied to dramatic structures, in the spirit of Roman Ingarden.

I argue that, unlike your brain, you are not composed of other things: you are simple. My argument centers on what I take to be an uncontroversial datum: for any pair of conscious beings, it is impossible for the pair itself to be conscious. Consider, for instance, the pair comprising you and me. You might pinch your arm and feel a pain. I might simultaneously pinch my arm and feel a qualitatively identical pain. But the pair we form would not (...) feel a thing.1 Pairs of people themselves are incapable of experience. Call this The Datum. What explains The Datum? I think the following exhaust the reasonable options. (1) Pairs of people lack a sufficient number of immediate parts. (2) Pairs of people lack immediate parts capable of standing in the right sorts of relations to each other and their environment. (3) Pairs of people lack immediate parts of the right nature. (4) Pairs of people are not structures (they are unstructured collections of their two immediate parts). (5) Some combination of (1) – (4). Finally, (6) pairs of people are not simple. (shrink)

David Lewis famously takes mereology “to be perfectly understood, unproblematic, and certain” (1991, 75). It is central to his thought, appearing in his discussions of set theory, modality, vagueness, structural universals, and elsewhere. He held views not only about how composition works and when it occurs, but also about the role of mereology in philosophy. In this essay, I will proceed by articulating four theses that Lewis holds about composition. (I would call them the four U’s, if only ‘unguilty’ were (...) a word!) Three of them are familiar; Lewis himself explicitly articulates and relies upon them. The fourth remains implicit, but it is nonetheless important. Here they are: Composition is unique —the same things cannot have two different fusions. Composition is unrestricted —any two things whatsoever have a fusion. (shrink)

I argue that it is intuitive and useful to think about composition in the light of the familiar functionalist distinction between role and occupant. This involves factoring the standard notion of parthood into two related notions: being a parthood slot and occupying a parthood slot. One thing is part of another just in case it fills one of that thing's parthood slots. This move opens room to rethink mereology in various ways, and, in particular, to see the mereological structure of (...) a composite as potentially outreaching the individual entities that are its parts. I sketch one formal system that allows things to have individual entities as parts multiple times over. This is particularly useful to David Armstrong, given Lewis's charge that his structural universals must do exactly that. I close by reflecting upon the nature and point of formal mereology. (shrink)

Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look counterintuitive (...) to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)

Given Quine's views on philosophical methodology, he should not have taken the axioms of classical mereology to be "self-evident", or "analytic"; but rather, he should have set out to justify them by what might be broadly called an "inference to the best explanation". He does very little to this end. In particular, he does little to examine alternative theories, to see if there might be anything they could explain better than classical mereology can. I argue that there is something important (...) that needs to be explained, namely, the way that properties "travel around in clusters" (eg. we often know that "when and where there is something with such-and-such property, there is also something with so-and-so other property", and so on). I argue that these clusterings of properties can be given various subtle (broadly "commonsense") explanations using a version of mereology that denies the classical axiom of "extensionality" (that is, denying that two distinct things must have distinct parts). I offer a challenge to the Quinean metaphysics: to show that these "non-extensional" explanations can be replaced by better explanations that use only classical, extensional mereology and set theory. (shrink)

In R. Holte and A. Howe (eds.), Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07).

The world contains a number of objects composed of other objects. A table is composed of a few pieces of wood and some nails; an H2O molecule is composed of two hydrogen atoms and an oxygen atom; and some say there is something composed of the table and the H2O molecule. When some things compose some further thing, the former are proper parts of the latter. (A proper part of a thing is a part that is not identical to that (...) thing). The proper parts compose a composite object and a composite object decomposes into its proper parts. (shrink)

Unger has recently argued that if you are the only thinking and experienc- ing subject in your chair, then you are not a material object. This leads Unger to endorse a version of Substance Dualism according to which we are immaterial souls. This paper argues that this is an overreaction. We argue that the specifically Dualist elements of Unger’s view play no role in his response to the problem; only the view’s structure is required, and that is available to Unger’s (...) opponents. We outline one such non-Dualist view, suggest how to resolve the dispute, respond to some objections, and argue that ours is but one of many views that survive Unger’s challenge. All these views are incompatible with microphysicalism. So Unger’s discussion does contain an insight: if you are the only conscious subject in your chair, then microphsyicalism is false. Unger’s mistake was to infer Substance Dualism from this; for microphysi- calism is not the only alternative to Dualism. (shrink)

Mereological Nihilism is the thesis that no material object has proper parts; every material object is a simple. Recent developments in plural semantics have made it possible to develop and motivate this position. In particular, some have argued that the tools of plural reference and quantification enable us to systematically paraphrase true statements apparently about composites into statements that only concern simples. Are composites really surplus to philosophical requirements? Given the resources of plural semantics, what must the world be like (...) if composites are to be theoretically indispensable? I will describe and defend the possibility of scenario in which mention of composites cannot be paraphrased. We will therefore come to appreciate one way in which the world would have to be in order for composites to be required and for Nihilism to fail. (shrink)

In “Tropes and Ordinary Physical Objects”, Kris McDaniel argues that ordinary physical objects are fusions of monadic and polyadic tropes. McDaniel calls his view “TOPO”—for “Theory of Ordinary Physical Objects”. He argues that we should accept TOPO because of the philosophical work that it allows us to do. Among other things, TOPO is supposed to allow endurantists to reply to Mark Heller’s argument for <span class='Hi'>perdurantism</span>. But, we argue in this paper, TOPO does not help endurantists do that; indeed, we (...) argue that anyone who accepts TOPO should reject endurantism. (shrink)

In this book Roberto Casati and Achille C. Varzi address some of the fundamental issues in the philosophy of spatial representation.

The IPAP Schizophrenia Algorithm was originally designed in the form of a flow chart to help physicians optimise the treatment of schizophrenic patients. We examined the current version from the perspective of recent work on terminologies and ontologies thereby drawing on the resources of Basic Formal Ontology, and this with the objective to make the algorithm appropriate for Semantic Web applications. We found that Basic Formal Ontology is a rich enough theory to represent all the entities involved and that applying (...) the theory to the IPAP schizophrenia algorithm results in a representation that can be used by software agents to perform monitoring and control in a referent tracking environment. (shrink)

"Lesniewski defined ontology, one of his three foundational systems, as 'a certain kind of modernized 'traditional logic' [On the foundations of mathematics (FM), p. 176]. In this respect it is worth bearing in mind that in the 1937-38 academic year Lesniewski taught a course called "Traditional 'formal logic' and traditional 'set theory' on the ground of ontology"; cf. Srzednicki and Stachniak, S. Lesniewski's Systems. Protothetic, 1988, p. 180. On this see Kotarbinski Gnosiology. The scientific approach to the theory of knowledge, (...) 1966, pp. 253-54 [the Polish original was published in 1929], which Lesniewski praised in [FM]: see in particular pp. 373 ff. Kotarbinski noted that Lesniewski "calls his system 'ontology' in harmony with certain terms used earlier (as in.. (shrink)

This collection brings together cutting-edge research on the metaphysics of human nature and soul-body dualism.Kevin Corcoran's collection, Soul, Body, and ...

I examine the link between extensionality principles of classical mereology and the anti-symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti-symmetry. I examine the notions of proper parthood, weak supplementation and non-well-foundedness. By rejecting anti-symmetry, the anti-extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non-extensional mereology in which anti-symmetry fails. If the notion of 'mereological equivalence' is made explicit, this non-anti-symmetric mereology recaptures all of the structure (...) of classical mereology. (shrink)

This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to (...) classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete. (shrink)

A principle is born: the Granovetter study -- Why do we like networks? -- Network stability -- Weak links as stabilizers of complex systems -- Atoms, molecules, and macromolecules -- Weak links and cellular stability -- Weak links and the stability of organisms -- Social nets -- Networks of human culture -- The global web -- The Ecoweb -- Conclusions and perspectives.

I compare a Lewisian defence of monism with Kit Fine's defence of pluralism. I argue that the Lewisian defence is, at present, the clearer in its explanatory intent and ontological commitments. I challenge Fine to explain more fully the nature of the entities that he postulates and the relationship between continuous material objects and the parts of those rigid embodiments in terms of which he proposes to explain crucial, modal and sortal, features of those objects.

Mereological principles are sometimes used to support general claims about the structure and arrangement of objects in the world. I focus initially on one such mereological principle, the weak supplementation principle (WSP). It is not obvious that (WSP) is prescribed by ordinary thinking about parthood. Further, (WSP) is not needed for a fairly strong formal characterization of the part–whole relation. For these reasons, some arguments relying on (WSP) might be countered by simply denying (WSP). I argue more generally that there (...) is no reason to assume that one core mereology functions as a common basis for all plausible metaphysical theories. (shrink)

Standard theories in mereotopology focus on relations of parthood and connection among spatial or spatio-temporal regions. Objects or processes which might be located in such regions are not normally directly treated in such theories. At best, they are simulated via appeal to distributions of attributes across the regions occupied or by functions from times to regions. The present paper offers a richer framework, in which it is possible to represent directly the relations between entities of various types at different levels, (...) including both objects and the regions they occupy. What results is a layered mereotopology, a theory which can handle multiple layers (analogous to the layers of a lasagna) of spatially or spatiotemporally coincident but mereologically non-overlapping entities. Keywords: Ontology, mereology, mereotopology, qualitative spatial reasoning, map layers, dynamic GIS.. (shrink)

Ted Sider’s paper “Hell and Vagueness” challenges a certain conception of Hell by arguing that it is inconsistent with God’s justice. Sider’s inconsistency argument works only when supplemented by additional premises. Key to Sider’s case is a premise that the properties upon which eternal destinies supervene are “a smear,” i.e., they are distributed continuously among individuals in the world. We question this premise and provide reasons to doubt it. The doubts come from two sources. The first is based on evidential (...) considerations borrowed from skeptical theism. A related but separate consideration is that supposing it would be an insurmountable problem for God to make just (and therefore non-arbitrary) distinctions in morally smeared world, God thereby has sufficient motivation not to actualize such worlds. Yet God also clearly has motivation only to actualize some member of the subset of nonsmeared worlds which don’t appear non-smeared. For if it was obvious who was morally fit for Heaven and who wasn’t, a new arena of great injustice is opened up. The result is that if there is a God, then he has the motivation and the ability to actualize from just that set of worlds which are not smeared but which are indiscernible from smeared worlds. (shrink)

SURVEYS (a) David Lewis, Parts of Classes (Blackwell, Oxford, 1991), §§3.4–3.6 (pp. 72–87) (b) Achille Varzi, ‘Mereology’, Stanford Encyclopedia of Philosophy, http:// plato.stanford.edu/entries/mereology/. (c) Michael C. Rea (ed.), Material Constitu- tion (Rowman & Littlefield, Lanham, MD, 1997), esp. the introduction. (d) van Cleve and Markosian, ‘Mereology’, Theodore Sider, John Hawthorne, and Dean W. Zimmerman (eds.), Contemporary Debates in Metaphysics (Blackwell, Oxford, 2007), ch. 8, pp. 319–63. (e) Peter M. Simons, Parts: A Study in Ontology (Oxford University Press, Oxford, 1987).

Universalism (the thesis that for any ys, those ys compose a further object) is an answer to the Special Composition Question. In the literature there are three arguments (the arguments from elegance) that are often relied upon, but rarely examined in-depth. I argue that these motivations cannot be had by the perdurantist, for to avoid a commitment to badly behaved superluminal objects perdurantists must answer the Proper Continuant Question. Any answer to that question necessarily ensures that there is a restricted (...) answer to the Special Composition Question that is just as elegant as universalism. Thus, if you are a perdurantist, the arguments from elegance fail to motivate universalism for there will always be a restricted composition that is just as good. (shrink)

Universalism (the thesis that distinct objects always compose a further object) has come under much scrutiny in recent years. What has been largely ignored is its role in the metaphysics of classes. Not only does universalism provide ways to deal with classes in a metaphysically pleasing fashion, its success on these grounds has been offered as a motivation for believing it. This paper argues that such treatments of classes can be achieved without universalism, examining theories from Goodman and Quine, Armstrong (...) and Lewis. In the case of each theory, universalism is drafted in to ensure that there are enough material objects to play a particular role. I argue that, for each theory, there's a better theory that ditches universalism and instead uses an alternative principle of composition demanding that the unrestricted composition of entities other than material objects (respectively: regions, states of affairs and singletons) play that role instead. I conclude that (1) non-universalists can consider accepting such theories of classes and (2) we should ignore any alleged motivation for universalism on the basis of dealing with classes. (shrink)

Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several hypotheses: (...) the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity. (shrink)

Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is interior parthood . This choice will have the advantage that filters may be defined with respect to it, constructing “points”, as Peter Roeper has done (...) (“Region-based topology”, Journal of Philosophical Logic , 26 (1997), 25–309). This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an approximate lattice , because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of “points” in a topological “space”. (shrink)

This paper contains a formal theory of functional parthood. Since the relation of functional parthood is defined here by means of the notion of design, the theory of functional parthood turns out to be a theory of design. The formal theory of design I defend here is a result of introducing a number of constraints that are to express the rational aspects of designing practice. The ontological background for the theory is provided by a conception of states of affairs. The (...) theory is accompanied with a formal model. I prove that the theory is sound and complete with respect to this model. (shrink)

Russellianism, roughly put, is the view that a sentence of the form ‘Ra1, . . ., an’ expresses a proposition that is composed of the universal expressed by the predicate in that sentence and the objects referred to by the names in the sentence. If ‘composed of’ is defined in terms of a parthood relation (rather than in terms of a constituency relation that is said not to be a parthood relation), the resulting version of Russellianism gives rise to a (...) pair of mereological puzzles. (1) As Frege suggested, it generates counterexamples to the view that any parthood relation will be governed by a transitivity principle (or by some ‘adicity-appropriate analogue’ of such a principle, in case the parthood relation in question is not two-place). (2) It generates counterexamples to the view that any parthood relation will be governed by a certain ‘supplementation’ principle (or by an adicity-appropriate analogue of that principle). Elsewhere I have suggested on independent grounds that parthood might be a four-place relation (expressed by ‘x, at its location y, is a part of z, at its location w’). Here I argue that, on one natural way of spelling out Russellianism in terms of such a relation, it avoids both puzzles. (shrink)

I defend coincidentalism (the view that some pluralities have more than one mereological fusion) and restricted composition (the view that some pluralities lack mereological fusions) against recent arguments due to Theodore Sider.

Though capturing powerful analytical principles, this excellent article misses ways in which psychology and neuroscience bear on reciprocity and decision-making. I suggest more explicit consideration of scale. We may go further beyond gene-culture dualism by articulating how varieties of living systems, while ultimately drawing from both genetic and cultural streams, evolve sufficiently as unitary targets of selection to mediate higher-level complex systems. (Published Online April 27 2007).

This article discusses three different approaches to human knowledge. The first is that of Peter Simons, a linguistic philosopher, who suggests that language has an underlying algebraic structure. The second approach is that of Ernest Nagel, a philosopher of science, who maintains that the key to knowledge lies in logical analysis. The third approach, due to Michael Polanyi, stresses the idea of tacit integration of parts into composite wholes. All three employ hierarchical schemes, the first two work from the top (...) down, whereas Polanyi works from the bottom up, using the idea of ‘emergence’. (shrink)

Three arguments for the conclusion that objects cannot endure in B-time even if they remain intrinsically unchanged are examined: Carter and Hestevolds enduring-objects-as-universals argument (American Philosophical Quarterly 31(4):269-283, 1994) and Barker and Dowe's paradox 1 and paradox 2 (Analysis 63(2):106-114, 2003, Analysis 65(1):69-74, 2005). All three are shown to fail.

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.

‘Fusion’ is a philosophical term of art, with a variety of uses. First, it is often a synonym for ‘sum’. In this sense, a is a fusion of b, c and d iff b, c and d are parts of a, and every part of a shares a part with b, c or d. So a cat is a fusion of the cells which compose it, and the same cat is a fusion of the molecules which compose it. Relatedly, ‘fusion’ (...) can refer to the occurrence of such composition: philosophers disagree about whether fusion is widespread, about whether it can be a vague matter, and so on. (shrink)

If the property _being a methane molecule_ is a universal, then it is a structural universal: objects instantiate _being a methane molecule_ just in case they have the right sorts of proper parts arranged in the right sort of way. Lewis argued that there can be no satisfactory account of structural universals; in this paper I provide a satisfactory account.

I argue that, despite van Inwagen's pessimism about the task, it is worth looking for answers to his General Composition Question. Such answers or 'principles of composition' tell us about the relationship between an object and its parts. I compare principles of composition with criteria of identity, arguing that, just as different sorts of thing satisfy different criteria of identity, they may satisfy different principles of composition. Variety in criteria of identity is not taken to reflect ontological variety in the (...) identity relation; I discuss whether variety in principles of composition should be taken to reflect ontological variety in the composition relation. (shrink)

In his Material Beings, Peter van Inwagen distinguishes two questions about parthood. What are the conditions necessary and sufficient for some things jointly to compose a whole? What are the conditions necessary and sufficient for a thing to have proper parts? The first of these, the Special Composition Question (SCQ), has been widely discussed, and David Lewis has argued that an important constraint on any answer to the SCQ is that it should not permit borderline cases of composition. This is (...) a far-reaching claim, since many plausible-seeming accounts of composition do permit borderline cases. Ned Markosian has recently directed our attention to the second, the neglected Inverse Special Composition Question (ISCQ). I will argue that those who accept Lewis’s constraint on answers to the SCQ should accept an analogous constraint on answers to the ISCQ, and I will discuss the effects of such a constraint. (shrink)

Vague existence can seem like the worst kind of vagueness in the world, or seem to be an entirely unintelligible notion. This bad reputation is based upon the rumour that if there is vague existence then there are non-existent objects. But the rumour is false: the modest brand of vague existence entailed by certain metaphysical theories of composition does not deserve its bad reputation.

0. Introduction: Mereology, Metaphysics, and Speculative Grammar 0.1 Mereology, Ancient and Contemporary 0.11 Mereology is, strictly speaking, the theory of ...

E.J. Lowe is one of the few philosophers who defend both the existence of spatially coincident entities and the Principle of Weak Extensionality that no two objects which have proper parts have exactly the same proper parts at the same time. Lowe maintains that when spatially coincident things like the statue and the lump of bronze are in a constitution relation, the constituted entity (the statue) has parts that the constituting entity (the lump) doesn’t, hence the compatibility with Weak Extensionality. (...) My contention is that his argument for why the statue has parts the lump of bronze lacks can also be used to show that the lump of bronze has parts the statue doesn’t. This will mean that there is no basis for saying the statue and the lump are in a constitution relation. I argue for accepting a modified account of constitution and abandoning the Principle of Weak Extensionality. (shrink)

: Pierre Bayle is the most forthright and systematic early modern proponent of the actual parts doctrine, the period's counterpart to the 'doctrine of arbitrary undetached parts' familiar from current analytic mereology and metaphysics. In this paper I introduce both the actual parts account of the internal structure of matter and the rival system of potential parts. I then identify Bayle as the leading advocate of the actual parts doctrine and examine his arguments for this account.

The contributions to this collection deal with the fundamental problem of unity, which plays a decisive role in many contemporary debates (even when this role ...

Ontological innocence You can undertake two commitments, once to object x and once to object y; or you could commit yourself to them all at once by committing yourself to the mereological fusion of x and y. It’s the same commitment either way. So once you have committed to some things, commitment to objects composed of those things is not a further commitment. (Cf. Lewis, Parts of Classes.).

Classical mereology (CM) is usually taken to be formulated in a tenseless language, and is therefore associated with a four-dimensionalist metaphysics. This paper presents three ways one might integrate the core idea of flat plenitude, i.e., that every suitable condition or property has exactly one mereological fusion, with a tensed logical setting. All require a revised notion of mereological fusion. The candidates differ over how they conceive parthood to interact with existence in time, which connects to the distinction between endurance (...) and perdurance. Similar issues arise for the integration of mereology with modality, and much of our discussion applies to this project as well. (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)

Our object is to study the interaction between mereology and David Lewis’ theory of subject-matters, elaborating his observation that not every subject matter is of the form: how things stand with such-and-such a part of the world. After an informal introduction to this point in Section 1, we turn to a formal treatment of the partial orderings arising in the two areas – the part-whole relation, on the one hand, and the relation of refinement amongst partitions of the set (...) of worlds, on the other. (We follow Lewis – approximately – in identifying subject-matters with such partitions.) We emphasize a certain duality, formulated in (2.6) and (2.7) in Section 2, between the corresponding lattice operations – mereological joins with partition-lattice meets, mereological meets with partition-lattice joins. Section 3 presents some issues that are raised by consideration of the informally familiar idea of logical subtraction. These include, in particular, a problem about the need for a notion of independence different from the usual logical notion(s) going by that name. The apparatus of Section 2 promises to throw some light on this problem, as we indicate in Section 4. Section 5 ties up some loose ends and suggests an area in which further work would be desirable. (shrink)

An axiomatic treatment of the relation part of is shown to lead naturally to an account of the ways in which parts of things are matched. The determination of matchings by the properties of parts and by the relations between parts is discussed and shown to be relevant to certain classificatory problems in science. The connexions between matchings and symmetries of parts are explored, and a general account is given of the ways in which ambiguities in the matching of parts (...) may be resolved. (shrink)

In his _Treatise on the Golden Lion_, Fazang says that wholes are _in_ each of their parts and that each part of a whole _is_ every other part of the whole. In this paper, I offer an interpretation of these remarks according to which they are not obviously false, and I use this interpretation in order to rigorously reconstruct Fazang's arguments for his claims. On the interpretation I favor, Fazang means that the presence of a whole's part suffices for the (...) presence of the whole and that the presence of any such part is both necessary and sufficient for the presence of any other part. I also argue that this interpretation is more plausible than its extant competitors. (shrink)

Lewis has objected to Armstrong's notion of a structural universal on the grounds that it violates the Principle of Uniqueness of Composition (PUC), which says that given some parts, there is only one whole that they compose. This paper reviews Armstrong's case for structural universals, and then attempts to reconcile structural universals with PUC by arguing for the existence of arrangement universals. The latter are not only a key to defending structural universals against Lewis' objection, but are in fact essential (...) to Armstrong's conception of structural universals in general. Three objections to my proposal are deflected, and two alternative proposals are shown to be inferior to it. (shrink)