It is well-known that the entangled quantum state of a composite object cannot be reduced to the states of its parts. This quantum holism provides a peculiar challenge to formulate an appropriate mereological model: When a system is in an entangled state, which objects are there on the micro and macro level, and which of the objects carries which properties? This paper chooses a modeling approach to answer these questions: It proceeds from a systematic overview of consistent mereological (...) models for entangled systems and discusses which of them is compatible with the quantum mechanical evidence (where quantum states are understood realistically). It reveals that entangled quantum systems neither describe undivided wholes nor objects that stand in irreducible relations. The appropriate model assumes that the entangled property is an irreducible non-relational plural property carried collectively by the micro objects, while there is no macro object. In this sense, quantum holism is an instance of property holism, not of object holism. (shrink)

Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings (...) clarity to a debate in which opponents frequently talk past one another. With the two views stated precisely, our investigation reveals the dependence of the mereologists’ ontological commitments on the semantics of plural quantifiers. Though we discuss the debate with respect to a simplified and idealized model, the insights provided will make more complex debates on composition more productive and deflationist criticisms of the debate less substantial. (shrink)

This paper addresses the question of what constitutes an apt interpreted model for the purpose of analyzing causation. I first collect universally adopted aptness principles into a basic account, flagging open questions and choice points along the way. I then explore various additional aptness principles that have been proposed in the literature but have not been widely adopted, the motivations behind their proposals, and the concerns with each that stand in the way of universal adoption. I conclude that the remaining (...) work of articulating aptness for a SEM analysis of causation is tied up with issue to do with modality, ontology, and mereology. Continuing this work is therefore likely to shed light on the relationship between these areas and causation more generally. (shrink)

The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models and evaluate their consistency and (...) distinctness. The main result is an exhaustive taxonomy of six distinct and precise models that both provide information about the mereological features as well as about the entangled property. The taxonomy is well-suited to serve as the basis for future systematic investigations. (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.

Product structures are represented in engineering models by depicting and linking components, features and assemblies. Their understanding requires knowledge of both design and manufacturing practices, and yet further contextual reasoning is needed to read them correctly. Since these representations are essen- tial to the engineering activities, the lack of a clear and explicit semantics of these models hampers the use of information systems for their assessment and exploita- tion. We study this problem by identifying different interpretations of structure rep- resentations, (...) and then discuss the formal properties that a suitable language needs for representing components, features and combinations of these. We show that the representation of components and features require a non-standard mereology. (shrink)

A model of analogical mapping is proposed that uses five principles to generate consistent and conflicting hypotheses regarding assignments of elements of a source domain to analogous elements of a target domain. The principles follow the fine conceptual structure of the domains. The principles are: (1) the principle of proportional analogy; (2) the principle of mereological analogy, (3) the principle of chain reinforcement; (4) the principle of transitive reinforcement; and (5) the principle of mutual inconsistency. A constraint-satisfaction network is (...) used to find the set of assignments that preserves the greatest relational structure of the source. In contrast to the model proposed here, most models of analogical mapping use only the principle of proportional analogy. The use of many principles is shown to be superior in that it permits smoother integration of pragmatic factors and results in a more efficient mapping process. (shrink)

Coherence and correspondence are classical contenders as theories of truth. In this paper we examine them instead as interacting factors in the dynamics of belief across epistemic networks. We construct an agent-based model of network contact in which agents are characterized not in terms of single beliefs but in terms of internal belief suites. Individuals update elements of their belief suites on input from other agents in order both to maximize internal belief coherence and to incorporate ‘trickled in’ elements of (...) truth as correspondence. Results, though often intuitive, prove more complex than in simpler models (Hegselmann & Krause 2002, 2006; Grim, Singer, Reade & Fisher 2015). The optimistic finding is that pressures toward internal coherence can exploit and expand on small elements of truth as correspondence is introduced into epistemic networks. Less optimistic results show that pressures for coherence can also work directly against the incorporation of truth, particularly when coherence is established first and new data is introduced later. (shrink)

The author attempts to show how mereology, taken together with certain topological notions, can yield the foundations for future investigations in formal ontology. He also attempts to show how the mereological framework allows for the direct and natural formulation of a series of theses - for example pertaining to the concept of a boundary - which can be only indirectly formulated (if at all) in set-theoretic terms. The far-reaching ain of the present framework is to serve as a basis (...) for a formal ontology of the common-sense world. The author is interested in producing formally precise theories of structures of certain sorts in such a way that it is the structures themselves that intrest him and not formal machinery that has been set up to describe them. Hence the axioms are chosen primarily for the sake of the light they throw on the intended subject-matters (and not for their logical independence). The world itself - or its picture given in ordinary experience - is the only model the paper concentrates upon. Thus for example the presented system allows to prove that every boundary is the boundary of something, and that in particular no point exists in isolation from a large extended whole that is its boundary. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

Cognitive Set Theory is a mathematical model of cognition which equates sets with concepts, and uses mereological elements. It has a holistic emphasis, as opposed to a reductionistic emphasis, and it therefore begins with a single universe (as opposed to an infinite collection of infinitesimal points).

I defend a one category ontology: an ontology that denies that we need more than one fundamental category to support the ontological structure of the world. Categorical fundamentality is understood in terms of the metaphysically prior, as that in which everything else in the world consists. One category ontologies are deeply appealing, because their ontological simplicity gives them an unmatched elegance and spareness. I’m a fan of a one category ontology that collapses the distinction between particular and property, replacing it (...) with a single fundamental category of intrinsic characters or qualities. We may describe the qualities as qualitative charactersor as modes, perhaps on the model of Aristotelian qualitative (nonsubstantial) kinds, and I will use the term “properties” interchangeably with “qualities”. The qualities are repeatable and reasonably sparse, although, as I discuss in section 2.6, there are empirical reasons that may suggest, depending on one’s preferred fundamental physical theory, that they include irreducibly intensive qualities. There are no uninstantiated qualities. I also assume that the fundamental qualitative natures are intrinsic, although physics may ultimately suggest that some of them are extrinsic. On my view, matter, concrete objects, abstract objects, and perhaps even spacetime are constructed from mereological fusions of qualities, so the world is simply a vast mixture of qualities, including polyadic properties (i.e., relations). This means that everything there is, including concrete objects like persons or stars, is a quality, a qualitative fusion, or a portion of the extended qualitative fusion that is the worldwhole. I call my view mereological bundle theory. (shrink)

Fine (2017a) sets out a theory of content based on truthmaker semantics which distinguishes two kinds of consequence between contents. There is entailment, corresponding to the relationship between disjunct and disjunction, and there is containment, corresponding to the relationship between conjunctions and their conjuncts. Fine associates these with two notions of parthood: disjunctive and conjunctive. Conjunctive parthood is a very useful notion, allowing us to analyse partial content and partial truth. In this chapter, I extend the notion of disjunctive parthood (...) in terms of a structural relation of refinement, which stands to disjunctive parthood much as mereological parthood stands to conjunctive parthood. Philosophically, this relation may be modelled on the determinable- determinate relation, or on a fact-to-fact notion of grounding. I discuss its connection to two other Finean notions: vagueness (understood via precisification) and arbitrary objects. I then investigate what a logic of truthmaking with refinement might look like. I argue that (i) parthood naturally gives rise to a relevant conditional; (ii) refinement underlies a relevant notion of disjunction; and so (iii) truthmaker semantics with refinement is a natural home for relevant logic. The resulting formal models draw on Fine’s (1974) semantics for relevant logics. Finally, I use this understanding of relevant semantics to investigate the status of the mingle axiom. (shrink)

This article aims to bring some work in contemporary analytic metaphysics to discussions of the Real Presence of Christ in the Eucharist. I will show that some unusual claims of the Real Presence doctrine exactly parallel what would be happening in the world if objects were to time-travel in certain ways. Such time-travel would make ordinary objects multiply located, and in the relevantly analogous respects. If it is conceptually coherent that objects behave in this way, we have a model for (...) the behaviour of the Eucharist which shows the doctrine to be coherent, at least with respect to the issues discussed. (shrink)

“There’s Plenty of Room at the Bottom”, said the title of Richard Feynman’s 1959 seminal conference at the California Institute of Technology. Fifty years on, nanotechnologies have led computer scientists to pay close attention to the links between physical reality and information processing. Not all the physical requirements of optimal computation are captured by traditional models—one still largely missing is reversibility. The dynamic laws of physics are reversible at microphysical level, distinct initial states of a system leading to distinct final (...) states. On the other hand, as von Neumann already conjectured, irreversible information processing is expensive: to erase a single bit of information costs ~3 × 10−21 joules at room temperature. Information entropy is a thermodynamic cost, to be paid in non-computational energy dissipation. This paper addresses the problem drawing on Edward Fredkin’s Finite Nature hypothesis: the ultimate nature of the universe is discrete and finite, satisfying the axioms of classical, atomistic mereology. The chosen model is a cellular automaton with reversible dynamics, capable of retaining memory of the information present at the beginning of the universe. Such a CA can implement the Boolean logical operations and the other building bricks of computation: it can develop and host all-purpose computers. The model is a candidate for the realization of computational systems, capable of exploiting the resources of the physical world in an efficient way, for they can host logical circuits with negligible internal energy dissipation. (shrink)

This dissertation attempts to settle some challenging historiographic issues concerning the origin and development of the concept of economic equilibrium. Specifically, our research goal is to identify the philosophical and historical drivers of the mathematization of economic theory. To this end, we attempt to answer three fundamental research questions. First, why (and not how) has economics become a mathematical science? Second, what are the major methodological blunders that lie at the foundations of Modern General Equilibrium Theory? Third, is the contemporary (...) criticism of Modern General Equilibrium Theory meaningful and well-founded? In order, chapters 1-3 address the first question, chapters 4 and 5 address the second, whereas chapter 6 addresses the third question. Regarding the first question, we investigate the methodological relationships between Modern Physics, Modern Philosophy, and Walras’s Theory of General Equilibrium. Interestingly, our findings reveal that while the study of motion in Modern Physics relies upon a clear distinction between static and dynamic equilibrium, early mathematical economics borrows its methodology from Modern Physics but relies upon an Aristotelian conception of equilibrium. Furthermore, we identify exciting analogies between Kant’s philosophy and Walras’s Elements. Finally, we show that the so-called Walras Paradox also features another unexplored dimension. Namely, Walras’s work overall relies upon a bottom-up approach to mathematics. Yet Walras’s work includes problems that require a top-down approach to mathematics to be solved. Regarding the second question, we delve into the tight relationship between the History of Mathematics in the 19th Century, the Philosophy of Mathematics in the 20th Century, and the development of Modern General Equilibrium Theory in the 20th Century. Notably, we find that the top-down approach to mathematics provides economists with a reliable methodology to resolve the problems in Walras’s original work. Hence, the mathematization of General Equilibrium Theory in the 20th Century is a child of its time that carries the inapplicability of pure mathematics to real-world problems along with itself. Therefore, although the mathematization of General Equilibrium Theory is an unprecedented milestone in economic theory, the foundations of Modern General Equilibrium Theory inherit the methodological shortcomings of Contemporary Mathematics. That is why the Sonnenschein-Mantel-Debreu does not overtake the Aristotelian conception of equilibrium. Accordingly, we rebut the claim that Debreu and colleagues' mathematization of General Equilibrium Theory resolves the fundamental methodological shortcomings of Walras’s original work. Eventually, we use our answers to our first and second research questions to address the contemporary criticism of General Equilibrium Theory. On the one hand, we show that the latter criticism does not account for the fact that General Equilibrium Theory inherits the scientific realism and determinism of Modern Physics. In other words, we argue that the inability of General Equilibrium models to manage uncertainty effectively has nothing to do with its mathematization in the 20th Century. Instead, it results from the unexplored dimension of the Walras Paradox, which we uncover. On the other hand, we show that common accusations of inconsistency, incompleteness, and undecidability in General Equilibrium Theory are ill-founded. That is because other rigorous alternatives to axiomatization in economics are not paradox-free. On these grounds, we conclude that a much better option is to employ a topic-neutral language to provide rigorous presentations of contested concepts in economics. Particularly, we show that formal mereology offers a convenient methodological framework to resolve the disagreement between the Neoclassical and Institutionalist economists’ respective definitions of the concept of the market. In this way, we show that the latter concept is definable as a process. But, more importantly, we note that formal mereology also offers a convenient framework to reformulate other economic concepts concisely and rigorously. In this regard, we observe that formal mereology might provide a resolution for Hayek’s Problem because it would enable economists to define general equilibrium as a perduring socioeconomic process. -/- In case you want a copy of my dissertation, please email me. (shrink)

Amie Thomasson challenges advocates of layered conceptions of reality to explain “how layers are distinguished” and “what holds them together” by “examining the world” (2014). One strategy for answering such questions is mereological, treating inter-layer relations as parthood relations, where layers exist whenever composition does, and the number of layers will be equivalent to the number of answers to Peter Van Inwagen’s Special Composition Question, while answers to his General Composition Question explain what holds the layers together (1987). Various (...) answers have been proffered for these questions, from the physicalist atomism of Richard Feynman (2015), Hilary Putnam (1958), and Kit Fine (1992) to the holism of Jonathan Schaffer (2010), the two-layer emergentism of Van Inwagen himself (1995), Tim Maudlin’s three-layered “flash ontology” (2011), and Rob Koons two-layered “thermal substances” (2019). In this PhD project, I seek to meet Thomasson’s challenge by identifying which of these proposals are compatible with plausible interpretations of quantum physics. Atomist answers may have difficulty with relativity, while holistic and emergentist models have trouble giving an account of experimental conditions. Maudlin and Koons’ views, meanwhile, may make testable predictions about the scope of entanglement. Examining the world can lead us to sharply winnow our theories about how layers are distinguished and what holds them together. (shrink)

In common treatments of deontic logic, the obligatory is what is true in all deontically ideal possible worlds. In this article, I offer a new semantics for Standard Deontic Logic with Leibnizian intensions rather than possible worlds. Even though the new semantics furnishes models that resemble Venn diagrams, the semantics captures the strong soundness and completeness of Standard Deontic Logic. Since, unlike possible worlds, many Leibnizian intensions are not maximally consistent entities, we can amend the semantics to invalidate the inference (...) rule which ensures that all tautologies are obligatory. I sketch this amended semantics to show how it invalidates the rule in a new way. (shrink)

Mereological nihilism is the view that no objects have proper parts. Despite how counter‐intuitive it is, it is taken quite seriously, largely because it solves a number of puzzles in the metaphysics of material objects – or so its proponents claim. In this article, I show that for every puzzle that mereological nihilism solves, there is a similar puzzle that (a) it doesn’t solve, and (b) every other solution to the original puzzle does solve. Since the solutions to (...) the new puzzles apply just as well to the old puzzles, the old puzzles provide no motivation to be a mereological nihilist. (shrink)

Mereological nihilism (henceforth just "nihilism") is the thesis that composition never occurs. Nihilism has often been defended on the basis of its theoretical simplicity, including its ontological simplicity and its ideological simplicity (roughly, nihilism's ability to do without primitive mereological predicates). In this paper I defend nihilism on the basis of the theoretical unification conferred by nihilism, which is, roughly, nihilism's capacity to allow us to take fewer phenomena as brute and inexplicable. This represents a respect in which (...) nihilism enjoys greater theoretical simplicity than its rivals which has not yet been explored, and which is immune to many of the objections which have been leveled against previous arguments for nihilism from nihilism's theoretical simplicity. Composition as identity might be thought to confer a similar degree of theoretical unification as nihilism. I end the paper by arguing that this is not the case. (shrink)

Mereological nihilism is the thesis that composite objects—objects with proper parts—do not exist. Nihilists generally paraphrase talk of composite objects F into talk of there being “xs arranged F-wise” . Recently several philosophers have argued that nihilism is defective insofar as nihilists are either unable to say what they mean by such phrases as “there are xs arranged F-wise,” or that nihilists are unable to employ such phrases without incurring significant costs, perhaps even undermining one of the chief motivations (...) for nihilism. In this paper I defend nihilism against these objections. A key theme of the paper is this: if nihilists need to employ such phrases as “there are xs arranged F-wise,” non-nihilists will need to do so as well. Accordingly, any costs incurred by the nihilist when she employs such phrases will be shared by everyone else. What’s more, such phrases are intelligible when employed by the nihilist, as well as when they are employed by the non-nihilist, insofar as analyses of such phrases will not essentially involve mereological concepts incompatible with nihilism. (shrink)

When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates (...) the assertoric syllogistic. I argue that this mereological validation offers advantages over recent discussions in Morison, Malink, Ebert and Vlasits. (shrink)

Mereological nihilism is the thesis that composition never occurs. Sider has defended nihilism on the basis of its relative ideological simplicity. In this paper I develop the argument from ideological simplicity, and defend it from some recent objections. Along the way I discuss the best way to formulate nihilism, what it means for a theory to exhibit lesser or greater degrees of ideological simplicity, the relationship between the parthood relation and the identity relation, and the notion that we should (...) judge the ideological simplicity of competing theories on the basis of the kinds of ideological commitments required by those theories. (shrink)

Mereological nihilists hold that composition never occurs, so that nothing is ever a proper part of anything else. Substance dualists generally hold that we are each identical with an immaterial soul. In this paper, I argue that every popular objection to substance dualism has a parallel objection to composition. This thesis has some interesting implications. First, many of those who reject composition, but accept substance dualism, or who reject substance dualism and accept composition, have some explaining to do. Secondly, (...) one popular objection to mereological nihilism, one which contends that mereological nihilism is objectionable insofar as it is incompatible with the existence of people, is untenable. (shrink)

My interest in this chapter is to investigate this crossroad as applied to mental properties, considered powers. In particular, I scrutinize the possibility of taking the phenomenal property of feeling pain as a complex power or disposition. This possibility comes in handy in discussing panpsychism, the view that the ultimate elements of reality are phenomenal properties, which would ground physical properties as well.

This paper approaches Husserl’s analysis of time-consciousness from a mereological perspective. Taking as inspiration Bergson’s idea that pure durée is a multiplicity of interpenetration, I will show, from within Husserlian phenomenology, that the absolute flow can indeed be described as a whole of interpenetrating parts. This mereological perspective will inform my re-consideration of the much-discussed issue of Husserl’s self-criticism concerning the schema of content and apprehension. It will also reveal a fundamental similarity between Husserl’s conception of the absolute (...) flow and Sartre’s conception of lived temporality. This paper consists of four sections. Section 2 presents the basic elements of Husserl’s mereology. Section 3 introduces the difficulty encountered by Husserl’s early account of time that makes use of the schema. I will examine Barry Dainton’s criticism of Husserl’s theory of time-consciousness against the background of the older debate between Meinong and Stern, a debate that has informed Husserl’s own account. Section 4 distinguishes two common criticisms of the schema from Husserl’s own self-criticism, which is in turn divided into two steps. It is shown how the second step of this self-criticism implies the interpenetration of the absolute flow and responds to Dainton’s criticism. Finally, Sect. 5 concludes with some comparative remarks. I will show how Husserl’s notion of absolute flow, as mereologically interpreted, anticipates Sartre’s conception of consciousness as self-transcendence, as well as how it accommodates the apparently conflicting mereological intuitions of Aristotle and Bergson. (shrink)

This article motivates and develops a reductive account of the structure of certain physical quantities in terms of their mereology. That is, I argue that quantitative relations like "longer than" or "3.6-times the volume of" can be analyzed in terms of necessary constraints those quantities put on the mereological structure of their instances. The resulting account, I argue, is able to capture the intuition that these quantitative relations are intrinsic to the physical systems they’re called upon to describe and (...) explain. (shrink)

In this paper I develop a version of universalism that is non-mereological. Broadly speaking, non-mereological universalism is the thesis that for any arbitrary set of objects and times, there is a persisting object which, at each of those times, will be constituted by those of the objects that exist at that time. I consider two general versions of non-mereological universalism, one which takes basic simples to be enduring objects, and the other which takes simples to be instantaneous (...) objects. This yields three versions of endurantism, of which I ultimately defend the version I call universalist endurantism. Universalist endurantism is the thesis that for any arbitrary set S of instantaneous simples that exist at the same instant, there exists a fusion of the members of S, and for any arbitrary set S* of instantaneous fusions each of which exist at a different instant, there exists an enduring object O that is constituted by those fusions at those instants. Universalist endurantism is ‘non-mereological’ in that the relation that holds between instantaneous fusions and persisting objects is not the part/whole relation, but rather, is the relation of constitution, thus allowing that the persisting objects are three rather than four dimensional. I argue that universalist endurantism not only has the various benefits of mereological universalism in allowing vagueness to be explicated as semantic indeterminacy, but in addition allows the endurantist to hold that some properties are genuinely intrinsic and are exemplified simpliciter. (shrink)

This paper presents and defends an account of the coincidence of biological organisms with mereological sums of their material components. That is, an organism and the sum of its material components are distinct material objects existing in the same place at the same time. Instead of relying on historical or modal differences to show how such coincident entities are distinct, this paper argues that there is a class of physiological properties of biological organisms that their coincident mereological sums (...) do not have. The account answers some of the most pressing objections to coincidence, for example the so-called grounding problem , that material coincidence seems to require that coinciding objects have modal differences that do not supervene on any other properties. (shrink)

In this paper I offer an argument against one important version of panentheism, that is, mereological panentheism. Although panentheism has proven difficult to define, I provide a working definition of the view, and proceed to argue that given this way of thinking about the doctrine, mereological accounts of panentheism have serious theological drawbacks. I then explore some of these theological drawbacks. In a concluding section I give some reasons for thinking that the classical theistic alternative to panentheism is (...) preferable, all things considered. (shrink)

Mereological nihilism is the philosophical position that there are no items that have parts. If there are no items with parts then the only items that exist are partless fundamental particles, such as the true atoms (also called philosophical atoms) theorized to exist by some ancient philosophers, some contemporary physicists, and some contemporary philosophers. With several novel arguments I show that mereological nihilism is the correct theory of reality. I will also discuss strong similarities that mereological nihilism (...) has with empirical results in quantum physics. And I will discuss how mereological nihilism vindicates a few other theories, such as a very specific theory of philosophical atomism, which I will call quantum abstract atomism. I will show that mereological nihilism also is an interpretation of quantum mechanics that avoids the problems of other interpretations, such as the widely known, metaphysically generated, quantum paradoxes of quantum physics, which ironically are typically accepted as facts about reality. I will also show why it is very surprising that mereological nihilism is not a widely held theory, and not the premier theory in philosophy. (shrink)

The goal of this paper is to raise a few questions about Bayne s mereological account of the unity of consciousness. In Section 1, I raise a few clarificatory questions about the account and the thesis that consciousness is necessarily unified. In Sections 2 and 3, I offer an alternative view of unity of consciousness and contrast it with Bayne's view. I call this view the connectivity account. These sections prepare the ground for the main question of this article: (...) why should we prefer Bayne's mereological view to the connectivity view? (shrink)

The relative merits of standard mereology have received quite a bit of attention in recent years from metaphysicians concerned with the part/whole properties of material objects. A question that has not been pursued to the same degree, however, is what sort of semantic repercussions a commitment to mereological sums in the standard sense might have in particular on the predicted behavior of singular terms and our practices of using such terms to refer to objects. The apparent mismatch between our (...) actual referential practices and the persistence conditions attributed to material objects by the supporters of standard mereology puts these philosophers, other things being equal, at a disadvantage compared to those whose ontology matches more closely the observed behavior of singular terms, as they are commonly used in ordinary discourse. To alleviate this problem, David Lewis leans heavily on his distinction between natural and non-natural properties. I argue in this paper that Lewis’ already heavily burdened natural/non-natural distinction among properties is not enough to avoid Quinean indeterminacy for singular terms. Those who are in the business of giving an analysis of constructions involving full-fledged predication, as opposed to the mere spatial overlap of denotations, will thus want to go in for an ontology that places more stringent structural constraints on the referents of singular terms than would be supplied by standard mereology. (shrink)

I demonstrate here that it is possible for an event to be identical with one of its proper parts, refuting the key premise in Lawrence Lombard's argument for the essentiality of an event's time. I also propose and defend an alternative to his criterion of event identity.

This article’s purpose is to defend the depiction of ordinary-sized physical objects as mereological aggregates (MAs), to clarify what the ontology of an MA is, and to show why mereological essentialism (ME) applies to MAs that seem to be ubiquitous if we are to adopt what Frank Jackson calls “Serious Metaphysics” and refuse to broaden our ontology beyond what is (allegedly) bequeathed to us by physics and chemistry. To accomplish this goal, first, I clarify certain background issues that (...) inform what follows and I identify certain constraints that relate to the contemporary ambivalence towards ME. Second, I present a primer on Husserlian mereology that provides a superior account of parts and wholes than the inadequate approach identified in the previous section. Third, I will offer a defense of ME as the correct approach to providing an ontological account of MAs. Finally, I will evaluate two defeaters against my thesis. (shrink)

In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological (...) concept of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator. (shrink)

How does Aristotle think about sentences like ‘Every x is y’ in the Prior Analytics? A recently popular answer conceives of these sentences as expressing a mereological relationship between x and y: the sentence is true just in case x is, in some sense, a part of y. I argue that the motivations for this interpretation have so far not been compelling. I provide a new justification for the mereological interpretation. First, I prove a very general algebraic soundness (...) and completeness result that unifies the most important soundness and completeness results to date. Then I argue that this result vindicates the mereological interpretation. In contrast to previous interpretations, this argument shows how Aristotle’s conception of predication in mereological terms can do important logical work. (shrink)

Corruptionism is the view that following physical death, the human being ceases to exist but their soul persists in the afterlife. Survivalism holds that both the human being and their soul persist in the afterlife, as distinct entities, with the soul constituting the human. Each position has its defenders, most of whom appeal both to metaphysical considerations and to the authority of St Thomas Aquinas. Corruptionists claim that survivalism violates a basic principle of any plausible mereology, while survivalists tend to (...) reject the principle, though without as much detail as one would like. In this paper I examine both the key exegetical issues and the mereological question, arguing that Aquinas cannot be shown to have supported the principle in question, and that the principle should be rejected on independent grounds. If correct, some key planks in support of survivalism are established, with others to await further examination. (shrink)

Comparing Buddhist and contemporary analytic views about mereological composition reveals significant dissimilarities about the purposes that constrain successful answers to mereological questions, the kinds of considerations taken to be probative in justifying those answers, and the value of mereological inquiry. I develop these dissimilarities by examining three questions relevant to those who deny the existence of composite wholes. The first is a question of justification: What justifies denying the existence of composite wholes as more reasonable than affirming (...) their existence? The second is a question of ontology: Under what conditions are many partless individuals arranged composite-wise? The third is a question of reasonableness: Why, if there are no composites available to experience, do “the folk” find it reasonable to believe there are? I motivate each question, sketch some analytic answers for each, develop in more detail answers from the Theravādin Buddhist scholar Buddhaghosa, and extract comparative lessons. (shrink)

When do several objects compose a further object? The last twenty years have seen a great deal of discussion of this question. According to the most popular view on the market, there is a physical object composed of your brain and Jeremy Bentham’s body. According to the second-most popular view on the market, there are no such objects as human brains or human bodies, and there are also no atoms, rocks, tables, or stars. And according to the third-ranked view, there (...) are human bodies, but still no brains, atoms, rocks, tables, or stars. Although it’s pleasant to have so many crazy-sounding views around, I think it would also be nice to have a commonsense option available. The aim of this paper is to offer such an option. The approach I offer begins by considering a mereological question other than the standard one that has been the focus of most discussions in the literature. I try to show that the road to mereological sanity begins with giving the most straightforward and commonsensical answer to this other question, and then extending that answer to further questions about the mereology of physical objects. On the approach I am recommending, it turns out that all of the mereological properties and relations of physical objects are determined by their spatial properties and relations. (shrink)

This chapter explores a potential analogy between mereological principles and laws of nature. Against a backdrop of what Marmodoro has termed ‘power structuralism’ (and a rejection of a Humean worldview), the connection between parthood and modality may be richer than has hitherto been considered. Mereological principles delineate possibilities for parts and wholes, and putting powers at the centre of a discussion about parthood can furnish a novel conception of mereological laws, much as dispositionalism has done so for (...) natural laws; namely, these principles express connections between fundamental dispositional properties. By extending dispositionalism to comprehend mereology in this way, we can help fulfil its promise to provide a foundational, naturalistic metaphysics, as foundational mereological debates then begin to mirror those relating to dispositionalist views of laws of nature: we may treat natural and mereological laws in tandem, as holding either necessarily or contingently, with associated strategies for dealing with supposed counterexamples to one’s preferred set of mereological principles. We can thus bring new life to the debate over whether questions of composition admit of contingent or only necessary answers. (shrink)

Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non-mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to mereological sums. In particular, I show that on one hand some prima facie attractive candidates for the role of an explanatory plural abstraction principle for mereological sums (...) (in terms of pluralities of summed entities) are not really explanatory; on the other hand, singular abstraction principles (in terms of single summed entities) are materially inadequate. Nonetheless, explanatory criteria of identity and conditions of existence for mereological sums are provided by classical extensional mereology independent of abstraction principles. Thus, given classical extensional mereology, the reasons why, according to Linnebo, mathematical abstracted entities are thin also hold for mereological sums. Finally, I contend that interpretational modalities can be used to characterise the process by which a subject adds sums of previously admitted entities to the domain of quantification. (shrink)

A number of philosophers have argued in favour of extended simples on the grounds that they are needed by fundamental physics. The arguments typically appeal to theories of quantum gravity. To date, the argument in favour of extended simples has ignored the fact that the very existence of spacetime is put under pressure by quantum gravity. We thus consider the case for extended simples in the context of different views on the existence of spacetime. We show that the case for (...) extended simples based on physics is far more complex than has been previously thought. We present and then map this complexity, in order to present a much more textured picture of the argument for extended simples. (shrink)

In this paper I present two new arguments against the possibility of an omniscient being. My new arguments invoke considerations of cardinality and resemble several arguments originally presented by Patrick Grim. Like Grim, I give reasons to believe that there must be more objects in the universe than there are beliefs. However, my arguments will rely on certain mereological claims, namely that Classical Extensional Mereology is necessarily true of the part-whole relation. My first argument is an instance of a (...) problem first noted by Gideon Rosen and requires an additional assumption about the mereological structure of certain beliefs. That assumption is that an omniscient being’s beliefs are mereological simples. However, this assumption is dropped when I present my second argument. Thus, I hope to show that if Classical Extensional Mereology is true of the part-whole relation, there cannot be an omniscient being. (shrink)

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain (...) localized around approximately-classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. This formalism could be relevant to the emergence of spacetime from quantum entanglement. (shrink)

According to the Weak Supplementation Principle (WSP)—a widely received principle of mereology—an object with a proper part, p , has another distinct proper part that doesn't overlap p . In a recent article in this journal, Nikk Effingham and Jon Robson employ WSP in an objection to endurantism. I defend endurantism in a way that bears on mereology in general. First, I argue that denying WSP can be motivated apart from the truth of endurantism. I then go on to offer (...) an explanation of WSP's initial appeal, argue that denying WSP fails to have untoward consequences for the rest of mereology, and show that the falsity of WSP is consistent with a primary guiding thought behind it. (shrink)

The interactive theorem prover Isabelle/HOL is used to verify elementary theorems of classical extensional mereology.

In Mathematics is megethology. Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed (...) in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification. (shrink)

It is an axiom of late neoplatonic metaphysics that all things are in all, but in each in an appropriate manner (ὀικείως, ET 103). These manners or modes of being are indicated by adverbial forms such as παραδειματικῶς or εἰκονικῶς. Thus, for example, the Forms are in the World Soul in the mode of images, while the objects in the sensible realm below Soul are in it in the manner of paradigms (in Tim. II 150.27). Among the many modes of (...) being distinguished by Proclus we find existence ὁλικῶς and μερικῶς – in the manner of a whole and in the manner of a part. This paper investigates the nature and significance of these mereological modes of being. (shrink)