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)

Hybrid languages are introduced in order to evaluate the strength of “minimal” mereologies with relatively strong frame definability properties. Appealing to a robust form of nominalism, I claim that one investigated language \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {m}}$\end{document} is maximally acceptable for nominalistic mereology. In an extension \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {gem}}$\end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {m}}$\end{document}, a modal analog (...) for the classical systems of Leonard and Goodman and Leśniewski is introduced and shown to be complete with respect to 0-deleted Boolean algebras. We characterize the formulas of first-order logic invariant for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\textsf {gem}}$\end{document}-bisimulations. (shrink)

The principle of Summation, which is a technically sharpened version of the familiar claim that a whole is a sum of its parts, is presented by Peter van Inwagen as a trivial truth. I argue to the contrary, that it is incompatible with the natural assumption that a whole may gain or lose parts non-instantaneously. For, as I show, the latter assumption implies that something can be determinately a whole without being determinately a sum of parts, and this, in turn, (...) indicates the falsity of Summation. I point out that the tension between Summation and the possibility of non-instantaneous gain or loss of parts compels us to rethink the relations between the concepts of whole and sum, and may have far reaching consequences for the mereology of physical objects. (shrink)

Compliments have received only cursory attention from speech act theorists and are usually characterised as run-of-the-mill illocutionary acts. Yet both intentionalist and conventionalist theories of illocutionary force struggle to accommodate ordinary language uses of ‘compliment’. I argue that this is because there are in fact two kinds of compliment: illocutionary compliments and perlocutionary compliments. This account illuminates the practice of complimenting, as well as its converse, insulting, and illustrates the complex relationship between illocutionary force and perlocutionary effect.

We propose a formal framework to examine the relationship between models and observations. To make our analysis precise,models are reduced to first-order theories that represent both terminological knowledge – e.g., the laws that are supposed to regulate the domain under analysis and that allow for explanations, predictions, and simulations – and assertional knowledge – e.g., information about specific entities in the domain of interest. Observations are introduced into the domain of quantification of a distinct first-order theory that describes their nature (...) and their organization and takes track of the way they are experimentally acquired or intentionally elaborated. A model mainly represents the theoretical knowledge or hypotheses on a domain, while the theory of observations mainly represents the empirical knowledge and the given experimental practices. We propose a precise identity criterion for observations and we explore different links between models and observations by assuming a degree of independence between them. By exploiting some techniques developed in the field of social choice theory and judgment aggregation, we sketch some strategies to solve inconsistencies between a given set of observations and the assumed theoretical hypotheses. The solutions of these inconsistencies can impact both the observations – e.g., the theoretical knowledge and the analysis of the way observations are collected or produced may highlight some unreliable sources – and the models – e.g. empirical evidences may invalidate some theoretical laws. (shrink)

Embracing an inter-disciplinary approach grounded on Gärdenfors’ theory of conceptual spaces, we introduce a formal framework to analyse and compare selected theories about technical artefacts present in the literature. Our focus is on design-oriented approaches where both designing and manufacturing activities play a crucial role. Intentional theories, like Kroes’ dual nature thesis, are able to solve disparate problems concerning artefacts but they face both the philosophical challenge of clarifying the ontological nature of intentional properties, and the empirical challenge of testing (...) the attribution of such intentional properties to artefacts. To avoid these issues, we propose an approach that, by identifying different modalities to characterise artefact types, does not commit to intentional qualities and is able to empirically ground compliance tests. (shrink)

Are there atoms in the constitution of things? Or is everything made of atomless ‘gunk’ whose proper parts have proper parts? Anaxagoras is the first gunk lover in the history of metaphysics. For him gunk is not only a theoretical possibility that cannot be ruled out in principle. Rather, it is a view that follows cogently from his metaphysical analysis of the physical world of our experience. What is distinctive about Anaxagoras’s take on gunk is not only what motives the (...) view, but also the particular type of gunk that he develops. It is qualitative gunk, rather than material gunk. Anaxagoras’s ontology was developed before matter was ‘invented’. It includes quality tropes only; they are gunky. The resulting metaphysical view – a world of qualitative gunk – is new, in the sense of being hitherto unexplored; and yet, it is derived from Anaxagoras’s writings. Drawing on Anaxagoras’s insights, this paper offers a sketch of what qualitative gunk ontology l.. (shrink)

Building on previous scholarly work on the mathematical roots of assertoric syllogistic we submit that for Aristotle, the semantic value of the copula in universal affirmative propositions is the relation of divisibility on positive integers. The adequacy of this interpretation, labeled here ‘arithmetical dictum’, is assessed both theoretically and textually with respect to the existing interpretations, especially the so-called ‘mereological dictum’.

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.

Simple locative sentences show a variety of pseudo-quantificational interpretations. Some locatives give the impression of universal quantification over parts of objects, others involve existential quantification, and yet others cannot be characterized by either of these quantificational terms. This behavior is explained by virtually all semantic theories of locatives. What has not been previously observed is that similar quantificational variability is also exhibited by locative sentences containing indefinites with the ‘a’ article. This phenomenon is especially problematic for traditional existential treatments of (...) indefinites. We propose a solution where indefinites denote properties and are assigned locations similarly to other spatial descriptions. This Property-Eigenspace Hypothesis accounts for the correlation between the interpretations of locative indefinites and the pseudo-quantificational effects with simple entity-denoting NPs. Thereby, the proposal opens up a new empirical domain for property-based theories of indefinites, with implications for the analysis of collective descriptions, generics, negative polarity items and part–whole structure. (shrink)

In the literature on mereology it is often accepted that mereological universalism entails extensionalism. More precisely, many accept that, if parthood is assumed to be a partial order, the thesis that every plurality of entities has a mereological fusion entails the thesis that different composite entities have different proper parts. Central to this idea is the principle known as ‘Weak Supplementation’ which many take to impose an important constraint on the relation of proper parthood. In this paper I argue that (...) this claim is false as the principle that I will call ‘Minimal Supplementation’ appears to be capable of doing all the work done by Weak Supplementation but without entailing extensionalism if conjoined with universalism and core mereology. (shrink)

Most of the theories of location on the market appear to be ideologically parsimonious at least in the sense that they take as primitive just one locative notion and define all the other locative notions in terms of it. Recently, however, the possibility of some exotic metaphysical scenarios involving gunky mixtures and extended simple regions of space has been argued to pose a significant threat to parsimonious theories of locations. The aim of this paper is to show that a theory (...) taking as primitive a notion of plural pervasive location and allowing for irreducibly plural locative facts can account for all the putatively problematic scenarios for parsimonious theories of location. Furthermore, I will also argue that the notion of plural pervasive location is compatible with the possibility of multilocation. (shrink)

There are two main ways in which the notion of mereological fusion is usually defined in the current literature in mereology which have been labelled ‘Leśniewski fusion’ and ‘Goodman fusion’. It is well-known that, with Minimal Mereology as the background theory, every Leśniewski fusion also qualifies as a Goodman fusion. However, the converse does not hold unless stronger mereological principles are assumed. In this paper I will discuss how the gap between the two notions can be filled, focussing in particular (...) on two specific sets of principles that appear to be of particular philosophical interest. The first way to make the two notions equivalent can be used to shed some interesting light on the kind of intuition both notions seem to articulate. The second shows the importance of a little-known mereological principle which I will call ‘Mild Supplementation’. As I will show, the mereology obtained by adding Mild Supplementation to Minimal Mereology occupies an interesting position in the landscape of theories that are stronger than Minimal Mereology but weaker than what Achille Varzi and Roberto Casati have labelled ‘Extensional Mereology’. (shrink)

This paper argues, contrary to Fodor’s well-known position, that the iconic and discursive modes of representation are not mutually exclusive categories. It is argued that there exists at least a third kind of representation which blends the semantic properties of icons and the syntactic properties of discourses. We reason that this iconic-discursive genus behaves differently from other representational formats, such as distributed representations or maps, previously put forward as challenging Fodor’s basic distinction. A reflection follows about how this kind of (...) representation impacts on the Fodorian issues for which the original dual distinction was argumentatively instrumental, namely, the kinds of codes and possible inter-code relations accessible to the representational mind. The suggestion is put forward that iconic-discursive representations may facilitate trade-offs between the world and the representational mind, as well as between the differently complex levels of representation that mediate between percepts and concepts. We conclude that such aspects of the computational mind, which until now appeared to be stubbornly resistant with respect to a conciliation of Hume’s empiricism and Fodor’s computationalism, may be more easily accessed and understood taking advantage of the biosemiotics perspective and acknowledging the richness of the biosemiotics codes accessible to cognition. (shrink)

A widespread opinion holds that norms and codes of conduct as such can only be established via words, that is, in some lexical form. This perspective can be criticized: some norms produced by human acts are not word-based at all. For example, many norms are actually conveyed through graphics (e. g. road signs and land-use maps), sounds (e. g. the referee’s whistle), a silent gesture (the traffic warden’s signal to halt). In this article, we will focus on the norms that (...) are created by means of drawings and can be termed “drawn norms” or “graphical norms.” Specifically, we will inquire into the phenomenon of graphical norms with particular regard to traffic signs and land-use plans, and we will discuss the philosophical and legal problems to which these phenomena give rise. (shrink)

The literature suggests two main answers to the question of what it is for a material object to be located at a region of spacetime. Both have a number of virtues. However, both suffer from well-known problems. According to one answer, location is a primitive relation with no informative metaphysical analysis. But this makes a number of necessary truths seem mysterious and leaves them unexplained. According to the other answer, to be located at a region is just to be identical (...) to that region. But this is inconsistent with a number of independently plausible theses about material objects and their locations. In this paper, I explore a new theory of location and argue that it has the virtues of these familiar theories but not their vices. I then explore some further connections the new theory has with some contemporary issues in metaphysics. (shrink)

Say that mereological harmony is the view that there is at least some mirroring between the mereological structure of material objects and the mereological structure of their locations: each, in some way, mirrors the other. As it turns out, there is a confusing array of systems of harmony available to the substantivalist. In this paper, I attempt to bring some order to these systems. I explore some systems found in the literature, as well as some natural systems which haven’t been (...) discussed. Along the way, I explore a number of metaphysical consequences of the different systems of harmony. The paper ends with a roadmap of possible views for the substantivalist. (shrink)

Philosophers disagree whether composition as identity entails mereological universalism. Bricker :264–294, 2016) has recently considered an argument which concludes that composition as identity supports universalism. The key step in this argument is the thesis that any objects are identical to some object, which Bricker justifies with the principle of the universality of identity. I will spell out this principle in more detail and argue that it has an unexpected consequence. If the universality of identity holds, then composition as identity not (...) only leads us to universalism, but also leads to the view that there are no mereological atoms. (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)

Mental capacities for perceiving, remembering, thinking, and planning involve the processing of structured mental representations. A compositional semantics of such representations would explain how the content of any given representation is determined by the contents of its constituents and their mode of combination. While many have argued that semantic theories of mental representations would have broad value for understanding the mind, there have been few attempts to develop such theories in a systematic and empirically constrained way. This paper contributes to (...) that end by developing a semantics for a ‘fragment’ of our mental representational system: the visual system’s representations of the bounding contours of objects. At least three distinct kinds of composition are involved in such representations: ‘concatenation’, ‘feature composition’, and ‘contour composition’. I sketch the constraints on and semantics of each of these. This account has three principal payoffs. First, it models a working framework for compositionally ascribing structure and content to perceptual representations, while highlighting core kinds of evidence that bear on such ascriptions. Second, it shows how a compositional semantics of perception can be compatible with holistic, or Gestalt, phenomena, which are often taken to show that the whole percept is ‘other than the sum of its parts’. Finally, the account illuminates the format of a key type of perceptual representation, bringing out the ways in which contour representations exhibit domain-specific form of the sort that is typical of structured icons such as diagrams and maps, in contrast to typical discursive representations of logic and language. (shrink)

Analog representation is often cast in terms of an engineering distinction between smooth and discrete systems. The engineering notion cuts across interesting representational categories, however, so it is poorly suited to thinking about kinds of representation. This paper suggests that analog representations support a pattern of interaction, specifically open-ended searches for content across levels of abstraction. They support the pattern by sharing a structure with what they represent. Continuous systems that satisfy the engineering notion are exemplars of this kind because (...) they are uninterpretable unless they are structure-preserving. Analog representations, so understood, include pictures, images, diagrams, and most graphs. This conception of analogicity also fits well with a line of thought about what makes perceptual states distinctive: they satisfy a “parts principle”. (shrink)

This note is a reply to ‘On the Lumping Semantics of Counterfactuals’ by Makoto Kanazawa, Stefan Kaufmann and Stanley Peters. It shows first that the first triviality result obtained by Kanazawa, Kaufmann, and Peters is already ruled out by the constraints on admissible premise sets listed in Kratzer (1989). Second, and more importantly, it points out that the results obtained by Kanazawa, Kaufmann, and Peters are obsolete in view of the revised analysis of counterfactuals in Kratzer (1990, 2002).

When some objects are the parts of another object, they compose that object and that object is composite. This article is intended as an introduction to the central questions about composition and a highly selective overview of various answers to those questions. In §1, we review some formal features of parthood that are important for understanding the nature of composition. In §2, we consider some answers to the question: which pluralities of objects together compose something? As we will see, the (...) dominant answers are all of them and none of them. In §§3-4, we examine one of the main arguments that has driven philosophers to these extreme answers: the argument from vagueness. In §5, we turn to the question of whether composition is unique: is it sometimes the case that some things compose more than one thing? Finally, in §6, we turn from the question of which composites exist to the question of which composites exist fundamentally. (shrink)

It is common to think that it’s possible for entities to spatially coincide in multiple ways: with overcrowding, and without overcrowding. Typically, we can distinguish between these by claiming that uncrowded spatial overlap involves a sharing of parts, and crowded spatial overlap does not. However, if we think that mereologically unusual entities, such as extended simples or some kinds of gunk, can also spatially overlap in crowded and uncrowded ways, we lose the ability to distinguish between those varieties of spatial (...) overlap via appeal to shared parts. Thus, we should either reject the possibilities that generated this difficulty, or we must look for an alternative explanation of these varieties of spatial overlap. (shrink)

Current formulations of Four-Dimensionalism may be objected to on grounds that they are too inflexible: the formulations do not seem to allow for enough variety in the views they are paired with. For instance, Kit Fine has noted that formulations of Four-Dimensionalism in terms of instantaneous parts may be too demanding for Four-Dimensionalists who believe nothing is instantaneous. And Trenton Merricks has argued that one can think something persists four-dimensionionally without taking it to have proper temporal parts, and claims that (...) our formulation of Four-Dimensionalism should be revised to allow for this. I will add my own worries to those of Fine and Merricks. I will note that current formulations of Four-Dimensionalism are not sufficiently neutral with respect to the structure of time, with respect to how liberally objects decompose into parts, and with respect to whether objects and the regions they fill match in mereological structure. I will show that we can formulate Four-Dimensionalism in a sufficiently neutral way, while still producing a view that can do the work we typically require of Four-Dimensionalism. (shrink)

Achille Varzi has shown that it is harder to deny Extensionality than we may have thought: he's argued that if we define proper parthood as parthood with distinctness, cases we take to violate Extensionality don’t really involve sharing of all proper parts. Aaron Cotnoir has responded by showing that, if we instead define proper parthood as asymmetric parthood, we can take Extensionality to be violated in these cases. I will offer a new response to this argument. Even granting Varzi's definition (...) of proper parthood, there are versions of Extensionality very similar to the one Varzi and Cotnoir discuss. One of these is motivated by the same intuitions as Varzi's Extensionality, and is violated in cases traditionally taken to be anti-Extensional. Thus, even granting Varzi's definition of proper parthood, anti-Extensionalists can capture a sense in which their cases violate Extensionality, without this merely amounting to a violation of Uniqueness of Composition. (shrink)

The objectives of this paper are twofold. The first is to present a differentiation between two kinds of deferred uses of indexicals: those in which indexical utterances express singular propositions (I term them deferred reference proper) and those where they express general propositions (called descriptive uses of indexicals). The second objective is the analysis of the descriptive uses of indexicals. In contrast to Nunberg, who treats descriptive uses as a special case of deferred reference in which a property contributes to (...) the proposition expressed, I argue that examples in which a general proposition is indeed expressed by an indexical cannot be treated by assuming that the property is a deferred referent of the pronoun. I propose an analysis of descriptive uses of indexicals by means of a pragmatic mechanism of ‘descriptive anaphora’, which attempts to explain the special kind of contribution of the property retrieved from the context to the proposition that is characteristic of the descriptive interpretation. (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)

I argue that relations between non-collocated spatial entities, between non-identical topological spaces, and between non-identical basic building blocks of space, do not exist. If any spatially located entities are not at the same spatial location, or if any topological spaces or basic building blocks of space are non-identical, I will argue that there are no relations between or among them. The arguments I present are arguments that I have not seen in the literature.

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)

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have (...) divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures. (shrink)

Until recently, an almost perfect parallelism seemed to hold between theories of identity through time and across possible worlds,as every account in the temporal case(endurantism,perdurantism, exdurantism) was mirrored by a twin account in the modal case (trans-world identity, identity-via-parts, identity-via-counterparts). Nevertheless, in the recent literature, this parallelism has been broken because of the implementation in the debate of the relation of location. In particular, endurantism has been subject to a more in-depth analysis, and different versions of it, corresponding to different (...) ways an entity can be located in time, emerged. In this article, we provide a precise map of the conceptions at stake, complete the debate by introducing a version of endurantism not yet considered in the debate — we call transcendentism — and show that it allows us to provide an effective interpretation of the relation of trans-world identity and an intuitive solution in the temporal case. (shrink)

Ned Markosian has recently defended a new theory of composition, which he calls regionalism : some material objects xx compose something if and only if there is a material object located at the fusion of the locations of xx. Markosian argues that regionalism follows from what he calls the subregion theory of parthood. Korman and Carmichael agree. We provide countermodels to show that regionalism does not follow from, even together with fourteen potentially implicit background principles. We then show that regionalism (...) does follow from five of those background principles together with and two additional principles connecting parthood and location, which we call and. While the additional principles are not uncontroversial, our conjecture is that many will find them attractive. We conclude by mentioning that fills a previously unnoticed gap in the formal theory of location presented in Parsons. (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)

Many bioethical arguments rely implicitly on the assumption that the concept of “human part” is one on which everyone must agree, because it is unambiguous. But various parties interpret this “unambiguous” term in incompatible ways, leading to contention. This article is an informal presentation of a topomereological system on whose preferred interpretation several distinct but related meanings of “human part” can be isolated: part of a human body, part of the completion of a human body, and part of a human (...) being. A case is analyzed (the first total artificial heart (TAH) implantation), demonstrating in the process much of the apparatus of the system. By means of a casuistic methodology, the analysis is translated into recommendations for the ethical conduct of future TAH research. The more general conclusion, however, is that formal methods may provide useful tools for clarifying thought processes and organizing arguments in debates over bioethical issues. (shrink)

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.

The paper set up a small “philosophical lab” for thought experiments using Digital Universes as its main tool. Digital Universes allow us to examine how mereology affects the debate on New Realism of Ferraris and shed new light on the whole notion of Realism. The semi-formal framework provides a convenient way to model the varieties of realism that are important for the program of New Realism: we then draw the natural consequences of this approach into the ontology of our world, (...) arguing that the same considerations that apply to Digital Universe would hold for chess, institutions and social objects as well. Once a particular version of mereology is chosen, there are unavoidable consequences that the very underlying structure of social ontology. We then propose a new New Realism to tackle social objects: social objects turn out to be nothing more than mereological sums, picked up by some description. (shrink)

In this paper, we argue that time travel is problematic for the endurantist. For it appears to be possible, given time travel, to construct a wall out of a single time travelling brick. This commits the endurantist to one of the following: (a) the wall is composed of the time travelling brick many times over; (b) the wall does not in fact exist at all; (c) the wall is identical to the brick. We argue that each of these options is (...) unsatisfactory. (shrink)

This paper argues that phenomenal or internal metrical spaces are redundant posits. It is shown that we need not posit an internal space-time frame, as the physical space-time suffices to explain geometrical perception, memory and planning. More than the internal space-time frame, the idea of a phenomenal colour space has lent credibility to the idea of internal spaces. It is argued that there is no phenomenal colour space that underlies the various psychophysical colour spaces; it is parasitic upon physical and (...) psychophysical colour spaces. The argumentation is further extended to other sensory spaces and generalised quality spaces. (shrink)

This paper resolves a paradox concerning colour constancy. On the one hand, our intuitive, pre-theoretical concept holds that colour constancy involves invariance in the perceived colours of surfaces under changes in illumination. On the other, there is a robust scientific consensus that colour constancy can persist in cerebral achromatopsia, a profound impairment in the ability to perceive colours. The first stage of the solution advocates pluralism about our colour constancy capacities. The second details the close relationship between colour constancy and (...) contrast. The third argues that achromatopsics retain a basic type of colour constancy associated with invariants in contrast processing. The fourth suggests that one person-level, conscious upshot of such processing is the visual awareness of chromatic contrasts ‘at’ the edges of surfaces, implicating the ‘colour for form’ perceptual function. This primitive type of constancy sheds new light on our most basic perceptual capacities, which mark the lower borders of representational mind. (shrink)

I argue that medieval solutions to the limit decision problem imply four-dimensionalism, i.e. the view according to which substances that persist through time are extended through time as well as through space, and have different temporal parts at different times.

The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, (...) the paper considers an alternative approach that focuses the blame on antisymmetry but allows us to keep natural supplementation axioms. Third, we look at counterexamples to the idempotency of composition and the associated ‘parts just once’ principle. We explore options for developing weaker mereologies that avoid such commitments. (shrink)

Perichoresis, or “mutual indwelling,” is a crucial concept in Trinitarian theology. But the philosophical underpinnings of the concept are puzzling. According to ordinary conceptions of “indwelling” or “being in,” it is incoherent to think that two entities could be in each other. In this paper, I propose a mereological way of understanding “being in,” by analogy with standard examples in contemporary metaphysics. I argue that this proposal does not conflict with the doctrine of divine simplicity, but instead affirms it. I (...) conclude by discussing how mutual indwelling relates to the concepts of unity and identity. (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)

I reply to Hawthorne and Uzquiano’s arguments for the incompatibility between mereological universalism and plenitudinous co-location. I argue that a mereology in which antisymmetry for parthood fails is independently motivated, and allows for both universalism and plenitudinous co-location. There can be as many angels in a place as there are cardinalities.

Mereological principles are often controversial; perhaps the most stark contrast is between those who claim that Weak Supplementation is analytic—constitutive of our notion of proper parthood—and those who argue that the principle is simply false, and subject to many counterexamples. The aim of this paper is to diagnose the source of this dispute. I’ll suggest that the dispute has arisen by participants failing to be sensitive to two different conceptions of proper parthood: the outstripping conception and the non-identity conception. I’ll (...) argue that the outstripping conception, can deliver the analyticity of Weak Supplementation on at least one sense of ‘analyticity’. I’ll also suggest that the non-identity conception cannot do so independently of considerations to do with mereological extensionality. (shrink)

Mereological principles are often controversial; perhaps the most stark contrast is between those who claim that Weak Supplementation is analytic—constitutive of our notion of proper parthood—and those who argue that the principle is simply false, and subject to many counterexamples. The aim of this paper is to diagnose the source of this dispute. I’ll suggest that the dispute has arisen by participants failing to be sensitive to two different conceptions of proper parthood: the outstripping conception and the non-identity conception. I’ll (...) argue that the outstripping conception (together with a specific set of definitions for other mereological notions), can deliver the analyticity of Weak Supplementation on at least one sense of ‘analyticity’. I’ll also suggest that the non-identity conception cannot do so independently of considerations to do with mereological extensionality. (shrink)

This paper develops an endurantist theory of persistence. The theory is built around one basic tenet, which concerns existence at a time – the relation between an object and the times at which that object is present. According to this tenet, which I call transcendentism, for an object to exist at a time is for it to participate in events that are located at that time. I argue that transcendentism is a semantically grounded and metaphysically fruitful. It is semantically grounded, (...) insofar as a semantic analysis of our temporal talk favors it over rivals. It is metaphysically fruitful, insofar as the theory of persistence that can be built around it – the transcendentist theory of persistence, to give it a name – requires neither temporal parts nor the problematic commitments to which all extant forms of endurantism are committed, such as the possibility of extended simples or multilocation. (shrink)