Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses. He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that each slot (...) may be occupied by at most one entity. Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems. I fully develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which are first considered by Yi (1999: 168 ff.). Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations. Pocket theory also avoids a serious drawback of anti-positionalism. (shrink)

Some philosophers assume that our ordinary parts-whole concepts are intuitive and univocal. Moreover, some assume that mereology—the formal theory of parts-whole relations—adequately captures these intuitive and univocal notions. Lewis, for example, maintains that mereology is “perfectly understood, unproblematic, and certain.” Following his lead, many assume that expressions such as ‘is part of’ are univocal, topic-neutral, and that compositional monism is true. This paper explores the rejection of –. I argue that our ordinary parts-whole expressions are polysemous; they have multiple distinct, (...) but related, interpretations or meanings. I canvass several criteria by which to test for polysemy, and apply these criteria to some of our parts-whole terminology. I also examine some philosophical examples involving abstracta and abstract parts, which give us additional reasons to think that our parts-whole expressions are polysemous and topic-specific. Yet if so, then compositional pluralism is true. (shrink)

I develop a novel argument against the claim that ordinals are sets. In contrast to Benacerraf’s antireductionist argument, I make no use of covert epistemic assumptions. Instead, my argument uses considerations of ontological dependence. I draw on the datum that sets depend immediately and asymmetrically on their elements and argue that this datum is incompatible with reductionism, given plausible assumptions about the dependence profile of ordinals. In addition, I show that a structurally similar argument can be made against the claim (...) that cardinals are sets. (shrink)

Structural universals are a kind of complex universal. They have been put to work in a variety of philosophical theories but are plagued with problems concerning their compositional nature. In this article, we will discuss the following questions. What are structural universals? Why believe in them? Can we give a consistent account of their compositional nature? What are the costs of doing so?

Kathrin Koslicki argues that ordinary material objects like tables and motorcycles have formal proper parts that structure the material proper parts. Karen Bennett rejects a key premise in Koslicki's argument according to which the material ingredient out of which a complex material object is made is a proper part of that object. Koslicki defends this premise with a principle motivated by its power to explain three important phenomena of material composition. But these phenomena can be equally well explained by a (...) weaker principle that does not support the questioned premise in Koslicki's argument, Bennett argues. I show that Bennett's weaker principle, together with an appropriate strengthening of a different premise in Koslicki's original argument, still yields a sound argument for the existence of formal parts. (shrink)

This thesis explores the possibility of composite consciousness: phenomenally conscious states belonging to a composite being in virtue of the consciousness of, and relations among, its parts. We have no trouble accepting that a composite being has physical properties entirely in virtue of the physical properties of, and relations among, its parts. But a long­standing intuition holds that consciousness is different: my consciousness cannot be understood as a complex of interacting component consciousnesses belonging to parts of me. I ask why: (...) what is it about consciousness that makes us think it so different from matter? And should we accept this apparent difference? (shrink)

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)

Some philosophers have claimed that kinds can be construed as mereologically complex structural properties. This essay examines several strategies aimed at construing a certain class of natural kinds, namely isomeric chemical kinds, in accordance with this view. In particular, the essay examines views which posit structural proper parts in addition to micro-constitutive parts to individuate isomeric chemical kinds. It then goes on to argue that the phenomenon of chirality in stereochemistry gives the proponent of kinds-as-complex-properties evidence for positing the existence (...) of causal-cum-dispositional individuating proper parts, in addition to structural parts, for chemical enantiomeric kinds. (shrink)

This paper offers a critical reconstruction of the motivations that led to the development of mereology as we know it today, along with a brief description of some problems that define current research in the field.

David Lewis objected to theories that posit necessary connections between distinct entities and to theories that involve a magical grasping of their primitives. In On the Plurality of Worlds, Lewis objected to nondescript ersatzism on these grounds. The literature contains several reconstructions of Lewis’ critique of nondescript ersatzism but none of these interpretations adequately address his main argument because they fail to see that Lewis’ critique is based on broader methodological considerations. I argue that a closer look at his methodology (...) reveals the broader objection he presented against nondescript ersatzism. This objection, I further argue, remains a challenge for the ersatzer who posits structure-less entities as possible worlds. (shrink)

In this paper I outline the main features of Karen Bennett’s (Australasian Journal of Philosophy 1–21, 2011) non-classical mereology, and identify its methodological costs. I argue that Bennett’s mereology cannot account for the composition of structural universals because it cannot explain the mereological difference between isomeric universals, such as being butane and being isobutane. I consider responses, which come at costs to the view.

We discuss the one–many problem as it appears in the Philebus and find that it is not restricted to the usually understood problem about the identity of universals across particulars that instantiate them (the Hylomorphic Dispersal Problem). In fact some of the most interesting aspects of the problem occur purely with respect to the relationship between Forms. We argue that contemporary metaphysicians may draw from the Philebus at least three different one–many relationships between universals themselves: instantiation, subkind and part, and (...) thereby construct three new ‘problems of the one and the many’ (an Eidetic Dispersal Problem, a Genus–Species Problem, and an Eidetic Combination Problem), which are as problematic as the version generally discussed. We then argue that this taxonomy sheds new and interesting light on certain discussions of higher-order universals in recent Australian analytic philosophy. (shrink)

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

Whilst God is said to be omnipresent, some religions also claim that God is specially present, or more present at/in certain locations. For example, a claim of special presence shared by Christians and Jews is that God was specially present at/in the first Temple. The chapter canvases various ways in which one can make sense of this claim whilst still affirming the omnipresence of God. This includes offering different accounts of special presence relying on derivative notions of presence, and offering (...) other views of special presence that rely upon fundamental accounts of presence. The chapter itself does not argue for one view in particular, but instead offers a map of possible options and future areas for research. (shrink)

One of the standard puzzles in ordinary-object metaphysics concerns what happens when an object and one of its undetached parts apparently begin to coincide. I distinguish two versions of this puzzle: the problem of extraordinary undetached parts and the problem of ordinary undetached parts. Then I present a novel phasalist solution to the problem of ordinary undetached parts. My solution is designed to supplement the recently-defended view that ordinary undetached parts exist but extraordinary ones do not.

David Lewis is typically interpreted as a class nominalist. One consequence of class nominalism, which he embraced, is that the reduction of ordered pairs, triples, etc to unordered sets of sets is conventional. The reaction by his Australian counterparts D.M. Armstrong and Peter Forrest was that Lewis was not being ontologically serious. This chapter evaluates this debate over serious ontology. It is argued that in one sense Lewis is ontologically serious, but that his additional commitment to structuralism about classes should (...) push him to adopt a trope-theoretic account of naturalness, which opens up another way to respond to the charge of not doing serious ontology. This conclusion is supported by certain remarks he makes in his correspondence, thus revealing how his thinking about properties appears to have evolved from property-egalitarianism to a sparse theory of tropes. (shrink)

It is usually agreed that reality is temporal in the sense of containing entities that exist in time, but some philosophers, roughly those who have been traditionally called A-theorists, hold that reality is temporal in a far more profound sense than what is implied by the mere existence of such entities. This hypothesis of deep temporality typically involves two ideas: that reality is temporally compartmentalised into distinct present, past, and future ‘realms’, and that this compartmentalisation is temporally dynamic in the (...) sense that the boundaries of those temporal realms change from one moment to the next. The truth of something like this hypothesis is commonly thought to require that at least some of the facts that fundamentally constitute reality be tensed. While this seems plausible, realism about fundamental tensed facts does not seem to entail deep temporality. Nor is it clear exactly what realism about tense amounts to, given that no informative answer has been given to the question of what it is for a fact to be tensed. In this paper, I introduce a novel approach, perspectivalism about temporal reality, that seeks to vindicate the hypothesis of deep temporality by ascribing to reality a certain kind of temporally perspectival structure, which also provides a straightforward answer to the question of what the tensedness of facts consists in as well as to the question of what it is for reality to be constituted by such facts. (shrink)

In this paper I investigate the idea that in conceptual analysis we are in a substantial way concerned with revealing metaphysical grounds. I argue that a recent proposal fails, according to which we aim to reveal what complex concepts are grounded in. The notion ofcomposition, rather than that ofgrounding, is the best way to understand the intuitive hierarchy of concepts. In an analysis we reveal thecomponentsorpartsof complex concepts and their structure. Finally, I propose an alternative role for grounding in our (...) accounts of analysis: in analyses we reveal truths about the composition of concepts that serve as grounds for truths about theirfunctions, which are what we want to understand. (shrink)

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts without proper parts. Typically, this thesis is characterized by an axiom stating that everything has atomic parts. The present paper argues that the success of this standard characterization depends on how the notions of sum and composition are defined. In particular, we put forward a novel definition of mereological sum that: (i) is not equivalent to existing definitions in the literature, if no strong decomposition principle (...) is assumed; (ii) can be used to argue that the standard characterization of atomism fails, because having atomic parts is not sufficient to be a sum of atoms; and (iii) provides a purely mereological distinction between structured and unstructured wholes, contributing to the ongoing debate on this crucial topic. (shrink)

Classical mereology seems unable to characterise the identity conditions of word types. For example, the same letter types ordered differently result in different word types; but mereological fusions of the same letters are identical, regardless of the order of the letters. We show, however, that by combining classical mereology with plural logic one can give a definition of word types that satisfies the identity criteria of word types. This means that it is not necessary to abandon classical mereology in order (...) to give an analysis of the mereological structure of word types. (shrink)

Some philosophers defend the possibility of synchronic multilocation, and have even used it to defend other substantive metaphysical theses. But just how strong is the case for the possibility of synchronic multilocation? The answer to this question depends in part on whether synchronic multilocation is wedded to other controversial metaphysical notions. In this paper, I consider whether the possibility of synchronic multilocation depends on the possibility of time travel, and I conclude that the answer hinges on the nature of time (...) and persistence. (shrink)

In this paper I investigate the idea that in conceptual analysis we are in a substantial way concerned with revealing metaphysical grounds. I argue that a recent proposal fails, according to which we aim to reveal what complex concepts are grounded in. The notion ofcomposition, rather than that ofgrounding, is the best way to understand the intuitive hierarchy of concepts. In an analysis we reveal thecomponentsorpartsof complex concepts and their structure. Finally, I propose an alternative role for grounding in our (...) accounts of analysis: in analyses we reveal truths about the composition of concepts that serve as grounds for truths about theirfunctions, which are what we want to understand. (shrink)

2020 update of the entry "Properties".

sProblems about the nature of integral parts and wholes were central to twelfth-century discussions of the individuation and persistence over time of both substances and artifacts. This paper examines in detail Abaelard’s contribution to these discussions arguing that Abaelard proposes a solution to these problems which preserves our common sense intuitions about identity over time. In Abaelard’s work we find an explicit solution to the problem of the identity over time of living things which appeals to the persistence of the (...) vegetative soul through the loss or addition of corporeal matter. In work from the school of the Montani we apparently also have an account of Abaelard’s solution to the problem of the identity over time of artifacts which distinguishes between the role of a part in an integral whole and the material which plays that role such that the role persists when the matter is replaced. (shrink)

Slot mereology reduces parthood to slot-filling: a material object is structured by a certain arrangement of slots; and the fillers of these slots are the object's proper parts. My aim in this essay is to go further and reduce slot-filling to essence and grounding. In combination, the reduction of parthood to slot-filling and the reduction of slot-filling to essence and grounding yields the reduction of parthood to essence and grounding. If this overarching reduction succeeds, it promises new metaphysical foundations for (...) neo-Aristotelian mereology. (shrink)

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are not (...) mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. (shrink)

A paper exploring what we can learn about part/whole by focusing on the differences in the existence conditions of fusions and ordinary things, rather than the differences in their persistence conditions.

In 2013, Bennett proposed a mereological theory in which the parthood relation is defined on the basis of two primitive relations: a is a part of b iff a fills a slot owned by b. However, this theory has issues counting how many parts an entity has. We explore the various counting problems and propose a new theory to solve them. Keeping the core idea of Bennett’s slots, this theory introduces mereological relations between slots. This theory enables us to solve (...) all known counting problems and to go beyond the limits of Bennett’s theory by theorising expected features of mereological theories: supplementation principles and mereological sum and fusion. The theory is illustrated on ontological issues on the nature of structural universals and informational entities. (shrink)

In this paper, we present an extensional system of mereology suitable to account for the intuitive distinction between heaplike and non-heaplike entities. Since the need to capture this distinction has been a key motivation for non-extensional mereologies, we first assess the main non-extensional systems advanced in the last years and highlight some mereological and metaphysical difficulties they involve. We then advance a novel program, according to which the distinction between heaplike and non-heaplike entities can be accounted for by bringing together (...) the parthood relation characterized by classical extensional mereology and an Aristotelian extensional notion of potential parthood. Thus, while rejecting the thesis of mereological monism, our proposal is consistent with the thesis of mereological extensionalism. We show that within this framework it is possible to characterize the above-mentioned distinction, to define the relation of material constitution, and to capture three fundamental standpoints in metaphysics. (shrink)

I present in this article a new theory of structural properties or, more precisely, of structural kinds, such as being methane. According to this theory, structural kinds are kinds that are both emergent and sustained in their existence. In the first section, I introduce structural properties and four problems that affect the most widely held conception of them, namely, the pictorial conception. In the second section, I introduce some theses about emergence, powers, emergent powers, relations and structures that I have (...) defended in other works and that constitute the basis on which my theory of structural kinds is built up. In the third section, I eventually develop my theory in full detail and show how it can solve the problems mentioned in the second section. Finally, in the fourth section, I face five objections and briefly compare my account with some other accounts of structural properties. (shrink)

The paper suggests two revisions of K. Bennett's system of slot mereology. The revisions do not touch on the philosophical rationale for this system, but are focused on certain logical deficiencies in her formalisation.

This paper investigates two intuitionistic mereological systems based on Tarski’s axiomatisation of general mereology. These systems use two intuitionistically non-equivalent formalisations of the notion of fusion. I study extensionality and supplementation properties as well as some variants of these systems, and defend parthood as a suitable primitive notion for intuitionistic mereology if working with Tarski’s axiomatisation. Furthermore, I arrive at an equi-interpretability result for one of the atomistic variants with intuitionistic plural logic. I discuss to what extent these results support (...) the philosophical pertinence of the mereological systems under investigation as intuitionistic theories of parthood, thereby reacting to a conceptual challenge that we are confronted with when engaging in intuitionistic mereology. (shrink)

A well-known difficulty that affects all accounts of laws of nature according to which the latter are higher-order facts involving relations between universals (the so-called DTA accounts, from Dretske in Philosophy of Science 44:248–268, 1977; Tooley in Canadian Journal of Philosophy 7:667–698, 1977 and Armstrong (What is a Law of Nature?, Cambridge University Press, Cambridge, 1983)) is the Inference Problem: how can laws construed in that way determine the first-order regularities that we find in the actual world? Bird (Analysis 65:147–55, (...) 2005) has argued that there is no solution to the Inference Problem which is consistent with both categorical monism (that is, the view that all natural properties are categorical) and basic tenets of Armstrong’s account of the laws of nature. This paper shows that, given Armstrong’s view about laws as first-order structural universals whose instantiation ‘produce’ nomic regularities and under specific plausible metaphysical assumptions concerning nomic relations which are consistent with a broadly construed DTA approach to laws, there is no extra difficulty regarding the Inference Problem in a categorical monistic context besides the ones that beset structural universals in general. (shrink)

Perdurance is a mode of persistence. The heart of perdurance is a space-time analogy: a perduring object is extended in time in a way that is analogous to how a composite object is extended in space. This paper is a discussion of perdurance in light of the distinction between mereologically structured and unstructured objects. I show that while the standard formulation of perdurance captures the space-time analogy for unstructured objects, it fails to capture the space-time analogy for temporally and spatially (...) structured objects. I conclude that there are substantially different ways for an object to be space-like temporally extended. (shrink)

Contemporary theories of universals have two things in common: first, they are unable to account for necessary connections between universals that form a structure. Second, they leave teleology out of their accounts of instantiation. These facts are not unrelated; the reason why contemporary theories have such trouble is they neglect the ancient idea that universals are ends at which nature aims. If we want a working theory of universals, however, we must return to this idea. Despite its unpopularity among realists, (...) teleology is not a disposable eccentricity, and its dismissal is not an improvement on ancient views. (shrink)

ABSTRACTBy the Many Categories problem, I mean the prima facie violation of Ockham’s Razor by realists about universals: there is, it might seem, just too much variety. Thus, David Armstrong posits both properties and relations. He also theorises about determinates of determinables. Another influential realist, E. J. Lowe distinguishes non-substantial from substantial universals. Yet again, both Armstrong and Lowe include in their ontology abstract particulars in addition to universals. My aim in this paper is to offer a unification of these (...) categories using an operator-theory. First, I show how operators provide a theory of abstract particulars of relations and of impure relational properties. Then, using impure relational properties I derive the Fregeanion Principle. After some metaphysics of mathematics, I provide a theory of determinables. Finally, I consider kinds and substances. (shrink)