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)

In formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room for a type (...) of fundamentalism combined with infinite descent as long as this descent is “boring,” that is, the same structure repeats ad infinitum. A start is made in the article towards a systematic account of this type of infinite descent. The philosophical prospects and scientific tenability of the account are briefly evaluated using an example from physics. (shrink)

Standard principles of mereology, such as the transitivity and asymmetry of proper parthood, have been questioned, using various multi-location scenarios. The most famous of these is Borges’s Aleph, although the literature is rife with other examples that allegedly show that some mereological principle is at odds with some form of multi-location. However, the scenarios only support this conclusion given various bridge principles that link location to parthood. I argue that the bridge principles that guarantee the desired conclusion are controversial partly (...) because they give the wrong result in other situations, in particular cases of co-location. Moreover, less controversial bridge principles do not provide an incompatibility result between standard mereological principles and multi-location. Hence, multi-location does not threaten any standard mereological principles. (shrink)

The standard definition of atomicity—the thesis that everything is ultimately composed of entities that lack proper parts—is satisfied by a model that is not atomistic. The standard definition is therefore an incorrect characterization of atomicity. I show that the model satisfies the axioms of all but the strongest mereology and therefore that the standard definition of atomicity is only adequate given some controversial metaphysical assumptions. I end by proposing a new definition of atomicity that does not require extensionality or unrestricted (...) summation. (shrink)

It is natural to think that social groups are concrete material particulars, but this view faces an important objection. Suppose the chess club and nature club have the same members. Intuitively, these are different clubs even though they have a common material basis. Some philosophers take these intuitions to show that the materialist view must be abandoned. I propose an alternative explanation. Social groups are concrete material particulars, but there is a psychological explanation of nonidentity intuitions. Social groups appear coincident (...) but nonidentical because they are perceived to be governed by conflicting social norms. (shrink)

We contribute to the ongoing discussion on mathematical structuralism by focusing on a question that has so far been neglected: when is a structure part of another structure? This paper is a first step towards answering the question. We will show that a certain conception of structures, abstractionism about structures, yields a natural definition of the parthood relation between structures. This answer has many interesting consequences; however, it conflicts with some standard mereological principles. We argue that the tension between abstractionism (...) about structure and classical mereology is an interesting result and conclude that the mereology of abstract structures is a subject that deserves further exploration. We also point out some connections between our discussion of the mereology of structures and recent work on non-well-founded mereologies. (shrink)

In response to the paper by Cotnoir and Bacon published in RSL 2/2012, we would like to add some remarks regarding supplementation principles. It is known that in a classical mereology, the Strong Supplementation Principle (SSP) together with antisymmetry enforces the Weak Supplementation Principle (WSP). Instead, in the nonwellfounded mereology, the failure of extensionality causes the failure of antisymmetry (Cotnoir, 2010), hence the investigated model is also nonantisymmetric. Cotnoir supposes that the failure of antisymmetry implies the failure of (WSP) when (...) (PP1) is applied, however gives no explicit argument, which we would like to supply in this paper. Additionally, when (PP2) is applied, (SSP) implies (WSP), hence the failure of antisymmetry does not necessarily imply the failure of (WSP). (shrink)

Process aspects are prevalent in many domains of reality, and consciousness is no exception. Nevertheless, while the processual approach implicitly underlies the theories of consciousness, an explicit statement of the question is scarcely found in the literature. This paper tries to bridge this gap. Here, I argue that conscious experience fulfils all the requirements for a processual analysis: it is complex, functionally/causally determined, and has a temporal basis. Then, I revisit an old concept, self-transformative processes, which refers to processes that (...) change themselves. These processes are very common. A stretched bow is the classical Heraclitean example. However, it is easy to misunderstand what self-transformativeness is. To provide a well-formed description, I characterize self-transformative processes in terms of composition (using a non-classic mereology) and in terms of functionality (by developing the concept of self-modulating variables). Finally, I apply self-transformative processes to explain consciousness. Traces of self-transformativeness can be found in many theories of consciousness, particularly when they are stressed about their internal mechanisms. Here, I focus on Integrated Information Theory as a paradigmatic example of a mathematically well-described theory, and I demonstrate that quantitative self-transformativeness is a requirement at the very core of the integration of the information. (shrink)

This paper consists of two parts. The first concerns the logic of vagueness. The second concerns a prominent debate in metaphysics. One of the most widely accepted principles governing the ‘definitely’ operator is the principle of Distribution: if ‘p’ and ‘if p then q’ are both definite, then so is ‘q’. I argue however, that epistemicists about vagueness should reject this principle. The discussion also helps to shed light on the elusive question of what, on this framework, it takes for (...) a sentence to be borderline or definite. In the second part of the paper, I apply this result to a prominent debate in metaphysics. One of the most influential arguments in favour of Universalism about composition is the Lewis-Sider argument from vagueness. An interesting question, however, is whether epistemicists have any particular reasons to resist the argument. I show that there is no obvious reason why epistemicists should resist the argument but there is a non-obvious one: the rejection of Distribution argued for in the first part of the paper provides epistemicists with a unique way of resisting the argument from vagueness. (shrink)

The paper explores the proof theory of non-wellfounded mereology with binary fusions and provides a cut-free sequent calculus equivalent to the standard axiomatic system.

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.

We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.

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)

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)

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)

This paper explores a novel notion of self-explanation that combines ideas from two sources: the tripartite account of explanation, according to which a proposition can help explain another either in the capacity of a reason why the latter obtains or in the capacity of an explanatory link, and the notion of an empty-base explanation, which generalizes the ideas of explanation by zero-grounding and explanation by status. After having introduced these ideas and the novel notion of self-explanation, I argue that the (...) latter has the potential to resist extant arguments against the possibility of self-explanation. In the remainder of the paper, I discuss candidates for such self-explanatory propositions and suggest possible applications for Humeanism about laws of nature, the debate on the grounds of ground, the rationalist tradition, and philosophical theology. (shrink)

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions. Instead they are higher-order, fine-grained structures. (...) I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed λ-calculus, whose λ-terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context. (shrink)

In a series of papers, 137–158; 1994, Midwest Studies in Philosophy, 23, 61–74, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in. In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points (...) in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the second-order quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine’s principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine’s various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki’s main objection to Fine’s theory. In the appendix we present proofs of the inexpressibility results of Section 6. (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.

Those who accept the necessity of mereological universalism face what has come to be known as the ‘junk argument’ due to Bohn [2009], which proceeds from the incompatibility of junk with universalism and the possibility of junk, to conclude that mereological universalism isn't metaphysically necessary. Most attention has focused on ; however, recent authors have cast doubt on . This paper undertakes a defence of premise against three main objections. The first is a new objection to the effect that Bohn's (...) defence of that premise presupposes far too much. I show that one can defend premise from a much weaker set of assumptions. The second objection, due to Contessa [2012], is that those who accept unrestricted composition should only accept the existence of binary sums rather than infinitary fusions. I argue that this conception of unrestricted composition is problematic: it is in conflict with an intuitive remainder principle. The final objection is .. (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)

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)

Does a commitment to mereological universalism automatically bring along a commitment to the controversial doctrine of mereological extensionalism—the view that objects with the same proper parts are identical? A recent argument suggests the answer is ‘yes’. This paper attempts a systematic response to the argument, considering nearly every available line of reply. It argues that only one approach—the mutual parts view—can yield a viable mereology where universalism does not entail extensionalism.

Contemporary metaphysicians have been drawn to a certain attractive picture of the structure of the world. This picture consists in classical mereology, the priority of parts over wholes, and the well-foundedness of metaphysical priority. In this short note, I show that this combination of theses entails superatomism, which is a significant strengthening of mereological atomism. This commitment has been missed in the literature due to certain sorts of models of mereology being overlooked. But the entailment is an important one: we (...) must either accept superatomism or reject one (or other) of the most widespread theses of contemporary metaphysics. (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)

In this paper, we address an infamous argument against divisibility that dates back to Zeno. There has been an incredible amount of discussion on how to understand the critical notions of divisibility, extension, and infinite divisibility that are crucial for the very formulation of the argument. The paper provides new and rigorous definitions of those notions using the formal theories of parthood and location. Also, it provides a new solution to the paradox of divisibility which does not face some threats (...) that can possibly undermine the standard Lebesgue measure solution to such a paradox. (shrink)

We address an argument by Floridi (Synthese 168(1):151–178, 2009; 2011a), to the effect that digital and analogue are not features of reality, only of modes of presentation of reality. One can therefore have an informational ontology, like Floridi’s Informational Structural Realism, without commitment to a supposedly digital or analogue world. After introducing the topic in Sect. 1, in Sect. 2 we explain what the proposition expressed by the title of our paper means. In Sect. 3, we describe Floridi’s argument. In (...) the following three sections, we raise three difficulties for it, (i) an objection from intuitions: Floridi’s view is not supported by the intuitions embedded in the scientific views he exploits (Sect. 4); (ii) an objection from mereology: the view is incompatible with the world’s having parts (Sect. 5); (iii) an objection from counting: the view entails that the question of how many things there are doesn’t make sense (Sect. 6). In Sect. 7, we outline two possible ways out for Floridi’s position. Such ways out involve tampering with the logical properties of identity, and this may be bothersome enough. Thus, Floridi’s modus ponens will be our (and most ontologists’) modus tollens. (shrink)

In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...) the abstract with the concrete, the physical with the non-physical, and the possible with the impossible, just to name a few. -/- Proposed by David Lewis (1991) alongside his defence of classical mereology (the major theory of parthood which permits such transcategorial composites through its principle of unrestricted composition) it is my contention that mixed fusions are an under-examined consequence of indiscriminate mereological fusion which harbour a multitude of complications. In my attempt to discern their substantive character, throughout this thesis I make a case study of mixed fusions and uncover several problematic consequences which I think follow from their most plausible assessment. -/- These include: (1) that mixed fusions’ probable membership relations may lead to dubious foundational loops in the mereological Universe, or (2) otherwise that mixed fusions oblige an implausible ontological priority of the mereological Universe as a whole; (3) that mixed fusions contradict the reductive account of set theory they are proposed within, by plausibly being seen to have the same members as their class parts, and (4) that mixed fusions therefore confound a mereological thesis of Composition as Identity, which some (including Lewis) use to support classical mereology – a consequence which is potentially self-defeating; (5) that mixed fusions as sums of abstract and concrete entities both subvert Lewis’s (1986) system of modal realism, while (6) also undermining less expansive theories of possible worlds; and finally, (7) that even where some of the foregoing is resisted, it remains implausible that mixed fusions are ontologically innocent, because their supposed distinction from their parts in this case ensures that they need to be counted as additional entities in one’s ontology. -/- To be clear, I do not advance a theory of mereological hybrid nihilism in the sense of denying all cases of transcategorial composition. (I only cover a few select instances of mereological hybridism via mixed fusions after all.) Rather, I deny that mereological hybridism is plausible in full generality, by demonstrating that any cases of it are at least limited by the constraints that I identify. This in turn vindicates a call for a restriction on parthood theories and composition principles which allow certain types of categorially mixed entities – including restricting classical mereology with its principle of unrestricted composition. -/- Although theories of parthood like the standard classical mereology are not ordinarily developed for the sake of mereological hybrids like mixed fusions, these and other transcategorial composites are still among the logical consequences of such parthood systems operating with sufficient generality. The significance of my thesis, then, comes from showcasing how some of these kinds of entities do not conform to the systems in which they are included as required, and hence I argue for the rejection of unrestricted mereological hybridism as well as any mereological principles which support it. (shrink)

The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness. Accordingly, the notion of fundamentality is often associated with these two other technical notions.

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...) forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

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

The debate about the ontological innocence of mereology has generally been framed as a debate about the plausibility of Universal Fusion. Ontologically loaded fusions must be more than the sum of their parts, and this seems to violate parsimony if fusion is universal. Less attention has been paid to the question of what sort of emergence mereological fusions must exhibit if they are irreducible to their parts. The philosophy of science literature provides several models of such strong emergence. Examining those (...) models suggests that the difficulty with emergent fusions has at least as much to do with extensionality as it does with Universal Fusion. Some accounts of emergence fail to ensure irreducibility when combined with extensional mereologies. The most promising model for the strong emergence of ontologically loaded fusions fails to validate Anti-Symmetry, which naturally leads to failures of extensionality. These results suggest that the focus on Universal Fusion may have been misplaced. (shrink)