Mereology without Weak Supplementation

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

On the mereological structure of complex states of affairs

The aim of this paper is to elucidate the mereological structure of complex states of affairs without relying on the problematic notion of structural universals. For this task tools from graph theory, lattice theory, and the theory of relational systems are employed. Our starting point is the mereology of similarity structures. Since similarity structures are structured sets, their mereology can be considered as a generalization of the mereology of ordinary sets. In general, the mereological systems arising from similarity structures turn out to be not Boolean but Heyting systems. Employing Armstrong??s notion of thick particulars, similarity structures are shown to capture the mereological structure of complex ??chemical states of affairs?? such as ??being butane?? or ??being isobutane??; structural universals are not needed.     

Emergentism and supervenience physicalism

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

Kasimir Twardowski on the content of presentations

In On the Content and Object of Presentations, Kasimir Twardowski presents an interesting line of thought concerning the content of a presentation and its relation to the object of that presentation. This way of thinking about content is valuable for understanding phenomenal intentionality, and it should also be important for the project of “naturalizing” the mental (or at least for discovering the neural correlates of the phenomenal). According to this view, content is that by virtue of which a presentation of an object presents a certain object and no other. In the cases in which an object is presented as simple, there is nothing more that can be said about the relation of content and object. It is sui generis: the relation of content to an object by virtue of which it presents that object. Further, the content of a presentation is never itself directly presented. The content can only be gotten at indirectly, as the content by which such and such object is presented. Where the presented object is complex—as is of course the normal case—a lot that is useful can be said about the structure of the content. In this paper, I lay out Twardowski's theory of the content of presentations. Since the business of content is to present its object, I briefly present the basics of Twardowski's mereology of objects.     

Słupecki's Generalized Mereology and Its Flaws

One of the streams in the early development of set theory was an attempt to use mereology, a formal theory of parthood, as a foundational tool. The first such attempt is due to a Polish logician, Stanis?aw Le?niewski (1886–1939). The attempt failed, but there is another, prima facie more promising attempt by Jerzy S?upecki (1904–1987), who employed his generalized mereology to build mereological foundations for type theory. In this paper I (1) situate Le?niewski's attempt in the development of set theory, (2) describe and evaluate Le?niewski's approach, (3) describe S?upecki's strategy without unnecessary technical details, and (4) evaluate it with a rather negative outcome. The issues discussed go beyond merely historical interests due to the current popularity of mereology and because they are related to nominalistic attempts to understand mathematics in general. The introduction describes very briefly the situation in which mereology entered the scene of foundations of mathematics — it can be safely skipped by anyone familiar with the early development of set theory. Section 2 describes and evaluates Le?niewski's attempt to use mereology as a foundational tool. In Section 3, I describe an attempt by S?upecki to improve on Le?niewski's work, which resulted in a system called generalized mereology. In Section 4, I point out the reasons why this attempt is still not successful. Section 5 contains an explanation of why Le?niewski's use of Ontology in developing arithmetic also is not nominalistically satisfactory.     

Mereology and mathematics: Christian Wolff's foundational programme

ABSTRACT

How did the traditional doctrine of parts and wholes evolve into contemporary formal mereology? This paper argues that a crucial missing link may lie in the early modern and especially Wolffian transformation of mereology into a systematic sub-discipline of ontology devoted to quantity. After some remarks on the traditional scholastic approach to parts and wholes (Sect. 1), Wolff's mature mereology is reconstructed as an attempt to provide an ontological foundation for mathematics (Sects. 2–3). On the basis of Wolff's earlier mereologies (Sect. 4), the origin of this foundational project is traced back to one of Wolff's private conversations with Leibniz (Sect. 5) and especially to the former's appropriation of the latter's notion of similarity as a means to define quantity (Sect. 6). Despite some hesitancy concerning the ultimate characterization of quantity (Sect. 7), Wolff's contribution was historically significant and influential. By developing a quantitative, extensional account of mereological relations, Wolff departed from the received doctrine and paved the way for the later revival of mereology at the intersection of ontology and mathematics.     

Russell's 1925 logic

In a recent series of articles, J. P. Moreland has attempted to revive the idea that bare particulars are indispensable for individuating concrete particulars. The success of the project turns on Moreland's proposal that while bare particulars are indeed 'partially clad'--that is, exemplify at least some properties--they are nevertheless 'bare' in that they lack internal constituents. I argue that 'partially clad' bare particulars (PCBPs) are impervious not only to traditional objections, but also those recently urged in this journal by D. W. Mertz. The real problem with Moreland's view, I contend, is that together with his containment model of predication, it leads to the unwanted conclusion that PCBPs actually contain themselves as constituents, thereby ensnaring them in a vicious (individuative) circularity.     

Can Truthmaker Theorists Claim Ontological Free Lunches?

Truthmaker theorists hold that propositions about higher‐level entities (e.g. the proposition that there is a heap of sand) are often made true by lower‐level entities (e.g. by facts about the configuration of fundamental particles). This generates a problem: what should we say about these higher‐level entities? On the one hand, they must exist (since there are true propositions about them), on the other hand, it seems that they are completely superfluous and should be banished for reasons of ontological parsimony. Some truthmaker theorists—most prominently David Armstrong—have tried to solve this puzzle by arguing that these entities are ‘an ontological free lunch’, i.e. real existents that are still ‘no addition of being’. This answer is prima facie attractive, but I argue in this paper that the standard approaches to truthmaking—modal theories and grounding theories—are unable to vindicate the doctrine of the ontological free lunch, and thus fail to solve the problem of higher‐level entities. Fortunately, there is a non‐standard account of truthmaking available, the reductive explanation account, which succeeds where the standard approaches fail.     

Against the Compositional View of Facts

It is commonly assumed that facts would be complex entities made out of particulars and universals. This thesis, which I call Compositionalism, holds that parthood may be construed broadly enough so that the relation that holds between a fact and the entities it ‘ties’ together counts as a kind of parthood. I argue, first, that Compositionalism is incompatible with the possibility of certain kinds of fact and universal, and, second, that such facts and universals are possible. I conclude that Compositionalism is false. What all these kinds of fact and universal have in common is a violation of supplementation principles governing any relation that may be intelligibly regarded as a kind of parthood. Although my arguments apply to Compositionalism generally, I focus on recent work by David Armstrong, who is a prominent and explicit Compositionalist.     

A Comprehensive Picture of the Decidability of Mereological Theories

The signature of the formal language of mereology contains only one binary predicate which stands for the relation “being a part of” and it has been strongly suggested that such a predicate must at least define a partial ordering. Mereological theories owe their origin to Le?niewski. However, some more recent authors, such as Simons as well as Casati and Varzi, have reformulated mereology in a way most logicians today are familiar with. It turns out that any theory which can be formed by using the reformulated mereological axioms or axiom schemas is in a sense a subtheory of the elementary theory of Boolean algebras or of the theory of infinite atomic Boolean algebras. It is known that the theory of partial orderings is undecidable while the elementary theory of Boolean algebras and the theory of infinite atomic Boolean algebras are decidable. In this paper, I will look into the behaviors in terms of decidability of those mereological theories located in between. More precisely, I will give a comprehensive picture of the said issue by offering solutions to the open problems which I have raised in some of my papers published previously.     

How the Dead Live

This paper maintains (following Yougrau 1987; 2000 and Hinchliff 1996) that the dead and other former existents count as examples of non-existent objects. If the dead number among the things there are, a further question arises: what is it to be dead—how should the state of being dead be characterised? It is argued that this state should be characterised negatively: the dead are not persons, philosophers etc. They lack any of the (intrinsic) qualities they had while they lived. The only facts involving the dead are facts about the relations they stand in—including the relations they bear to the qualities they formerly instantiated, and the intentional relations they stand in to us. Given an appropriate conception of qualities the dead can be said to be quality-less objects: bare particulars. The ‘Bare Particular Theory’ of individuals, it is argued, is coherent if and only if it concedes that the bare particulars it allows for don’t exist. The account of the dead and other former existents as bare particulars does justice to the misfortune of death, and points the way to a general theory of nonexistent objects.     

Heidegger the Metaphysician: Modes‐of‐Being and Grundbegriffe

Modes‐of‐being (Seinsarten) figure centrally in Heidegger's masterwork Being and Time. Testimony to this is Heidegger's characterisation of two of his most celebrated enquiries—the Existential analytic and the Zeug analysis—as investigations into the respective modes‐of‐being of the entities concerned. Yet despite the importance of this concept, commentators disagree widely about what a mode‐of‐being is. In this paper, I systematically outline and defend a novel and exegetically grounded interpretation of this concept. Strongly opposed to Kantian readings, such as those advocated by Taylor Carman and Cristina Lafont, I interpret a mode‐of‐being as a universal that defines a district (Bezirk)—that is, a natural class of entities that ought to be conceptualised in a special way. As such, every mode‐of‐being plays an important metaphysical and epistemic role: serving both to unify a natural class of a high degree of generality and as the interpretandum of an act yielding the basic‐concepts (Grundbegriffe) pertaining to the entities therein. In explicating and arguing for this interpretation, I attribute a characteristically Aristotelian philosophical position to the early Heidegger, encompassing both metaphysical and epistemological realism and a conceptualist theory of universals.     

Metaphysics and the Future-Like-Ours Argument Against Abortion

Don Marquis’s “future-like-ours” argument against the moral permissibility of abortion is widely considered the strongest anti-abortion argument in the philosophical literature. In this paper, I address the issue of whether the argument relies upon controversial metaphysical premises. It is widely thought that future-like-ours argument indeed relies upon controversial metaphysics, in that it must reject the psychological theory of personal identity. I argue that that thought is mistaken—the future-like-ours argument does not depend upon the rejection of such a theory. I suggest, however, that given a widely-accepted view about contraception and abstinence, the argument is committed to contentious metaphysics after all, as it relies upon a highly controversial assumption about mereology. This commitment is not only relevant for those who are inclined to endorse the argument but reject the mereological view in question, but in addition entails dialectical and epistemological liabilities for the argument, which on some views will be fatal to the argument’s overall success.     

Tensed Mereology

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

What Are Quantities?

This paper presents a view of quantities as ‘adverbial’ entities of a certain kind—more specifically, determinate ways, or modes, of having length, mass, speed, and the like. In doing so, it will be argued that quantities as such should be distinguished from quantitative properties or relations, and are not universals but are particulars, although they are not (Fregean) objects, either. A main advantage of the adverbial view over its rivals will be found in its superior explanatory power with respect to both certain fundamental principles of quantity and ordinary quantitative reasoning involving quantitative relations like three times as long as and 2 metres longer than.     

Bennett on Parts Twice Over

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.     

Parts, classes and Parts of Classes: an anti-realist reading of Lewisian mereology

This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean (and Gentzenian) rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology with class theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has to be when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis—which is central to his marriage of class theory with mereology—as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR. This is the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual.     

Does Universalism Entail Extensionalism?

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.     

Perceptual Particularity

Perception grounds demonstrative reference, yields singular thoughts, and fixes the reference of singular terms. Moreover, perception provides us with knowledge of particulars in our environment and justifies singular thoughts about particulars. How does perception play these cognitive and epistemic roles in our lives? I address this question by exploring the fundamental nature of perceptual experience. I argue that perceptual states are constituted by particulars and discuss epistemic, ontological, psychologistic, and semantic approaches to account for perceptual particularity.