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.     

The philosophical–anthropological foundations of Bennett and Hacker’s critique of neuroscience

Bennett and Hacker criticize a number of neuroscientists and philosophers for attributing capacities which belong to the human being as a whole, like perceiving or deciding, to a “part” of the human being, viz. the brain. They call this type of mistake the “mereological fallacy”. Interestingly, the authors say that these capacities cannot be ascribed to the mind either. They reject not only materialistic monism but also Cartesian dualism, arguing that many predicates describing human life do not refer to physical or mental properties, nor to the sum of such properties. I agree with this important principle and with the critique of the mereological fallacy which it underpins, but I have two objections to the authors’ view. Firstly, I think that the brain is not literally a part of the human being, as suggested. Secondly, Bennett and Hacker do not offer an account of body and mind which explains in a systematic way how the domain of phenomena which transcends the mental and the physical relates to the mental and the physical. I first argue that Helmuth Plessner’s philosophical anthropology provides the kind of account we need. Then, drawing on Plessner, I present an alternative view of the mereological relationships between brain and human being. My criticism does not undercut Bennett and Hacker’s diagnosis of the mereological fallacy but rather gives it a more solid philosophical–anthropological foundation.     

Indiscernible universals

Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow a theory of universals to identify particulars with bundles of universals, and that postulating indiscernible universals can allow a theory of universals to develop an account of the resemblance of quantitative universals that avoids the objections that Armstrong’s account faces. Finally, I shall respond to some objections and I shall undermine the criterion of distinction between particulars and universals that says that the distinction between particulars and universals lies in that while there can be indiscernible particulars, there cannot be indiscernible universals.     

Ostrich Nominalism and Peacock Realism: A Hegelian Critique of Quine

Abstract

My aim in this paper is to offer a Hegelian critique of Quine’s predicate nominalism. I argue that at the core of Hegel’s idealism is not a supernaturalist spirit monism, but a realism about universals, and that while this may contrast to the nominalist naturalism of Quine, Hegel’s position can still be defended over that nominalism in naturalistic terms. I focus on the contrast between Hegel’s and Quine’s respective views on universals, which Quine takes to be definitive of philosophical naturalism. I argue that there is no good reason to think Quine is right to make this nominalism definitive of naturalism in this way – where in fact Hegel (along with Peirce) offers a reasonably compelling case that science itself requires some commitment to realism about universals, kinds, etc. Furthermore, even if Hegel is wrong about that, at least his case for realism is still a naturalistic one, as it is based on his views on concrete universality, which is an innovative form of in rebus realism about universals.     

Vague Objects within Classical Logic and Standard Mereology,and without Indeterminate Identity

Weatherson (The Philosophical Quarterly, 53, 481–501 2003) argues that whoever accepts classical logic, standard mereology and the difference between vague objects and any others, should conclude that there are no vague objects. Barnes and Williams (Pacific Philosophical Quarterly, 90, 176–187 2009) claim that a supporter of vague objects who accepts classical logic and standard mereology should recognize that the existence of vague objects implies indeterminate identity. Even though it is not clearly stated, they all seem to be committed to the assumption that reality is ultimately constituted by mereological atoms. This assumption is not granted by standard mereology which instead remains silent on whether reality is atomic or gunky; therefore, I contend that whoever maintains classical logic, standard mereology and the difference between vague objects and any others, is not forced to conclude with Weatherson that there are no vague objects; nor is she compelled to revise her point of view according to Barnes and Williams’s proposal and to accept that the existence of vague objects implies indeterminate identity.     

Why Leibniz thinks Descartes was wrong and the Scholastics were right

The bundle theory is a theory about the internal constitution of individuals. It asserts that individuals are entirely composed of universals. Typically, bundle theorists augment their theory with a constitutional approach to individuation entailing the thesis ‘identity of constituents is a sufficient ground for numerical identity’ (CIT). But then the bundle theory runs afoul of Black’s duplication case—a world containing two indiscernible spheres. Here I propose and defend a new version of the bundle theory that denies ‘CIT’, and which instead conjoins it with a structural diversity thesis, according to which being separated by distance is a sufficient ground for numerical diversity. This version accommodates Black’s world as well as the three-spheres world—a world containing three indiscernible spheres, arranged as the vertices of an equilateral triangle. In this paper, I also criticize Rodriguez-Pereyra’s alternative attempt to defend the bundle theory against Black’s case and the case of the three-spheres world.     

Aristotle on the perception of universals

Aristotle claims that ‘although we perceive particulars, perception is of universals; for instance of human being, not of Callias-the-human-being’ (APo II.19 100a16–b1). I offer an interpretation of this claim and examine its significance in Aristotle's epistemology.     

Exemplification and Parthood

Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several hypotheses: the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity.     

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.     

In Defence of Spatially Related Universals

Immanent universals, being wholly present wherever they are instantiated, are capable both of bi-location (one entity's being wholly present in two places at one time) and of co-location (two entities' being wholly present in the same place at one time). As a result, they can become involved in some bizarre situations, situations whose contradictory appearance cannot be dispelled by any of the relativizing techniques familiar to metaphysicians as solutions to the problem of change. Douglas Ehring takes this to be a fatal problem for immanent universals, but I do not. Although the old relativizing techniques don't solve the problem, I propose a new one that does. I spend half the paper defending the proposed solution against objections, and in the course of this task I have occasion to touch upon such topics as backward time travel and the distinction between universals and particulars. I close by putting forward--merely as an option--a new way to draw the distinction in question.     

Aboutness in imagination

I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine’s works on the notion. Imagination is understood as per Chalmers’ positive conceivability: the intentional state of a subject who conceives that p by imagining a situation—a configuration of objects and properties—verifying p. So far aboutness theory has been developed mainly for linguistic representation, but it is natural to extend it to intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint.     

Tensions in naturalistic,evolutionary explanations of aesthetic reception and production

Aesthetic universals may plausibly reflect biases in aesthetic reception that arose through evolutionary pressure. However, the role universals play in high-level aesthetic creativity is not well understood. After reviewing evolutionary aspects of aesthetics, some specific proposed aesthetic universals, and the nature of creativity in aesthetic domains, I examine a creative dynamic in which long-term pressure for novelty leads to inexorable tensions with canalized aesthetic biases. Examining the role of aesthetic universals in individuals’ creative processes, as well as more thorough trans-historical assessments of the development of universals, are proposed as methodological strategies for gaining traction on this issue. Such investigations have the potential to inform the role of the audience in shaping the evolution of artist styles, how universals play out in high versus low art, the possibility of identifying new aesthetic universals (perhaps particularly with conceptual art), and the relative value of novelty versus adaptive value in aesthetic creativity.     

A Lover’s Shame

Shame is one of the more painful consequences of loving someone; my beloved’s doing something immoral can cause me to be ashamed of her. The guiding thought behind this paper is that explaining this phenomenon can tell us something about what it means to love. The phenomenon of beloved-induced shame has been largely neglected by philosophers working on shame, most of whom conceive of shame as being a reflexive attitude. Bennett Helm has recently suggested that in order to account for beloved-induced shame, we should deny the reflexivity of shame. After arguing that Helm’s account is inadequate, I proceed to develop an account of beloved-induced shame that rightly preserves its reflexivity. A familiar feature of love is that it involves an evaluative dependence; when I love someone, my well-being depends upon her life’s going well. I argue that loving someone also involves a persistent tendency to believe that her life is going well, in the sense that she is a good person, that she is not prone to wickedness. Lovers are inclined, more strongly than they otherwise would be, to give their beloveds the moral benefit of the doubt. These two features of loving—an evaluative dependence and a persistent tendency to believe in the beloved’s moral goodness—provide the conditions for a lover to experience shame when he discovers that his beloved has morally transgressed.     

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 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.     

Tooley’s account of the necessary connection between law and regularity

Fred Dretske, Michael Tooley, and David Armstrong accept a theory of governing laws of nature according to which laws are atomic states of affairs that necessitate corresponding natural regularities. Some philosophers object to the Dretske/Tooley/Armstrong theory on the grounds that there is no illuminating account of the necessary connection between governing law and natural regularity. In response, Michael Tooley has provided a reductive account of this necessary connection in his book Causation (1987). In this essay, I discuss an improved version of his account and argue that it fails. First, the account cannot be extended to explain the necessary connection between certain sorts of laws—namely, probabilistic laws and laws relating structural universals—and their corresponding regularities. Second, Tooley’s account succeeds only by (very subtly) incorporating primitive necessity elsewhere, so the problem of avoiding primitive necessity is merely relocated.     

Nomic Universals and Particular Causal Relations: Which are Basic and Which are Derived?

Armstrong holds that a law of nature is a certain sort of structural universal which, in turn, fixes causal relations between particular states of affairs. His claim that these nomic structural universals explain causal relations commits him to saying that such universals are irreducible, not supervenient upon the particular causal relations they fix. However, Armstrong also wants to avoid Plato’s view that a universal can exist without being instantiated, a view which he regards as incompatible with naturalism. This construal of naturalism forces Armstrong to say that universals are abstractions from a certain class of particulars; they are abstractions from first-order states of affairs, to be more precise. It is here argued that these two tendencies in Armstrong cannot be reconciled: To say that universals are abstractions from first-order states of affairs is not compatible with saying that universals fix causal relations between particulars. Causal relations are themselves states of affairs of a sort, and Armstrong’s claim that a law is a kind of structural universal is best understood as the view that any given law logically supervenes on its corresponding causal relations. The result is an inconsistency, Armstrong having to say that laws do not supervene on particular causal relations while also being committed to the view that they do so supervene. The inconsistency is perhaps best resolved by denying that universals are abstractions from states of affairs.

How useful is the concept of the ‘harm threshold’ in reproductive ethics and law?

In his book Reasons and Persons, Derek Parfit suggests that people are not harmed by being conceived with a disease or disability if they could not have existed without suffering that particular condition. He nevertheless contends that entities can be harmed if the suffering they experience is sufficiently severe. By implication, there is a threshold which divides harmful from non-harmful conceptions. The assumption that such a threshold exists has come to play a part in UK policy making. I argue that Parfit’s distinction between harmful and non-harmful conceptions is untenable. Drawing on Kant’s refutation of the ontological argument for God’s existence, I suggest that the act of creation cannot be identical with the act of harming—nor indeed of benefiting—however great the offspring’s suffering may be. I suggest that Parfit is right that bringing children into existence does not usually harm them, but I argue that this must be applied to all conceptions, since Parfit cannot show how the harm threshold can be operationalised. If we think certain conceptions are unethical or should be illegal, this must be on other grounds than that the child is harmed by them. I show that a Millian approach in this context fails to exemplify the empirical and epistemological advantages which are commonly associated with it, and that harm-based legislation would need to be based on broader harm considerations than those relating to the child who is conceived.     

Etchemendy on Squeezing Arguments and Logical Consequence: a Reply to Griffiths

Owen Griffiths has recently argued that Etchemendy’s account of logical consequence faces a dilemma. Etchemendy claims that we can be sure that his account does not overgenerate, but that we should expect it to undergenerate. Griffiths argues that if we define the relationship between formal and natural language as being dependent on logical consequence, then Etchemendy’s claims are not true; and if we define the relationship as being independent of logical consequence, then we cannot assess the truth of the claims without further information. I argue that Griffiths misconstrues Etchemendy’s theory and overstates the first horn of the dilemma: Etchemendy does see the relationship as being dependent on logical consequence, but that does not mean that his claims are not true.