Mereological nihilism is the view that no objects have proper parts. Despite how counter‐intuitive it is, it is taken quite seriously, largely because it solves a number of puzzles in the metaphysics of material objects – or so its proponents claim. In this article, I show that for every puzzle that mereological nihilism solves, there is a similar puzzle that (a) it doesn’t solve, and (b) every other solution to the original puzzle does solve. Since the solutions to the new (...) puzzles apply just as well to the old puzzles, the old puzzles provide no motivation to be a mereological nihilist. (shrink)

Many have held that when a person visually attends to an object, her visual system deploys a representation that designates the object. Call the referential link between such representations and the objects they designate attentive visual reference. In this article I offer an account of attentive visual reference. I argue that the object representations deployed in visual attention—which I call attentive visual object representations —refer directly, and are akin to indexicals. Then I turn to the issue of how the reference (...) of an AVOR is determined relative to a context. After raising problems for existing accounts, I propose a mechanism of reference determination that is both causal and descriptive: For an AVOR to refer to a particular object, the object must appropriately cause the deployment of the AVOR, and the AVOR must be associated with descriptive information about some of the object's geometrical and mereological properties. (shrink)

Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things (...) as “It is indeterminate whether this particle is part of Kilimanjaro”. After reviewing some of the limitations of this approach, I will propose an alternative account, based on a new semantic relation—multiple reference—capable of holding in a one-many pattern between a term and several objects in the domain. I will explain how multiple reference works, what differentiates it from plural reference and how it might be used to accommodate at least some aspects of our ordinary discourse about vague objects. (shrink)

A remarkable development in twentieth-century mathematics is smooth infinitesimal analysis ('SIA'), introducing nilsquare and nilpotent infinitesimals, recovering the bulk of scientifically applicable classical analysis ('CA') without resort to the method of limits. Formally, however, unlike Robinsonian 'nonstandard analysis', SIA conflicts with CA, deriving, e.g., 'not every quantity is either = 0 or not = 0.' Internally, consistency is maintained by using intuitionistic logic (without the law of excluded middle). This paper examines problems of interpretation resulting from this 'change of logic', (...) arguing that standard arguments based on 'smoothness' requirements are question-begging. Instead, it is suggested that recent philosophical work on the logic of vagueness is relevant, especially in the context of a Hilbertian structuralist view of mathematical axioms (as implicitly defining structures of interest). The relevance of both topos models for SIA and modal-structuralism as appled to this theory is clarified, sustaining this remarkable instance of mathematical pluralism. (shrink)

It is widely assumed in psychology, philosophy, and linguistics that we count by identity. For example, to count the dogs by identity, we correlate each dog that isn't identical to the rest with a natural number, starting with one and assigning each successive dog the successive natural number. When we run out of distinct dogs, we've yielded a correct count. I argue that this model of counting is incorrect. We do not count by identity.

Some philosophers respond to Leibniz’s “shift” argument against absolute space by appealing to antihaecceitism about possible worlds, using David Lewis’s counterpart theory. But separated from Lewis’s distinctive system, it is difficult to understand what this doctrine amounts to or how it bears on the Leibnizian argument. In fact, the best way of making sense of the relevant kind of antihaecceitism concedes the main point of the Leibnizian argument, pressing us to consider alternative spatiotemporal metaphysics.

David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: it says there (...) aren't any genuine facts about individuals over and above their qualitative roles. (shrink)

The problem of the many poses the task of explaining mereological indeterminacy of ordinary objects in a way that sustains our familiar practice of counting these objects. The aim of this essay is to develop a solution to the problem of the many that is based on an account of mereological indeterminacy as having its source in how ordinary objects are, independently of how we represent them. At the center of the account stands a quasi-hylomorphic ontology of ordinary objects as (...) material objects with multiple individual forms. (shrink)

An encyclopedia entry which covers various revisionary conceptions of which macroscopic objects there are, and the puzzles and arguments that motivate these conceptions: sorites arguments, the argument from vagueness, the puzzles of material constitution, arguments against indeterminate identity, arguments from arbitrariness, debunking arguments, the overdetermination argument, and the problem of the many.

Kilimanjaro is a paradigmatic mountain, if any is. Consider atom Sparky, which is neither determinately part of Kilimanjaro nor determinately not part of it. Let Kilimanjaro(+) be the body of land constituted, in the way mountains are constituted by their constituent atoms, by the atoms that make up Kilimanjaro together with Sparky, and Kilimanjaro(–) the one constituted by those other than Sparky. On the one hand, there seems to be just one mountain in the vicinity of Kilimanjaro. On the other (...) hand, both Kilimanjaro(+) and Kilimanjaro(–)—and indeed many other similar things—seem to have an equal claim to be a mountain: all of them exhibit the grounds for something being a mountain—like being an elevation of the earth’s surface rising abruptly and to a large height from the surrounding level,1 or whathaveyou—; and there seems to be nothing in the vicinity with a better claim. Hence, the problem of the many. (shrink)

Recently four different papers have suggested that the supervaluational solution to the Problem of the Many is flawed. Stephen Schiffer has argued that the theory cannot account for reports of speech involving vague singular terms. Vann McGee and Brian McLaughlin say that theory cannot, yet, account for vague singular beliefs. Neil McKinnon has argued that we cannot provide a plausible theory of when precisifications are acceptable, which the supervaluational theory needs. And Roy Sorensen argues that supervaluationism is inconsistent with a (...) directly referential theory of names. McGee and McLaughlin see the problem they raise as a cause for further research, but the other authors all take the problems they raise to provide sufficient reasons to jettison supervaluationism. I will argue that none of these problems provide such a reason, though the arguments are valuable critiques. In many cases, we must make some adjustments to the supervaluational theory to meet the posed challenges. The goal of this paper is to make those adjustments, and meet the challenges. (shrink)

This piece gives an overview of the supervaluationist theory of vagueness. According to that theory, a sentence is true if and only if it is true on all ways of making it precise. This yields borderline case predications that are neither true nor false, but yet classical logic is preserved almost entirely. The article presents the view and some of its merits and briefly compares it with other theories of vagueness. It raises issues about higher-order vagueness and the definitely operator (...) and about the supervaluationist's accounts of truth and validity. (shrink)

widely held commitments: to phenomenal realism and to naturalism. Phenomenal realism is the view that we are phenomenally consciousness, and that there is no a priori or armchair sufficient condition for phenomenal consciousness that can be stated in nonphenomenal terms . 1,2 Block points out that while phenomenal realists reject.

Explanatory metaphysics aspires to explain the less fundamental in terms of the more fundamental. But we should recognize two importantly different approaches to this task. According to the generation approach, more basic features of reality generate (or give rise to) less basic features. According to the reduction approach, less perspicuous ways of representing reality reduce to (or collapse into) more perspicuous ways of representing reality. The main goals of this paper are to present the core differences between the two approaches (...) (§2), to demonstrate the distinction's significance (§3), to provide some resources for adjudicating between the approaches (§4), and to argue that the project of explanatory metaphysics needs both (§5). (shrink)

Most ordinary objects - cats, humans, mountains, ships, tables, etc. - have indeterminate mereological boundaries. If the theory of mereology is meant to include ordinary objects at all, we need it to have some space for mereological indeterminacy. In this paper, we present a novel degree-theoretic semantics - Boolean semantics - and argue that it is the best degree-theoretic semantics for modeling mereological indeterminacy, for three main reasons: (a) it allows for incomparable degrees of parthood, (b) it enforces classical logic, (...) and (c) it is compatible with all the axioms of classical mereology. Using Boolean semantics, we will also investigate the connection between vagueness in parthood and vagueness in existence/identity. We show that, contrary to what many have argued, the connection takes neither the form of entailment nor the form of exclusion. (shrink)

The problem of the many seems to problematize the platitude that we can think about particular things in the world. How is it that, given how very many cat-like candidates there are, we often manage to think and talk about a particular cat? I argue that this challenge stems from an under-examined assumption about the relationship between metaphysics and intentionality. I explore and develop a way of characterizing what it is to think and talk about the world, according to which (...) an abundant ontology poses no obstacle to our ability to think and talk about particular things. (shrink)

In this paper, I propose that 'true’ is polysemous, and thus ambiguous. I suggest that the semantic paradoxes both motivates taking 'true’ to be polysemous and shows that the concept truth is indefinitely extensible. In doing so, I explain that 'true’ is polysemous between the meanings corresponding to the subconcepts of the concept truth generated by such indefinite extensibility. I conclude that the proposal provides satisfying solutions to the semantic paradoxes.

This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction.

Animalism, the thesis that each of us is a human animal, is a prominent materialist account of what we are. Animalism is often motivated by an attractive line of reasoning, the Thinking Animal Argument. And, independently, animalism has been challenged by appeals to a metaphysical puzzle, the problem of the many. In this paper, I draw attention to the relationship between the Thinking Animal Argument and the problem of the many. I further argue that in virtue of this relationship, animalists (...) are left in an unfortunate position: animalists cannot hold onto their most successful argument without undermining animalism itself. (shrink)

There are two families of influential and stubborn puzzles that many theories of aboutness (intentionality) face: underdetermination puzzles and puzzles concerning representations that appear to be about things that do not exist. I propose an approach that elegantly avoids both kinds of puzzle. The central idea is to explain aboutness (the relation supposed to stand between thoughts and terms and their objects) in terms of relations of co-aboutness (the relation of being about the same thing that stands between the thoughts (...) and terms themselves). (shrink)

The notorious problem of the many makes it difficult to resist the conclusion that almost coincident with any ordinary object are a vast number of near-indiscernible objects. As Unger was aware in his presentation of the problem, this abundance raises a concern as to how—and even whether—we achieve singular thought about ordinary objects. This paper presents, clarifies, and defends a view which reconciles a plenitudinous conception of ordinary objects with our having singular thoughts about those objects. Indeed, this strategy has (...) independent application in the case of singular thoughts about other putatively ‘abundant’ phenomena, such as locations or lumps of matter. In essence, singular thought-vehicles need not express just one singular content. If there are many objects, one’s singular thought-vehicle may express as many thought-contents. (shrink)

David Lewis offers two solutions to the problem of the many, one of which relies on supervaluationism and the other on the notion of “almost-identity” for the most part. In this paper, I argue that Lewis’ other metaphysical views constitute reasons to prefer his second solution to the first one. Specifically, Lewis’ theory of propositions and his counterpart theory give rise to two similar problems of the many, which I call “the problem of many propositions” and “the problem of many (...) counterparts” respectively. While both Lewis’ solutions may solve the problem of the many with respect to objects in the actual world, I argue that only his second solution can solve the problem of many propositions and the problem of many counterparts. Therefore, for anyone who accepts Lewis’ metaphysical views on propositions and counterparts, they should embrace Lewis’ second solution to the problem of the many for the reason of unification. (shrink)

There is a defeasible constraint against double counting. When I count colours, for instance, I can’t freely count both a colour and its shades. Once we properly grasp this constraint, we can solve the problem of the many. Unlike other solutions, this solution requires us to reject neither our counting judgments, nor the metaphysical principles that seemingly conflict with them. The key is recognizing that the judgments and principles are compatible due to the targeted effects of the defeasible constraint.

Let NNG be the claim that necessitation is necessary for grounding, and let NSG be the claim that necessitation is sufficient for grounding. The consensus view is that grounding cannot be reduced to necessitation, and this is due to the (approximately) universally-accepted claim that NSG is false. Among deniers of NSG: grounding contingentists think NNG is also false, but they are in the minority compared to grounding necessitarians who uphold NNG. For one who would defend the claim that grounding is (...) reducible to necessitation, the task is formidable: she must defend NSG and NNG. I consider two prominent objections against NSG, and two more against NNG before developing a reductive account of grounding as minimal necessitation that avoids not only all four of the previously mentioned objections, but also an additional objection that targets minimal necessitation accounts in particular. If my arguments are compelling, then, insofar as we thereby have a strong prima facie case for thinking that grounding can be reduced to (minimal) necessitation, we have a strong prima facie case for thinking the consensus view is mistaken. (shrink)

Does vagueness underlie the mass/count distinction? My answer is no. I motivate this answer in two ways. First, I argue against Chierchia’s recent attempt to explain the distinction in terms of vagueness. Second, I give a more general argument that no such account will succeed.

As anyone who has flown out of a cloud knows, the boundaries of a cloud are a lot less sharp up close than they can appear on the ground. Even when it seems clearly true that there is one, sharply bounded, cloud up there, really there are thousands of water droplets that are neither determinately part of the cloud, nor determinately outside it. Consider any object that consists of the core of the cloud, plus an arbitrary selection of these droplets. (...) It will look like a cloud, and circumstances permitting rain like a cloud, and generally has as good a claim to be a cloud as any other object in that part of the sky. But we cannot say every such object is a cloud, else there would be millions of clouds where it seemed like there was one. And what holds for clouds holds for anything whose boundaries look less clear the closer you look at it. And that includes just about every kind of object we normally think about, including humans. Although this seems to be a merely technical puzzle, even a triviality, a surprising range of proposed solutions has emerged, many of them mutually inconsistent. It is not even settled whether a solution should come from metaphysics, or from philosophy of language, or from logic. Here we survey the options, and provide several links to the many topics related to the Problem. (shrink)

Cases of grounding failure present a puzzle for fundamental metaphysics. Typically, solutions are thought to lie either in adding ontology such as haecceities or in re‐describing the cases by means of the ideology of metaphysical indeterminacy. The controversial status of haecceities has led some to favour metaphysical indeterminacy as the way to solve the puzzle. We consider two further treatments of grounding failure each of which, we argue, is a more plausible alternative. As such, the initial dichotomy is a false (...) one, and these alternative options deserve consideration before resorting to the heavyweight machinery of metaphysical indeterminacy. -/- . (shrink)

This paper outlines a novel solution to the problem of the many and a conception of ordinary objects that implies it. The solution is that many collections of particles can simultaneously constitute a single object. The proposed conception of ordinary objects maintains that they are fundamentally subjects of change: the changes an object is able to survive explain its constitution.

Weatherson 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 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. (shrink)

Most meanings we express belong to large families of variant meanings, among which it would be implausible to suppose that some are much more apt for being expressed than others. This abundance of candidate meanings creates pressure to think that the proposition attributing any particular meaning to an expression is modally plastic: its truth depends very sensitively on the exact microphysical state of the world. However, such plasticity seems to threaten ordinary counterfactuals whose consequents contain speech reports, since it is (...) hard to see how we could reasonably be confident in a counterfactual whose consequent can be true only if a certain very finely tuned microphysical configuration obtains. This essay develops the foregoing puzzle and explores several possible solutions. (shrink)

The sorites paradox is the name given to a class of paradoxical arguments, also known as little by little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap (...) and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion. (shrink)

Following Hartry Field in distinguishing disquotational truth from a conception that grounds truth conditions in a community's usage, it is argued that the notions are materially inequivalent (since the latter allows truth-value gaps) and that both are needed. In addition to allowing blanket endorsements ("Everything the Pope says is true"), disquotational truth facilitates mathematical discovery, as when we establish the Gödel sentence by noting that the theorems are all disquotationally true and the disquotational truths are consistent. We require a more (...) substantial notion, however, if we intend to use truth values and truth conditions in explaining communication by language. (shrink)

El objetivo de este artículo es entender ciertas cuestiones que surgen cuando reconocemos que un buen número de predicados del lenguaje natural son indeterminados de dos maneras diferentes. Por ejemplo, el predicado ‘es una montaña’ es vago y susceptible al problema de los muchos. A lo largo de este artículo me enfocaré en cómo distinguir estos dos tipos de indeterminación, y en un problema que el supervaluacionismo iene cuando reconoce que un predicado puede ser vago y susceptible al problema de (...) los muchos. La dificultad es que el supervaluacionismo pierde su habilidad para capturar nuestras intuiciones acerca de cortes precisos. Finalmente, ofrezco una solución a dicho problema. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

Can we solve the Problem of the Many, and give a general account of the indeterminacy in definite descriptions that give rise to it, by appealing to metaphysically indeterminate entities? I argue that we cannot. I identify a feature common to the relevant class of definite descriptions, and derive a contradiction from the claim that each such description is satisfied by a metaphysically indeterminate entity.

In this paper I present some of Robert N. McLaughlin's critique of a truth functional approach to conditionals as it appears in his book On the Logic of Ordinary Conditionals. Based on his criticism I argue that the basic principles of logic together amount to epistemological and metaphysical implications that can only be accepted from a logical atomist perspective. Attempts to account for conditional relations within this philosophical framework will necessarily fail. I thus argue that it is not truth functionality (...) as such that is the problem, but the philosophical foundation of modern logic. (shrink)