Ziyu Guo

What determines the meaning of a context-sensitive expression in a context? It is standardly assumed that, for a given expression type, there will be a unitary answer to this question; most of the literature on the subject involves arguments designed to show that one particular metasemantic proposal is superior to a specific set of alternatives. The task of the present essay will be to explore whether this is a warranted assumption, or whether the quest for the one true metasemantics might be a Quixotic one. We argue that there are good reasons—much better than are commonly appreciated—for thinking the latter, but that there nevertheless remains significant scope for metasemantic theorizing. We conclude by outlining our preferred option, metasemantic pluralism.

This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach to resolving indeterminacy, before offering some brief closing reflections. We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic.

Platonism in the philosophy of mathematics faces metaphysical, metasemantic, and epistemological challenges. For all of these reasons, many philosophers and mathematicians have been attracted to anti-platonist theories. Three types of antiplatonist theories are especially prominent: pluralist platonism, fictionalism, and conventionalism. Some influential anti-platonist philosophers, including Balaguer and, more recently, Field, have argued that, despite appearances, the different versions of anti-platonism do not significantly differ from each other; I disagree. The goal of this paper is to survey and assess the relative merits of the three main versions of anti-platonism while provisionally assuming each version succeeds on its own terms. Despite the obvious philosophical similarities between the theories, I argue that pluralist platonist theories inherit the metaphysical challenges for platonism and fictionalist theories inherit the metasemantic challenges for plationism, while conventionalist theories inherit neither. My ultimate conclusion is that, though similar in several important respects, there are important philosophical differences separating these three versions of anti-platonism.

Conventionalism about mathematics has much in common with two other views: fictionalism and the multiverse view (aka plenitudinous platonism). The three views may differ over the existence of mathematical objects, but they agree in rejecting a certain kind of objectivity claim about mathematics, advocating instead an extreme pluralism. The early parts of the paper will try to elucidate this anti‐objectivist position, and question whether conventionalism really offers a third form of it distinct from fictionalism and the multiverse view. The paper then turns to anti‐objectivism about logic, and suggests that here too conventionalism offers no distinct alternative, and that there are limits on the extent of pluralism/anti‐objectivism. It also argues that these limits can't be used to argue for more extensive objectivity within mathematics, and also that they do allow for more limited pluralism within logic, e.g. as regards resolution of semantic and property‐theoretic paradoxes.

In this paper, we argue that a person is obligated to explain why p just in case she has a role-responsibility to answer the question “Why p?”. This entails that the normative force of explanatory obligations is fundamentally social. We contrast our view with other accounts of explanatory obligations or the so-called “need for explanation,” in which the aforementioned normative force is epistemic, determined by an inquirer's interests, or a combination thereof. We argue that our account outperforms these alternatives.

Several authors believe that there are certain facts that are striking and cry out for explanation—for instance, a coin that is tossed many times and lands in the alternating sequence HTHTHTHTHTHT…. According to this view, we have prima facie reason to believe that such facts are not the result of chance. I call this view the striking principle. Based on this principle, some have argued for far-reaching conclusions, such as that our universe was created by intelligent design, that there are many universes other than the one we inhabit, and that there are no mathematical or normative facts. Appealing as the view may initially seem, I argue that we lack sufficient reason to accept it.

In this chapter, Katharina Felka and Alex Steinberg consider a problem for structured accounts of content articulated by Stephen Schiffer and Adam Pautz. The problem has to do with the idea of reference shift—that is, the idea that material embedded in the complementizer clauses of propositional attitude ascriptions must function semantically to refer to something other than what it refers to in unembedded contexts. Focusing in particular on Frege’s theory of content, Felka and Steinberg state the problem as follows: If ‘Hesperus’ in the sentence ‘Ben believes that Hesperus is a planet’ refers not to Venus but rather to the sense associated with the lexical item ‘Hesperus’, and if existential quantification works in the normal way, then the sentence ‘There is something such that Ben believes that it is a planet’ would seem to be true just in case there is a sense which Ben believes to be a planet. But, unless Ben is a peculiar individual indeed, he would never mistake a sense for a planet. So it seems that certain intuitively true sentences are predicted to be false by theories that posit reference shift. Felka and Steinberg suggest that the best response to this kind of argument for proponents of reference shift is to hold that the value of a variable relative to an assignment function shifts in propositional attitude ascriptions just like the value of any other kind of expression.

When I first began to take an interest in the debate over nominalism in philosophy of mathematics, some twenty-odd years ago, the issue had already been under discussion for about a half-century. The terms of the debate had been set: W. V. Quine and others had given “abstract,” “nominalism,” “ontology,” and “Platonism” their modern meanings. Nelson Goodman had launched the project of the nominalistic reconstruction of science, or of the mathematics used in science, in which Quine for a time had joined him before turning against him. William Alston, Rudolf Carnap, and Michael Dummett had raised doubts about what the point of Goodman’s exercise could be, and though they had unfortunately been largely ignored, Quine’s contention that the exercise cannot be successfully completed had gained wide publicity as the so-called “indispensability” argument against nominalism. By contrast, two subtle discussions of Paul Benacerraf had been appropriated by nominalists and turned into the so-called “multiple reductions” and “epistemological” arguments for nominalism.

Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given this, I argue that semantics can fail to deliver determinate ontological commitments and determinate answers to ontological questions, more generally

The idea that there could be spatially extended mereological simples has recently been defended by a number of metaphysicians (Markosian 1998, 2004; Simons 2004; Parsons (2000) also takes the idea seriously). Peter Simons (2004) goes further, arguing not only that spatially extended mereological simples (henceforth just extended simples) are possible, but that it is more plausible that our world is composed of such simples, than that it is composed of either point-sized simples, or of atomless gunk. The difficulty for these views lies in explaining why it is that the various sub-volumes of space occupied by such simples, are not occupied by proper parts of those simples. Intuitively at least, many of us find compelling the idea that spatially extended objects have proper parts at every sub-volume of the region they occupy. It seems that the defender of extended simples must reject a seemingly plausible claim, what Simons calls the geometric correspondence principle (GCP): that any (spatially) extended object has parts that correspond to the parts of the region that it occupies (Simons 2004: 371). We disagree. We think that GCP is a plausible principle. We also think it is plausible that our world is composed of extended simples. We reconcile these two notions by two means. On the one hand we pay closer attention to the physics of our world. On the other hand, we consider what happens when our concept of something—in this case space—contains elements not all of which are realized in anything, but instead key components are realized in different features of the world.

In this paper I sketch a novel interpretationist account of linguistic content that has important consequences for thinking about intentionality. I solve the challenge presented by a foundational indeterminacy of reference argument to the effect that the meaning of linguistic expressions is radically indeterminate. Happily, my solution doesn’t require positing natural properties as “reference magnets”. Non-deflationist rivals to interpretationist metasemantics include various kinds of causal theories such as Fodor-style asymmetric-dependence accounts and Millikan-style teleosemantics. These accounts face their own indeterminacy challenges that have yet to be solved, as well as similar indeterminacy of reference challenges at the level of individual words. Moreover, they must contend with our apparent reference to things that we are not plausibly causally acquainted with. If indeterminacy of reference arguments can be answered and we can avoid dubious use of natural properties, an interpretationist account like my own will be the strongest contender..

Many writers have held that in his later work, David Lewis adopted a theory of predicate meaning such that the meaning of a predicate is the most natural property that is (mostly) consistent with the way the predicate is used. That orthodox interpretation is shared by both supporters and critics of Lewis's theory of meaning, but it has recently been strongly criticised by Wolfgang Schwarz. In this paper, I accept many of Schwarze's criticisms of the orthodox interpretation, and add some more. But I also argue that the orthodox interpretation has a grain of truth in it, and seeing that helps us appreciate the strength of Lewis's late theory of meaning.

Ontological monists hold that there is only one way of being, while ontological pluralists hold that there are many; for example, concrete objects like tables and chairs exist in a different way from abstract objects like numbers and sets. Correspondingly, the monist will want the familiar existential quantifier as a primitive logical constant, whereas the pluralist will want distinct ones, such as for abstract and concrete existence. In this paper, we consider how the debate between the monist and pluralist relates to the standard test for logicality. We deploy this test and show that it favors the monist.

'Ontology and Metaontology: A Contemporary Guide' is a clear and accessible survey of ontology, focussing on the most recent trends in the discipline. Divided into parts, the first half characterizes metaontology: the discourse on the methodology of ontological inquiry, covering the main concepts, tools, and methods of the discipline, exploring the notions of being and existence, ontological commitment, paraphrase strategies, fictionalist strategies, and other metaontological questions. The second half considers a series of case studies, introducing and familiarizing the reader with concrete examples of the latest research in the field. The basic sub-fields of ontology are covered here via an accessible and captivating exposition: events, properties, universals, abstract objects, possible worlds, material beings, mereology, fictional objects. The guide's modular structure allows for a flexible approach to the subject, making it suitable for both undergraduates and postgraduates looking to better understand and apply the exciting developments and debates taking place in ontology today.

In the last 35 years many philosophers have appealed to reference magnetism to explain how it is that we mean what we mean. The idea is that it is a constitutive principle of metasemantics that the interpretation that assigns the more natural meanings is correct, _ceteris paribus_. Among other things, magnetism has been used to answer the challenges of grue and quus, Quine’s indeterminacy of translation argument, and Putnam’s model-theoretic argument against realism. Critics of magnetism have usually objected to the base notion of naturalness. Here I assume naturalness for the sake of argument, but argue that even still, reference magnetism should be rejected. The supposed force of reference magnetism is arbitrarily weak, and the best explanation of this is that it simply does not exist.

Quantifier variance holds that different languages can have unrestricted quantifier expressions that differ in meaning, where an expression is a “quantifier” just in case it plays the right inferential role. Several critics argued that J.H. Harris’s “collapse” argument refutes variance by showing that identity of inferential role is incompatible with meaning variance. This standard, syntactic collapse argument has generated several responses. More recently, Cian Dorr proved semantic collapse theorems to generate a semantic collapse argument against variance. The argument is significantly different from standard collapse, so it requires a new response. Here I clarify and analyze the semantic collapse argument, and explain how variantists can and should respond to it. The paper also includes an appendix showing the difficulties of positing identity variance without quantifier variance. The argument in the appendix has yet to appear in print, but is familiar to specialists.

In the work of both Matti Eklund and John Hawthorne there is an influential semantic argument for a maximally expansive ontology that is thought to undermine even modest forms of quantifier variance. The crucial premise of the argument holds that it is impossible for an ontologically "smaller" language to give a Tarskian semantics for an ontologically "bigger" language. After explaining the Eklund-Hawthorne argument (in section I), we show this crucial premise to be mistaken (in section II) by developing a Tarskian semantics for a mereological universalist language within a mereological nihilist language (a case which we, and Eklund and Hawthorne, take as representative). After developing this semantics we step back (in section III) to discuss the philosophical motivations behind the Eklund- Hawthorne argument’s demand for a semantics. We ultimately conclude that quantifier variantists can meet any demand for a semantics that might reasonably be imposed upon them.

Recently a number of works in meta-ontology have used a variant of J.H. Harris's collapse argument in the philosophy of logic as an argument against Eli Hirsch's quantifier variance. There have been several responses to the argument in the literature, but none of them have identified the central failing of the argument, viz., the argument has two readings: one on which it is sound but doesn't refute quantifier variance and another on which it is unsound. The central lesson I draw is that arguments against quantifier variance must pay strict attention to issues of translation and interpretation. The paper also has a substantial appendix in which I prove the equivalence of plural mereological nihilism and standard first-order atomistic mereology; results of this kind are often appealed to in the literature on quantifier variance but without many details on the nature or proof of the result.

Philosophers often aim to demonstrate that the things we ordinarily think and say can be reconciled with our considered beliefs about the world. To this end, many philosophers try to paraphrase ordinary language claims by finding equivalent sentences that are less misleading. For instance, though we know that there is no British family that is the average one, we want to say that the average British family has 1.8 children, and we might do that by paraphrasing this claim as: there are nearly twice as many British children as British families. This article aims to introduce and distinguish different paraphrase strategies, sketch their role in metaphysical debates and highlight some crucial questions that proponents of such strategies face

Few if any distinctions are more easily recognisable and assented to than that between _objects_, that is, things which are some ways, and that which they are, that is, _ways for objects to be_ (‘ways of being’ for short). In this paper I present an argument designed to show that this distinction is indeterminate in the sense that the truth-conditions of predicational sentences leave open what should count as an object and a way of being. The bulk of the argument is inspired by the celebrated permutation argument advanced by Quine, Wallace, Putnam and others.

In "nominalism and realism" armstrong carefully demolishes various nominalist responses to plato's "one over many" problem but simply dismissed the quinean response as "ostrich nominalism". The paper argues that plato's problem is pseudo. So to ignore it is not to behave like an ostrich. Rather to adopt realism because of this problem that isn't there is to be a "mirage realist." there are some good reasons that lead armstrong to realism but he is largely a mirage realist. Quine does not ignore any real problem for nominalism and so is not an ostrich nominalist.

Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist are mere notational variants of those proposed by the monist, in which case the debate between the two positions would not seem to be substantive. Jason Turner has given an ingenious response to this worry, in terms of a principle that he calls ‘logical realism’. This paper offers a counter-response on behalf of the ‘notationalist’. I argue that, properly applied, the principle of logical realism is no threat to the claim that the languages in question are notational variants. Indeed, there seems to be every reason to think that they are.

The notion of subject matter is a key concern of contemporary philosophy of language and logic. A central task for a theory of subject matter is to characterise the notion of sentential subject matter, that is, to assign to each sentence of a given language a subject matter that may count as its subject matter. In this paper, we elaborate upon David Lewis’ account of subject matter. Lewis’ proposal is simple and elegant but lacks a satisfactory characterisation of sentential subject matter. Drawing on linguistic literature on focus and on the question under discussion, we offer a neo-Lewisian account of subject matter, which retains all the virtues of Lewis’ but also includes an attractive characterisation of sentential subject matter.