ABSTRACTBy the Many Categories problem, I mean the prima facie violation of Ockham’s Razor by realists about universals: there is, it might seem, just too much variety. Thus, David Armstrong posits both properties and relations. He also theorises about determinates of determinables. Another influential realist, E. J. Lowe distinguishes non-substantial from substantial universals. Yet again, both Armstrong and Lowe include in their ontology abstract particulars in addition to universals. My aim in this paper is to offer a unification of these (...) categories using an operator-theory. First, I show how operators provide a theory of abstract particulars of relations and of impure relational properties. Then, using impure relational properties I derive the Fregeanion Principle. After some metaphysics of mathematics, I provide a theory of determinables. Finally, I consider kinds and substances. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. I argue (...) for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

In this paper, we offer a brief, critical survey of contemporary work on truth. We begin by reflecting on the distinction between substantivist and deflationary truth theories. We then turn to three new kinds of truth theory—Kevin Scharp's replacement theory, John MacFarlane's relativism, and the alethic pluralism pioneered by Michael Lynch and Crispin Wright. We argue that despite their considerable differences, these theories exhibit a common "pluralizing tendency" with respect to truth. In the final section, we look at the underinvestigated (...) interface between metaphysical and formal truth theories, pointing to several promising questions that arise here. (shrink)

Mathematical concepts play at least three roles in the application of mathematics: an inferential role, a representational role, and an expressive role. In this paper, I argue that, despite what has often been alleged, platonists do not fully accommodate these features of the application of mathematics. At best, platonism provides partial ways of handling the issues. I then sketch an alternative, anti-realist account of the application of mathematics, and argue that this account manages to accommodate these features of the application (...) process. In this way, a better account of mathematical applications is, in principle, available. (shrink)

A feature of agnostic views—views that officially express ignorance about the existence of something —is that they are widely perceived to be epistemically more cautious than views that are committed to the entities in question. This is often seen as giving agnostics a debating advantage: all things being equal, fence-sitters have smaller argumentative burdens. Otávio Bueno argues in this way for what he calls “agnostic nominalism,” the view that we don’t know whether ontologically-independent Platonic objects exist. I show that agnostic (...) nominalism, so called, can be sustained only in ways that don’t give agnostic nominalists debating advantages: the position must either be deduced from antecedently-held broader sceptical assumptions or it requires manufacturing potential referents for one’s terms that artificially generate grounds for scepticism. Neither maneuver leads to an agnostic nominalism with a debating advantage over its nominalist opponents. (shrink)

It is widely held that there is a problem of talking about or otherwise representing things that not exist. But what exactly is this problem? This paper presents a formulation of the problem in terms of the conflict between the fact that there are truths about non-existent things and the fact that truths must be answerable to reality, how things are. Given this, the problem of singular negative existential statements is no longer the central or most difficult aspect of the (...) problem of non-existence, despite what some philosophers say. (shrink)

Many naive realists endorse a negative disjunctivist strategy in order to deal with the challenge presented by the possibility of phenomenologically indistinguishable halucination. In the first part of this paper I argue that this approach is methodologically inconsistent because it undercuts the phenomenological motivation that underlies the the appeal of naive realism. In the second part of the paper I develop an alternative to the negative disjunctivist account along broadly Meinongian lines. In the last section of this paper I consider (...) and evaluate a somewhat similar but rival view of hallucination developed by Mark Johnston. (shrink)

Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...) description of Mars. But whereas Mars is a physical object, the number 3 is (according to platonism) an abstract object. And abstract objects, platonists tell us, are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 3 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects. This view has been endorsed by Plato, Frege (1884, 1893-1903, 1919), Gödel (1964), and in some of their writings, Russell (1912) and Quine (1948, 1951), not to mention numerous more recent philosophers of mathematics, e.g., Putnam (1971), Parsons (1971), Steiner (1975), Resnik (1997), Shapiro (1997), Hale (1987), Wright (1983), Katz (1998), Zalta (1988), and Colyvan (2001). (shrink)

Are there nonexistent objects, i.e., objects that do not exist? Some examples often cited are: Zeus, Pegasus, Sherlock Holmes, Vulcan (the hypothetical planet postulated by the 19th century astronomer Le Verrier), the perpetual motion machine, the golden mountain, the fountain of youth, the round square, etc. Some important philosophers have thought that the very concept of a nonexistent object is contradictory (Hume) or logically ill-formed (Kant, Frege), while others (Leibniz, Meinong, the Russell of Principles of Mathematics) have embraced it wholeheartedly. (...) This entry is an examination of the many questions which arise in connection with the view that there are nonexistent objects. The following are particularly salient: What reasons are there (if any) for thinking that there are nonexistent objects? If there are nonexistent objects, then what kind of objects are they? How can they be characterized? Is it possible to provide a consistent theory of nonexistent objects? What is the explanatory force of a consistent theory of nonexistent objects (if such a thing is possible)? (shrink)

Alonzo Church (1903–1995) was a renowned mathematical logician, philosophical logician, philosopher, teacher and editor. He was one of the founders of the discipline of mathematical logic as it developed after Cantor, Frege and Russell. He was also one of the principal founders of the Association for Symbolic Logic and the Journal of Symbolic Logic. The list of his students, mathematical and philosophical, is striking as it contains the names of renowned logicians and philosophers. In this article, we focus primarily on (...) Church’s philosophical contributions. (For an account of his life and academic history see the Introduction to The Collected Works of Alonzo Church (2019).) However, we also discuss his mathematical results when it is desirable to do so in order to pursue a philosophical issue. (shrink)

There is growing debate about what is the correct methodology for research in the ontology of artworks. In the first part of this essay, I introduce my view: I argue that semantic descriptivism is a semantic approach that has an impact on meta-ontological views and can be linked with a hermeneutic fictionalist proposal on the meta-ontology of artworks such as works of music. In the second part, I offer a synthetic presentation of the four main positive meta-ontological views that have (...) been defended in philosophical literature about artworks and of some criticisms that can be lodged against them: Amie Thomasson’s global descriptivism, Andrew Kania’s local descriptivism, Julian Dodd’s folk-theoretic modesty, and David Davies’ rational accountability view. In the conclusion, I show the advantages of my view. (shrink)

What are words and how should we individuate them? There are two main answers on the philosophical market. For some, words are bundles of structural-functional features defining a unique performance profile. For others, words are non-eternal continuants individuated by their causal-historical ancestry. These conceptions offer competing views of the nature of words, and it seems natural to assume that at most one of them can capture the essence of wordhood. This paper makes a case for pluralism about wordhood: the view (...) that there is a plurality of acceptable conceptions of the nature of words, none of which is uniquely entitled to inform us as to what wordhood consists in. (shrink)

Phenomenal intentionality theories have recently enjoyed significant attention. According to these theories, the intentionality of a mental representation (what it is about) crucially depends on its phenomenal features. We present a new puzzle for these theories, involving a phenomenon called ‘intentional identity’, or ‘co-intentionality’. Co-intentionality is a ubiquitous intentional phenomenon that involves tracking things even when there is no concrete thing being tracked. We suggest that phenomenal intentionality theories need to either develop new uniquely phenomenal resources for handling the puzzle, (...) or restrict their explanatory ambitions. (shrink)

This paper, written in Romanian, compares fictionalism, nominalism, and neo-Meinongianism as responses to the problem of objectivity in mathematics, and then motivates a fictionalist view of objectivity as invariance.

Natural languages generally distinguishes among different existence predicates for different types of entities, such as English 'exist', 'occur', and 'obtain'. The paper gives an in-depth discussion and analysis of a range of existence predicates in natural language within the general project of descriptive metaphysics, or more specifically ‘natural language ontology’.

According to Jody Azzouni’s “deflationary nominalism,” the singular terms of mathematical language applied or unapplied to science refer to nothing at all. What does exist, Azzouni claims, must satisfy the quaternary condition he calls “thick epistemic access” (TEA). In this paper I argue that TEA surreptitiously reifies some mathematical entities. The mathematical entity that I take TEA to reify is the Fourier harmonic, an infinite-duration monochromatic sinusoid applied throughout engineering and physics. I defend the reality of the harmonic, in Azzouni’s (...) account, not by satisfying all four TEA conditions with respect to it, but by showing that the harmonic renders satisfiable the TEA condition called “grounding,” specifically in Azzouni’s (Talking about nothing: numbers, hallucinations, and fictions. New York: Oxford University Press, 2010) example of a human visually perceiving a vase. The harmonic thereby plays what Azzouni calls an “epistemic role,” and merits inclusion in the deflationary nominalist ontology. Against the “coding” objection of Azzouni and Bueno (Br J Philos Sci 67:781–816, 2016), which would nominalize the harmonic to nonexistent status, I reply that in the context of grounding, the coding objection begs the question. (shrink)

Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical (...) knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology. (shrink)

Bradley Armour-Garb and James A. Woodbridge, in Pretense and Pathology, make an ambitious and far-ranging case that philosophical fictionalism (particularly the pretence variety that they favour) illuminates several long-standing philosophical puzzles posed by words in ordinary language, such as ‘exist’, ‘true’ and ‘means that’, as well as the more technical, ‘refers to’, ‘proposition’ and ‘satisfies’. Along the way, Armour-Garb and Woodbridge discuss topics in the philosophy of language, philosophical logic, ontology, epistemology and more. An important aspect of their project is (...) its nominalist aspiration: by showing (if they do) that pretence is involved when we use the foregoing terms, they hope to show that it’s false that these uses induce ontological commitments (to, e.g., propositions or properties). In this respect, their pretence approach is yet another attempt to undercut the family of indispensability arguments (pioneered by W.V.O. Quine) that prima facie force ontological commitments by means of indispensable language usage. (shrink)

Jody Azzouni argues that whilst it is indeterminate what the criteria for existence are, there is a criterion that has been collectively adopted to use ‘exist’ that we can employ to argue for positions in ontology. I raise and defend a novel objection to Azzouni: his view has the counterintuitive consequence that the facts regarding what exists can and will change when users of the word ‘exist’ change what criteria they associate with its usage. Considering three responses, I argue Azzouni (...) has best reason to take one that ultimately renders unsuccessful his arguments against mathematical abstracta. (shrink)

Can Quine’s criterion for ontological commitment be comparatively applied across different logics? If so, how? Cross-logical evaluations of discourses are central to contemporary philosophy of mathematics and metaphysics. The focus here is on the influential and important arguments of George Boolos and David Lewis that second-order logic and plural quantification don’t incur additional ontological commitments over and above those incurred by first-order quantifiers. These arguments are challenged by the exhibition of a technical tool—the truncation-model construction of notational equivalents—that compares the (...) ontological role and increased expressive strength of non-first-order ideology to first-order ideology. (shrink)

The paper argues that natural language quantification, as expressed by determiner phrases, is not polysemous. The foil for this claim is Hofweber, who contends that natural language quantification is polysemous between a domain reading and an inferential reading. The thesis is intended to support a more general division between externalist and internalist positions in semantics. The paper, to the contrary, argues that there is no linguistic evidence for polysemous quantification, and Hofweber’s proposal proves to be non-compositional. Further, an approach at (...) least consistent with internalism is available independent of an inferential reading, for natural language quantification can be read as ontologically neutral, which removes the rationale for the polysemy hypothesis. The paper remains neutral on so-called heavyweight vs. lightweight construals of quantification, which are not claims about natural language semantics. (shrink)

Terms such as ‘exist’, ‘actual’, etc., (hereafter, “ontic terms”) are recognized as having uses that are not ontologically committing, in addition to the usual commissive uses. (Consider, e.g., the Platonic and the neutral readings of ‘There is an even prime’.) In this paper, I identify five different noncommissive uses for ontic terms, and (by a kind of via negativa) attempt to define the commissive use, focusing on ‘actual’ as my example. The problem, however, is that the resulting definiens for the (...) commissive ‘actual’ is itself equivocal between a commissive and a noncommissive reading. I thus consider other proposals for defining the commissive use, including two proposals from David Lewis. However, each proposal is found to be equivocal in the same way—and eventually I argue that it is impossible to define an ontic term unequivocally. Even so, this is not meant to overshadow that we can understand an ontic term as univocally commissive, in certain conversational contexts. I close by illustrating the import of these observations for the Hirsch–Sider debate in metaontology. (shrink)

That certain paper bills have monetary value, that Vladimir Putin is the president of Russia, and that Prince Philip is the husband of Queen Elizabeth II: such facts are commonly called ‘institutional facts’. IFF are, by definition, facts that exist by virtue of collective recognition. The standard view or tacit belief is that such facts really exist. In this paper we argue, however, that they really do not—they really are just well-established illusions. We confront realism about IFF with six criteria (...) of existence, three established and three less so but highly intuitive. We argue that they all tell against the existence of IFF. An obvious objection to IFF non-realism is that since people’s behaviour clearly reflects the existence of IFF, denying their existence leaves an explanatory gap. We reject this argument by introducing a variant of the so-called ‘Thomas Theorem,’ which says that when people collectively recognize a fact as existing, they largely behave accordingly, regardless of whether that fact really exists or not. (shrink)

The paper presents an accommodation problem for extant semantic accounts of fiction. Some accounts of fiction are designed to accommodate one or another form of fictive statement exclusively, what I shall call in-fiction and out-fiction. Thus, typically, the accounts fail to do justice to their respective excluded form. A natural response, entertained by Kripke and in a different fashion by latter-day Meinongians, is to let the two different kinds of fiction have their respective accounts. It is very easy, however, to (...) mix in and out predicates, which amounts to a species of copredication, where a single nominal receives simultaneous distinct interpretations relative to distinct predicates without creating ambiguity. Copredication is a perfectly general phenomenon that arises for any nominal. The simple problem now is that copredication appears to render all extant accounts of fiction either essentially partial, in dealing with one kind of simple form of fiction but not another, or merely wrong in imagining that fiction comes in categorically distinct forms, for the coherence of copredication is enough to show that this is not so. The aim of the paper is to show to resolve this accommodation problem by the radical expedient of suggesting that the fiction/non-fiction distinction is not really a semantic one, but more one between different ways in which sentences are made true or false. (shrink)

First, I discuss the older “theory-centered” and the more recent semantic conception of scientific theories. I argue that these two perspectives are nothing more than terminological variants of one another. I then offer a new theory-centered view of scientific theories. I argue that this new view captures the insights had by each of these earlier views, that it’s closer to how scientists think about their own theories, and that it better accommodates the phenomenon of inconsistent scientific theories.

Dans ce livre très original, Markus Gabriel avance une théorie du soi humain qui surmonte les blocages inhérents aux positions standards en philosophie de l’esprit contemporaine. Son point de vue, le néo-existentialisme, est intégralement antinaturaliste, en ce sens qu’il rejette toute théorie selon laquelle l’ensemble de nos meilleures connaissances scientifiques naturelles serait pleinement capable de rendre compte de l’esprit humain. L’auteur montre plutôt que l’esprit humain consiste en une prolifération ouverte de vocabulaires mentalistes. Leur rôle dans la forme de vie (...) humaine consiste à rendre compte du fait que l’être humain ne se fond pas simplement dans la nature inanimée et le reste du règne animal. Les humains s’appuient sur un autoportrait qui les situe dans un contexte aussi large que possible au sein de l’univers. Ce qui distingue cet autoportrait de notre connaissance de la réalité naturelle, c’est que nous changeons en vertu de nos croyances, vraies ou fausses, au sujet de nous-mêmes. (shrink)

Many naive realists are inclined to accept a negative disjunctivist strategy in order to deal with the challenge presented by the possibility of phenomenologically indistinguishable hallucination. In the first part of this paper I argue that this approach is methodologically inconsistent because it undercuts the phenomenological motivation that underlies the appeal of naive realism. In the second part of the paper I develop an alternative to the negative disjunctivist account along broadly Meinongian lines. In the last section of this paper (...) I consider and evaluate a somewhat similar but rival view of hallucination developed by Mark Johnston. (shrink)

The standard view of truth-conditional semantics is that it is world-involving in the sense that a theory that specifies truth conditions eo ipso is a theory that specifies the way the world must be if the target sentences are to be true. It would appear to follow that the semantic properties of expressions, such as nominals, specify the very worldly objects that make true or false the sentences that host the nominals. Chomsky and others have raised a fundamental complaint against (...) this thought: perfectly quotidian nominals, such as London or book, may occur copredicatively as a single argument of categorically mismatched predicates, which prima facie preclude a coherent uniform construal of the nominal argument. The argument has hitherto been presented via examples that challenge the standard view. My aim here is to present the argument explicitly, defend it against some likely counterclaims, and resolve what might appear to be a decisive consideration against the conclusion of the argument, viz., if nominals as copredicatively occurring do not contribute uniform worldly entities, then how can the copredicative constructions be counted as true? (shrink)

The intuition that we can think about non-existent objects seems to be in tension with philosophical concerns about the relationality of intentionality. Tim Crane’s psychologism removes this tension by proposing a psychologistic account of intentionality according to which intentionality is a purely non-relational notion. I argue that his account has counterintuitive consequences regarding our thoughts about existing objects, and as such is insufficiently plausible to convince us to reject the relationality of intentionality.

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. (shrink)

Provides a certain conception of the target of a theory of intentionality in terms of five properties (aboutness, non-existence, aspectuality, generality, and semantic normativity) and provides a guided tour of how different styles of theories of intentionality can meet up these requirements.

The concept of intentional identity has aroused considerable interests since Geach. I argue, however, that the real import of intentional identity is still not duly appreciated. Drawing on three sets of close-knit data – intersubjective and intrasubjective intentional identity, along with cross-speaker anaphora, I submit coordination as the key to its proper understanding and propose a set of success conditions thereof.

In a number of places Mark Sainsbury has recently developed an attractive irrealist account of fiction and intentionality, on which there are no fictional objects or exotic intentional entities. A central component of his account is an ambitious argument, which aims to establish that the truth of intensional transitives such as “I think about Holmes” and “Alexander feared Zeus” does not require the existence of fictional or intentional objects. It would be good news indeed for the irrealist if Sainsbury’s argument (...) worked. However, I argue that Sainsbury’s argument fails. I conclude by considering how Sainsbury’s irrealist might explain our intuitions about such sentences, drawing upon another component of Sainsbury’s irrealism. (shrink)