Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to develop the (...) needed explanations by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. (shrink)

Kripke models, interpreted realistically, have difficulty making sense of the thesis that there might have existed things that do not in fact exist, since a Kripke model in which this thesis is true requires a model structure in which there are possible worlds with domains that contain things that do not exist. This paper argues that we can use Kripke models as representational devices that allow us to give a realistic interpretation of a modal language. The method of doing this (...) is sketched, with the help of an analogy with a Galilean relativist theory of spatial properties and relations. (shrink)

I am going to describe a variant formulation of classical extensional first-order logic and contrast it with the standard formulation. The formulation I will give is in one clear sense equivalent to the standard one, and it is a routine task to show that it is equivalent to it in this sense. So one might regard my formulation as a mere notational variation. But there are also ways in which the two formulations I will contrast are not equivalent, and I (...) will argue that these ways reflect an important conceptual difference between them. The differences become more important as one generalizes or extends classical logic in various ways, but they are there even in the classical systems. (shrink)

I argue that metaphysical views of material objects should be understood as 'packages', rather than individual claims, where the other parts of the package include how the theory addresses 'recalcitant data', and that when the packages meet certain general desiderata - which all of the currently competing views *can* meet - there is nothing in the world that could make one of the theories true as opposed to any of the others.

This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters. The essay proceeds by questioning traditional assumptions about the connection between the objects that are used to specify the truth-conditions of a sentence, on the one hand, and the objects whose existence is required in order for (...) the truth-conditions thereby specified to be satisfied, on the other. This allows one to set forth an assignment of truth-conditions to arithmetical sentences whereby nothing is required of the world in order for the truth-conditions of a truth of pure arithmetic to be satisfied. The essay then argues that such an assignment can be used to account for the a priori knowability of certain arithmetical truths. (shrink)

This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...) discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications. (shrink)

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...) but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

Serious actualism is the prima facie plausible thesis that things couldn’t have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga’s argument for the claim that propositions do not ontologically depend on the things that they are about and in Williamson’s argument for the claim that he, Williamson, is necessarily something. Salmon has put forward that which is, arguably, the most pressing challenge to serious actualists. Salmon’s objection is (...) based on a scenario intended to elicit the judgment that merely possible entities may nonetheless be actually referred to, and so may actually have properties. It is shown that predicativism, the thesis that names are true of their bearers, provides the resources for replying to Salmon’s objection. In addition, an argument for serious actualism based on Stephanou, 219–250 2007) is offered. Finally, it is shown that once serious actualism is conjoined with some minimal assumptions, it implies property necessitism, the thesis that necessarily all properties are necessarily something, as well as a strong comprehension principle for higher-order modal logic according to which for every condition there necessarily is the property of being a thing satisfying that condition. (shrink)

Pairs of sentences like the following pose a problem for ontology: (1) Jupiter has four moons. (2) The number of moons of Jupiter is four. (2) is intuitively a trivial paraphrase of (1). And yet while (1) seems ontologically innocent, (2) appears to imply the existence of numbers. Thomas Hofweber proposes that we can resolve the puzzle by recognizing that sentence (2) is syntactically derived from, and has the same meaning as, sentence (1). Despite appearances, the expressions ‘the number of (...) moons of Jupiter’ and ‘four’ do not function semantically as singular terms in (2). Hofweber’s primary evidence for this proposal concerns differences in the focus-related communicative functions of (1) and (2). In this paper I raise several serious problems for Hofweber’s proposal, and for his attempt to support it by appeal to focus-related phenomena. I conclude by offering independent evidence for an alternative, purely pragmatic resolution of the ontological puzzle. (shrink)

Ontology and the Ambitions of Metaphysics By HofweberThomasOxford University Press, 2016. xvi + 366 pp. £50.00.

This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers (...) an assessment of just how implausible the thesis really is. It argues that the intuitions against the thesis come down to a few special cases, which can be given special treatment. Finally, the paper considers some metaphysical ideas that might surround the thesis. Particularly, it might be maintained that an important variety of realism is incompatible with the thesis. The paper argues that this is not the case. (shrink)

This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers (...) an assessment of just how implausible the thesis really is. It argues that the intuitions against the thesis come down to a few special cases, which can be given special treatment. Finally, the paper considers some metaphysical ideas that might surround the thesis. Particularly, it might be maintained that an important variety of realism is incompatible with the thesis. The paper argues that this is not the case. (shrink)

This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...) the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations. (shrink)

The models of contingency in what propositions, properties and relations there are developed in Part 1 are related to models of contingency in what propositions there are due to Robert Stalnaker. It is shown that some but not all of the classes of models of Part 1 agree with Stalnaker’s models concerning the patterns of contingency in what propositions there are they admit. Further structural connections between the two kinds of models are explored.

Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists cannot (...) express what is communicated using various instances of talk of ‘possible things’, such as ‘there are uncountably many possible stars’. (shrink)

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...) are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all. (shrink)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

This paper is an investigation of the general logic of "identifications", claims such as 'To be a vixen is to be a female fox', 'To be human is to be a rational animal', and 'To be just is to help one's friends and harm one's enemies', many of which are of great importance to philosophers. I advocate understanding such claims as expressing higher-order identity, and discuss a variety of different general laws which they might be thought to obey. [New version: (...) Nov. 4th, 2016]. (shrink)

Many significant problems in metaphysics are tied to ontological questions, but ontology and its relation to larger questions in metaphysics give rise to a series of puzzles that suggest that we don't fully understand what ontology is supposed to do, nor what ambitions metaphysics can have for finding out about what the world is like. Thomas Hofweber aims to solve these puzzles about ontology and consequently to make progress on four metaphysical debates tied to ontology: the philosophy of arithmetic, the (...) metaphysics of ordinary objects, the problem of universals, and the question of whether the fact-like aspect of reality is independent of us. Crucial parts of the proposed solution involve considerations about quantification and its relationship to ontology, the place of reference in natural languages, the relationship between syntactic form and focus, whether there could be any ineffable facts, and others. (shrink)

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. (shrink)

Existence questions have been topics for heated debates in metaphysics, but this book argues that they can often be answered easily, by trivial inferences from uncontroversial premises. This 'easy' approach to ontology leads to realism about disputed entities, and to the view that metaphysical disputes about existence questions are misguided.

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

A sense of unity -- Basic objects : a reply to Xu -- Objectivity without objects -- The vagueness of identity -- Quantifier variance and realism -- Against revisionary ontology -- Comments on Theodore Sider's four dimensionalism -- Sosa's existential relativism -- Physical-object ontology, verbal disputes, and common sense -- Ontological arguments : interpretive charity and quantifier variance -- Language, ontology, and structure -- Ontology and alternative languages.

My focus here will be Rudolf Carnap’s views on ontology, as these are presented in the seminal “Empiricism, Semantics and Ontology” (1950). I will first describe how I think Carnap’s distinction between external and internal questions is best understood. Then I will turn to broader issues regarding Carnap’s views on ontology. With certain reservations, I will ascribe to Carnap an ontological pluralist position roughly similar to the positions of Eli Hirsch and the later Hilary Putnam. Then I turn to some (...) interrelated arguments against the pluralist view. The arguments are not demonstrative. Some possible escape routes for the pluralist are outlined. But I think the arguments constitute a formidable challenge. There should be serious doubt as to whether the pluralist view, as it emerges after discussion of these arguments, will be worth defending. Moreover, there is an alternative ontological view which equally well subserves the motivations underlying ontological pluralism. (shrink)

The basic question of ontology is “What exists?”. The basic question of metaontology is: are there objective answers to the basic question of ontology? Here ontological realists say yes, and ontological anti-realists say no. (Compare: The basic question of ethics is “What is right?”. The basic question of metaethics is: are there objective answers to the basic question of ethics? Here moral realists say yes, and moral anti-realists say no.) For example, the ontologist may ask: Do numbers exist? The Platonist (...) says yes, and the nominalist says no. The metaontologist may ask: is there an objective fact of the matter about whether numbers exist? The ontological realist says yes, and the ontological anti-realist says no. Likewise, the ontologist may ask: Given two distinct entities, when does a mereological sum of those entities exist? The universalist says always, while the nihilist says never. The metaontologist may ask: is there an objective fact of the matter about whether the mereological sum of two distinct entities exists? The ontological realist says yes, and the ontological anti-realist says no. Ontological realism is often traced to Quine (1948), who held that we can determine what exists by seeing which entities are endorsed by our best scientific theory of the world. In recent years, the practice of ontology has often presupposed an ever-stronger ontological realism, and strong versions of ontological realism have received explicit statements by Fine (this volume), Sider (2001; this volume), van Inwagen (1998; this volume), and others. (shrink)

Modal logicism is the view that a metaphysical possibility is just a non-absurd way for the world to be. I argue that modal logicists should see metaphysical possibility as "open ended'': any given possibilities can be used to characterize further possibilities. I then develop a formal framework for modal languages that is a good fit for the modal logicist and show that it delivers some attractive results.