This volume explores the use of higher-order logics in metaphysics. Seventeen original essays trace the development of higher-order metaphysics, discuss different ways in which higher-order languages and logics may be used, and consider their application to various central topics of metaphysics.

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate a (...) number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

This paper explores the impact of quantification into predicate position on the metaphysics of properties, arguing that two familiar debates about properties are fundamentally altered by recasting them in a second-order setting. Two theories of properties are outlined, differing over whether the existence of properties is expressed using first-order or second-order quantifiers. It is argued that the second-order theory: provides good reason to regard debate about the locations of properties as contentless; resolves debate about whether properties are particulars or universals (...) in favour of universals. (shrink)

There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception of (...) propositions, concerning their role in natural language semantics and apparent quantification over propositions within natural language. It will emerge that even if these arguments are sound, there need be no deep question about Quinean propositions’ true nature, contrary to much recent work on the metaphysics of propositions. (shrink)

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of (...) predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory. (shrink)

This chapter discusses ontological commitment to properties, understood as ontological correlates of predicates. We examine the issue in four metaontological settings, beginning with an influential Quinean paradigm on which ontology concerns what there is. We argue that this naturally but not inevitably avoids ontological commitment to properties. Our remaining three settings correspond to the most prominent departures from the Quinean paradigm. Firstly, we enrich the Quinean paradigm with a primitive, non-quantificational notion of existence. Ontology then concerns what exists. We argue (...) that this strengthens the Quinean case against ontological commitment to properties while also newly distinguishing between stronger and weaker forms of nominalism. Secondly, we enrich the Quinean paradigm with the ideology of fundamentality. Ontology then centrally concerns what’s fundamental. We argue that this leaves ontological commitment to properties wide open although Bradleyan regress threatens. Thirdly, we enrich the Quinean paradigm with primitive higher-order quantifiers. Ontology then expands to concern what there higher-order is and what there first-order is. We argue that this naturally but not inevitably incurs ontological commitment to properties. (shrink)

This paper uses the resources of higher-order logic to articulate a Fregean conception of predicate reference, and of word-world relations more generally, that is immune to the concept horse problem. The paper then addresses a prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright.

This paper explores the view that the vocabulary of metaphysical fundamentality is opaque, using Sider’s theory of structure as a motivating case study throughout. Two conceptions of fundamentality are distinguished, only one of which can explain why the vocabulary of fundamentality is opaque.

Some views articulate reality's hierarchical structure using relations from the fundamental to representations of reality. Other views instead use relations from the fundamental to constituents of non-representational reality. This paper argues against the first kind of view.

Unger has recently argued that if you are the only thinking and experiencing subject in your chair, then you are not a material object. This leads Unger to endorse a version of Substance Dualism according to which we are immaterial souls. This paper argues that this is an overreaction. We argue that the specifically Dualist elements of Unger’s view play no role in his response to the problem; only the view’s structure is required, and that is available to Unger’s opponents. (...) We outline one such non-Dualist view, suggest how to resolve the dispute, respond to some objections, and argue that ours is but one of many views that survive Unger’s challenge. All these views are incompatible with microphysicalism. So Unger’s discussion does contain an insight: if you are the only conscious subject in your chair, then microphsyicalism is false. Unger’s mistake was to infer Substance Dualism from this; for microphysicalism is not the only alternative to Dualism. (shrink)

This paper evaluates the argument for the contradictoriness of unity, that be- gins Priest’s recent book One. The argument is seen to fail because it does not adequately differentiate between different forms of unity. This diagnosis of the argument’s failure is used as a basis for two consistent accounts of unity. The paper concludes by arguing that reality contains two absolutely fundamental and unanalysable forms of unity, which are in principle presupposed by any theory of anything. These fundamental forms of (...) unity are closely related to the unity of propositions and facts. (shrink)

This chapter outlines a novel solution to the problem of the many, according to which objects can be simultaneously constituted by many collections of particles. To support this proposal, it develops a conception of objects that implies it. On this view, objects are fundamentally subjects of change: the changes an object can survive are explanatorily prior to its constitution. From this perspective, PM arises, and objects are multiply constituted because the changes that objects survive are too coarse-grained to distinguish among (...) the many different collections of particles that are candidates for constituting the relevant object. (shrink)

Central to discussion of supervaluationist accounts of vagueness is the extent to which they require revisions of classical logic and if so, whether those revisions are objectionable. In an important recent Journal of Philosophy article, J.R.G. Williams presents a powerful challenge to the orthodox view that supervaluationism is objectionably revisionary. Williams argues both that supervaluationism is non-revisionary and that even if it were, those revisions would be unobjectionable. This note shows that his arguments for both claims fail.

According to one prominent strand of mainstream logic and metaphysics, identity is indistinguishability. Priest has recently argued that this permits counterexamples to the transitivity and substitutivity of identity within dialetheic metaphysics, even in paradigmatically extensional contexts. This paper investigates two alternative regimentations of indistinguishability. Although classically equivalent to the standard regimentation on which Priest focuses, these alternatives are strictly stronger than it in dialetheic settings. Both regimentations are transitive, and one satisfies substitutivity. It is argued that both regimentations provide better (...) candidates to occupy the core theoretical role of numerical identity than does the standard regimentation. (shrink)

What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show how (...) they diverge under more complex assumptions about the structure of meaningful predication, such as cumulative type theory. We conclude by arguing that maximally strong generality is the more theoretically valuable conception. (shrink)

This paper outlines a heterodox and largely unexplored conception of objecthood according to which the notion of an individual object is a determinable. §1 outlines the view. §2 argues that the view is incompatible with a natural analysis of kind membership and, as a consequence, undermines the Quinean distinction between ontology and ideology. The view is then used to alleviate one source of Quinean hostility towards non-trivial restrictions on de re possibility in §3, and to elucidate Fine’s neo-Aristoteltian, non-modal conception (...) of essence in §4. §5 concludes. (shrink)

This paper evaluates Stalnaker’s recent attempt to outline a realist interpretation of possible worlds semantics that lacks substantive metaphysical commitments. The limitations of his approach are used to draw some more general lessons about the non-representational artefacts of formal representations. Three key conclusions are drawn. Stalnaker’s account of possible worlds semantics’ non-representational artefacts does not cohere with his modal metaphysics. Invariance-based analyses of non-representational artefacts cannot capture a certain kind of artefact. Stalnaker must treat instrumentally those aspects of possible worlds (...) formalism governing the interaction between quantification and modality, under any analysis whatsoever of non-representational artefacts. (shrink)

Unger’s Problem of the Many seems to show that the familiar macroscopic world is much stranger than it appears. From plausible theses about the boundaries of or- dinary objects, Unger drew the conclusion that wherever there seems to be just one cat, cloud, table, human, or thinker, really there are many millions; and likewise for any other familiar kind of individual. In Lewis’s hands, this puzzle was subtly altered by an appeal to vagueness or indeterminacy about the the boundaries of (...) ordinary objects. This thesis examines the relation between these puzzles, and also to the phenomenon of vagueness. Chapter 1 begins by distinguishing Unger’s puzzle of too many candidates from Lewis’s puzzle of borderline, or vague, candidates. We show that, contra Unger, the question of whether this is a genuine, as opposed to merely apparent, distinction cannot be settled without investigation into the nature of vagueness. Chapter 2 begins this investigation by developing a broadly supervaluationist account of vague- ness that is immune to the standard objections. This account is applied to Unger’s and Lewis’s puzzles in chapters 3 and 4. Chapter 3 shows that, despite its popularity, Lewis’s own approach to the puzzles is unsatisfactory: it does not so much solve the puzzle, as prevent us from expressing them; it cannot be extended to objects that self-refer; it is committed to objectionable theses about temporal and modal metaphysics and semantics. Chapter 4 develops a conception of ordinary objects that emphasises the role of identity conditions and change, and uses it to resolve both Problems of the Many. This allows us to diagnose the source of the puzzles: an overemphasis on mereology in contemporary material ontology. (shrink)

This chapter discusses Edgington’s probabilistic, degree-theoretic semantics for vagueness. After describing Edgington’s semantics, her suggestion that it and classical semantics provide non-competing descriptions of a single phenomenon is examined. It is argued that the suggestion should be rejected because classical semantics is incompatible with plausible principles about the relationship between the two frameworks. Edgington also argues that the many degrees assigned to sentences in her semantics are not new truth-values. It is argued that these arguments presuppose a certain non-semantic conception (...) of truth. Although Edgington’s arguments do force a distinction between two theoretical roles typically associated with the notion of truth, one properly semantic and one merely expressive, they do not preclude identification of the many degrees of her probabilistic formalism with new truth-values in the semantic sense. (shrink)

This is a review of "Properties and Propositions: The Metaphysics of Higher-Order Logic" by Robert Trueman. Following an overview of the main themes of the book, I discuss the metaphysical presuppositions of Trueman's Fregean notation for predicate abstraction and evaluate his argument for strict typing.

This is a review of John Heil's "The Universe as We Find It".

This is a critical notice of Tim Button's book "The Limits of Realism".