Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Hybrid contingentism combines first-order contingentism, the view that it is contingent what individuals there are, with higher-order necessitism, the view that it is non-contingent what properties and propositions there are (where these are conceived as entities in the range of appropriate higher-order quantifiers). This combination of views avoids the most delicate problems afflicting alternative contingentist positions while preserving the central contingentist claim that ordinary, concrete entities exist contingently. Despite these attractive features, hybrid contingentism is usually faced with rejection. The main (...) reason for this is an objection that crucially involves haecceitistic properties, properties such as being identical to Plato or being identical to Aristotle. The objection alleges that by accepting the necessary existence of such haecceities, hybrid contingentists incur an explanatory commitment that they are unable to discharge, namely that of explaining how it is that certain haecceities ‘lock onto’ their target individuals even when those individuals are absent. To defend hybrid contingentism against this charge, I first clarify the haecceities objection in several respects and consider, in particular, what notion of explanation the objection is operating with. After arguing that it can be fruitfully understood as a challenge to provide metaphysical grounds for certain haecceity facts, I develop a contingentist response to the objection that draws on recent work on the connection between ground and essence. (shrink)

Propositional contingentism is the view that what propositions there are is a contingent matter—certain propositions ontologically depend on objects which themselves only contingently exist. Possible worlds are, loosely, complete ways the world could have been. That is to say, the ways in which everything in its totality could have been. Propositional contingentists make use of possible worlds frequently. However, a neglected, but important, question concerns whether there are any notions of worlds which are both theoretically adequate and consistent with propositional (...) contingentism. Some notion of a possible world is adequate if the systematic connection between, at least, possibility and truth at some possible world holds. Here, I argue that no adequate notion of a possible world is available to at least those who subscribe to one natural formulation of propositional contingentism. I also show that this result contrasts with a simple and adequate definition of a possible world available to the necessitist—those who hold that necessarily everything necessarily exists. (shrink)

This paper outlines a defense of hybrid contingentism: that it is contingent which individuals there are, but not contingent what properties there are. Critics pursue two main lines of complaint. First, that the hybrid contingentist’s treatment of haecceitistic properties is metaphysically mysterious, and second, that hybrid contingentism involves an unjustified asymmetry in the associated modal logic. I suggest that these complaints may be too quick, at least in the setting of higher-order metaphysics. It is not at all obvious whether and (...) to what extent we should expect particular "symmetries" across the orders, and so whether (as Williamson (2013) argues) “the default preference is for a uniform metaphysics, on which being is contingent at all orders or none.”. (shrink)

This paper investigates the connection between two recent trends in philosophy: higher-orderism and conceptual engineering. Higher-orderists use higher-order quantifiers (in particular quantifiers binding variables that occupy the syntactic positions of predicates) to express certain key metaphysical doctrines, such as the claim that there are properties. I argue that, on a natural construal, the higher-orderist approach involves an engineering project concerning, among others, the concept of existence. I distinguish between a modest construal of this project, on which it aims at engineering (...) higher-order analogues of the familiar notion of first-order existence, and an ambitious construal, on which it additionally aims at engineering a broadened notion of existence that subsumes first-order and higher-order existence. After identifying a substantial problem for the ambitious project, I investigate a possible response which is based on adopting a cumulative type theory as the background higher-order logic. While effective against the problem at hand, this strategy turns out to undermine a major reason to embrace higher-orderism in the first place, namely the idea that higher-orderism dissolves a range of otherwise intractable debates in metaphysics. Higher-orderists are therefore best advised to pursue their engineering project on the modest variant and against the background of standard type theory. (shrink)

Critiques the higher-order hyperintensional theory developed by Cian Dorr in "To be F as to be G" as an exercise in overfitting.

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.

Maureen Donnelly has recently argued that directionalism, the view that relations have a direction, applying to their relata in an order, is unable to properly treat certain symmetric relations. She alleges that it must count the application of such a relation to an appropriate number of objects in a given order as distinct from its application to those objects in any other ordering of them. I reply by showing how the directionalist can link the application conditions of any fixed arity (...) relation, no matter its arity or symmetry, and its converse(s) in such a way that directionalism will yield the correct ways in which it can apply. I thus establish that directionalism possesses the same advantage Donnelly's own account of relations, relative positionalism, has over traditional positionalist accounts of relations, which do not properly treat symmetric relations. I then note some advantages that directionalism has over its closest competitors. This includes Donnelly's relative positionalism, since directionalism is not, like relative positionalism, committed to the involvement of relative properties in every irreducibly relational claim. I close by conceding that, as Donnelly notes, directionalism is committed to the primitive relation of order-sensitive relational application. But I don't find this notion as mysterious as Donnelly does. I conclude that, even if one construes this feature of directionalism as a drawback, the two views are at worst at a draw, other things being equal, since this drawback is mitigated by the advantage directionalism has over relative positionalism. (shrink)

On a highly influential way to think of modality, that I call ‘relationalism’, the modality of a state is explained by its being composed of properties, and these properties being related by a higher-order and primitively modal relation. Examples of relationalism are the Dretske-Tooley-Armstrong account of natural necessity, many dispositional essentialist views, and Wang’s incompatibility primitivism. I argue that relationalism faces four difficulties: that the selection between modal relations is arbitrary, that the modal relation cannot belong to any logical order, (...) that to explain how the modal relation can relate properties of different adicities additional ideological complexity has to be introduced, and that not all modal constraints are relational. From the discussion, I will extract desiderata for a successor theory of modality. (shrink)

Higher‐order metaphysicians take facts to be higher‐order beings, i.e., entities in the range of irreducibly higher‐order quantifiers. In this paper, I investigate the impact of this conception of facts on the debate about the reality of tense. I identify two major repercussions. The first concerns the logical space of tense realism: on a higher‐order conception of facts, a prominent version of tense realism, dynamic absolutism, turns out to conflict with the laws of (higher‐order tense) logic. The second concerns our understanding (...) of the positions occupying this logical space: on a higher‐order conception of facts, an attractive interpretation of the central tense realist notion of ‘facts constituting reality’ becomes unavailable. I discuss these results in the context of the more general project of higher‐order metaphysics and the (meta)metaphysics of time, drawing out their implications for the nature of the disputes both between realists and anti‐realists about tense and between different tense realist factions. (shrink)

Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.

Special quantifiers are quantifiers like 'something', 'everything', and 'several things'. They are special both semantically and syntactically and play quite an important role in philosophy, in discussions of ontological commitment to abstract objects, of higher-order metaphysics, and of the apparent need for propositions. This paper will review and discuss in detail the syntactic and semantic peculiarities of special quantifiers and show that they are incompatible with substitutional and higher-order analyses that have recently been proposed. It instead defends and develops in (...) formal detail a semantic analysis of special quantifiers as nominalizing quantifiers. On this analysis, special quantifiers involve both singular objectual quantification and implicit on non-singular (higher-order, plural, or mass) quantification. The analysis rests on a range of recent insights and proposals in generative syntactic theory, in particular the recognition of '–thing' as a light noun and a potential classifier as well as recent views of the decomposition of attitudinal and locutionary verbs in syntax. (shrink)

Commitment to sparseness amounts to the idea that there is an objective, worldly privileging of certain properties over others that makes the privileged properties suited to play certain roles, and is responsible for their playing such roles. In this chapter I offer a brief, opinionated overview of sparseness. I begin by examining a set of problems that I call “problems of abundance”, which generate canonical motivations for sparseness. I then survey some influential approaches to sparseness and the roles that they (...) attribute to sparse properties, noting that on most approaches sparse properties are deeply connected to inquiry. Finally I consider some problems for sparseness, focusing on the purported connections between sparseness and inquiry, particularly in philosophy of science and inquiry into the social world. (shrink)

Commitment to sparseness amounts to the idea that there is an objective, worldly privileging of certain properties over others that makes the privileged properties suited to play certain roles, and is responsible for their playing such roles. In this chapter I offer a brief, opinionated overview of sparseness. I begin by examining a set of problems that I call “problems of abundance”, which generate canonical motivations for sparseness. I then survey some influential approaches to sparseness and the roles that they (...) attribute to sparse properties, noting that on most approaches sparse properties are deeply connected to inquiry. Finally I consider some problems for sparseness, focusing on the purported connections between sparseness and inquiry, particularly in philosophy of science and inquiry into the social world. (shrink)

Substance dualism is the view that there are two fundamentally different kinds of substances: physical and mental. By contrast, according to property dualism there is only one kind of substance (physical) but two fundamentally different kinds of properties: physical and mental. Property nominalism is the view that there are neither repeatable nor non-repeatable fundamentally predicable entities (i.e. neither universals nor tropes) and that things being a certain way or being related in a certain way must ultimately be accounted for in (...) terms of concrete particulars. In this paper, we consider a number of different kinds of property nominalism and argue that none of them sits well with property dualism. We pay special attention to the question of what it could mean for a property to count as mental given different nominalistic accounts of properties. Our conclusion is that property nominalism and property dualism are not a stable match. This is surprising, since property dualism has usually been understood as a thesis that is neutral about the nature of fundamental ontological categories and the relation between them. (shrink)

This paper proposes and partially defends a novel philosophy of arithmetic—finitary upper logicism. According to it, the natural numbers are finite cardinalities—conceived of as properties of properties—and arithmetic is nothing but higher-order modal logic. Finitary upper logicism is furthermore essentially committed to the logicality of finitary plenitude, the principle according to which every finite cardinality could have been instantiated. Among other things, it is proved in the paper that second-order Peano arithmetic is interpretable, on the basis of the finite cardinalities’ (...) conception of the natural numbers, in a weak modal type theory consisting of the modal logic $\mathsf {K}$, negative free quantified logic, a contingentist-friendly comprehension principle, and finitary plenitude. By replacing finitary plenitude for the axiom of infinity this result constitutes a significant improvement on Russell and Whitehead’s interpretation of second-order Peano arithmetic, itself based on the finite cardinalities’ conception of the natural numbers. (shrink)

This paper gives a perspectival overview of the semantics of potential property-referring terms and presents new and surprising generalizations about explicit property-referring terms like 'the property of being wise', which raise fundamental issues regarding ontology and learnability and a core-periphery distinction in natural language ontology.

Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...) intensional predicates and argued for a Nominalization Theory of special quantifiers. In this paper, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for higher-order and substitutional analyses of special quantifiers. (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.