Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

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.

This is my entry on natural language ontology in the Stanford Encyclopedia of Philosophy.

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...) number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

Call a quantifier ‘unrestricted’ if it ranges over absolutely all objects. Arguably, unrestricted quantification is often presupposed in philosophical inquiry. However, developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. It has been argued that using a type theory as framework for our semantic theory provides a resolution of this problem, at least if a broadly Fregean interpretation of type theory is assumed. However, (...) the intelligibility of this interpretation has been questioned. In this paper I introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification. This alternative emerges very naturally by reflecting on the features on which the type-theoretic solution of the problem of unrestricted quantification relies. Although this alternative theory is formulated in a non-classical logic, it preserves the deductive strength of classical strict type theory in a natural way. The ideas developed in this paper make crucial use of Russell’s notion of range of significance. (shrink)

Prior’s puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of “the proposition that P” for “that P” within the complements of many propositional attitude verbs is invalid. I show that Prior’s puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of grammatical positions, (...) rather than merely in the complements of propositional attitude verbs. The generalized puzzle shows that a range of proposed solutions to the original puzzle fail, or are radically incomplete, and also reveals the connections between Prior’s puzzle and debates over the nature of semantic types and higher-order quantification. I go on to develop a novel, higher-order solution to the generalized form of the puzzle, and I argue that this higher-approach is superior to its first-order alternatives. (shrink)

2020 update of the entry "Properties".

Three different notions of concepts are outlined: one derives from Leibniz, while the other two derive from Frege. The Leibnizian notion is the subject of his "calculus of concepts" (which is really an algebra). One notion of concept from Frege is what we would call a "property", so that when Frege says "x falls under the concept F", we would say "x instantiates F" or "x exemplifies F". The other notion of concept from Frege is that of the notion of (...) sense, which played various roles within Frege's theory. This notion of concept can be generalized and, as such, accounts for our intuitive talk of "x's concept of ...", where the ellipsis can be filled in with a name for individual, a property, or a relation, etc. After outlining these three notions, I then discuss how (axiomatic) object theory offers a distinct, precise regimentation of each of the three notions. (shrink)

Legal philosophers make a number of bold, contentious claims about the nature of law. For instance, some claim that law necessarily involves coercion, while others disagree. Some claim that all law enjoys presumptive moral validity, while others disagree. We can see these claims in at least three, mutually exclusive ways: (1) We can see them as descriptions of law’s nature (descriptivism), (2) we can see them as expressing non-descriptive attitudes of the legal philosophers in question (expressivism), or (3) we can (...) see them as practical claims about how we should view law or order our society (pragmatism). This paper argues that we should understand these claims in the pragmatist way, as claims about how we should view law or order society. (shrink)

Although there is no consensus about what kinds are, there is a common understanding that kinds can be regarded as collections of objects that share certain properties. What these properties exactly are is often left unspecified. This paper explores the semantics of ad hoc kind-referring terms, where the determination of the relevant set of shared properties does not rely on “natural” properties or world knowledge. Rather, information provided by a nominal modifier, typically a relative clause, is used to impute the (...) required regular behavior on the kind-referring NP. Building on Carlson’s disjointness condition, I show that we can not only account for the ubiquity of these expressions, but we can also extend the analysis to other constructions that have traditionally not been taken to be kind referring, such as Amount and Degree Relative constructions. (shrink)

I investigate when we can (rationally) have attitudes, and when we cannot. I argue that a comprehensive theory must explain three phenomena. First, being related by descriptions or names to a proposition one has strong reason to believe is true does not guarantee that one can rationally believe that proposition. Second, such descriptions, etc. do enable individuals to rationally have various non-doxastic attitudes, such as hope and admiration. And third, even for non-doxastic attitudes like that, not just any description will (...) allow it. I argue that we should think of attitude formation like we do (practical) choices among options. I motivate this view linguistically, extending "relevant alternatives'' theories of the attitudes to both belief and to the other, non-doxastic attitudes. Given a natural principle governing choice, and some important differences between doxastic and non-doxastic "choices'', we can explain these puzzling phenomena. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

The aim of natural language ontology is to uncover the ontological categories and structures that are implicit in the use of natural language, that is, that a speaker accepts when using a language. This article aims to clarify what exactly the subject matter of natural language ontology is, what sorts of linguistic data it should take into account, how natural language ontology relates to other branches of metaphysics, in what ways natural language ontology is important, and what may be distinctive (...) of the ontological categories and structures reflected in natural language. (shrink)

Revised and reprinted; originally in Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer 133-251. -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category of entity, (...) are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

In the paper a theory of relevant properties is developed. The theory permits us to distinguish between properties that are relevant to an object and the properties that are irrelevant to it. Predication is meaningful only if a property is relevant to an object. On the base of introducing a special negative type of predication as opposed to usual sentential negation, a new notion of generalization for properties is defined. Context-free, as weIl as context-depended relevance of properties are considered.

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...) is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.

The paper is in two parts. In Part I, a semantics for embedded and query uses of interrogatives is put forward, couched within a situation semantics framework. Unlike many previous analyses,questions are not reductively analysed in terms of their answers. This enables us to provide a notion of ananswer that resolves a question which varies across contexts relative to parameters such as goals and inferential capabilities. In Part II of the paper, extensive motivation is provided for an ontology that distinguishes (...) propositions, questions, and facts, while at the same time the semantics provided captures an important commonality between questions and propositions: factsprove propositions andresolve questions. This commonality is exploited to provide an explanation for why predicates such as know carry presuppositions such as factivity and for a novel account of the behaviour of adverbially modified predicates with interrogative, declarative and fact-nominal arguments. (shrink)

Standard first-order logic plus quantifiers of all finite orders ("SFOLω") faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOLω models. The typed structure of SFOLω models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is (...) removed. The models of this class permit definitions of the quantifiers which allow a desirable flexibility in fixing the domain of quantification. Certain SFOLω type restrictions are thereby avoided. The resulting models of English validate all of the standard first-order logical truths and are free of the four deficiencies of SFOLω models. (shrink)

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional functions, crucial fine-grained intensional distinctions would (...) be lost. (shrink)

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses on: (1) (...) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes. (shrink)

This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is also (...) used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality. (shrink)

In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in (...) formal metaphysics by Williamson and Hale. There is a contingent Liar that has been taken to be a problem for type theory. But this is because this Liar has been presented without an explicit recourse to a truth predicate. Thus, type theory could avoid this paradox by incorporating such a predicate and accepting an appropriate theory of truth. There is however a contingent paradox of predication that more clearly undermines the viability of type theory. It is then suggested that a type-free property theory is a better option. One can pursue it, by generalizing the revision-theoretic approach to predication, as it has been done by Orilia with his system P*, based on T*. Although Gupta and Belnap do not explicitly declare a preference for T# over T*, they show that the latter has some advantages, such as the recovery of intuitively acceptable principles concerning truth and a better reconstruction of informal arguments involving this notion. A type-free system based on T# rather than T* extends these advantages to predication and thus fares better than P* in the intended applications of property theory. (shrink)

‘Drawing Metaphysical Consequences from a T-theory’. Pubblicato come quarto capitolo di Semantics, Tense, and Time: An Essay in the Metaphysics of Natural Language, Cambridge, Massachussetts, MIT Press, 1999. Per gentile concessione dell’autore e dell’editore. Traduzione italiana di Carlotta Pavese. L’idea che lo studio del linguaggio possa illuminare certe questioni metafisiche ha radici lontane nella storia della filosofia. Questa assunzione sembra già operante ai tempi del filosofo pre-soc...

This paper is devoted to the study of bare nominal arguments (i.e., determinerless NPs occurring in canonical argumental positions) from a crosslinguistic point of view. It is proposed that languages may vary in what they let their NPs denote. In some languages (like Chinese), NPs are argumental (names of kinds) and can thus occur freely without determiner in argument position; in others they are predicates (Romance), and this prevents NPs from occurring as arguments, unless the category D(eterminer) is projected. Finally, (...) there are languages (like Germanic or Slavic) which allow both predicative and argumental NPs; these languages, being the ‘union’ of the previous two types, are expected to behave like Romance for certain aspects of their nominal system (the singular count portion) and like Chinese for others (the mass and plural portions). This hypothesis (the ‘Nominal Mapping Parameter’) is investigated not just through typological considerations, but also through a detailed contrastive analysis of bare arguments in Germanic (English) vs. Romance (Italian). Some general consequences of this view, which posits a limited variation in the mapping from syntax into semantics, for current theories of Universal Grammar and acquisition are considered. (shrink)

It is almost universally acknowledged that first-order logic (FOL), with its clean, well-understood syntax and semantics, allows for the clear expression of philosophical arguments and ideas. Indeed, an argument or philosophical theory rendered in FOL is perhaps the cleanest example there is of “representing philosophy”. A number of prominent syntactic and semantic properties of FOL reflect metaphysical presuppositions that stem from its Fregean origins, particularly the idea of an inviolable divide between concept and object. These presuppositions, taken at face value, (...) reflect a significant metaphysical viewpoint, one that can in fact hinder or prejudice the representation of philosophical ideas and arguments. Philosophers have of course noticed this and have, accordingly, sought to alter or extend traditional FOL in novel ways to reflect a more flexible and egalitarian metaphysical standpoint. The purpose of this paper, however, is to document and discuss how similar “adaptations” to FOL—culminating in a standardized framework known as Common Logic —have evolved out of the more practical and applied encounter of FOL with the problem of representing, sharing, and reasoning upon information on the World Wide Web. (shrink)

In this paper I present a formal language in which complex predicates stand for properties and relations, and assignments of denotations to complex predicates and assignments of extensions to the properties and relations they denote are both homomorphisms. This system affords a fresh perspective on several important philosophical topics, highlighting the algebraic features of properties and clarifying the sense in which properties can be represented by their extensions. It also suggests a natural modification of current logics of properties, one in (...) which some complex predicates stand for properties while others do not. (shrink)

Russell’s type theory has been the standard property theory for years, relying on rigid type distinctions at the grammatical level to circumvent the paradoxes of predication. In recent years it has been convincingly argued by Bealer, Cochiarella, Turner and others that many linguistic and ontological data are best accounted for by using a type-free property theory. In the spirit of exploring alternatives and “to have as many opportunities as possible for theory comparison”, this paper presents another type-free property theory, to (...) be called P*, intended for applications in Montague-style natural language semantics and formal ontology. The theory is philosophically grounded on Gupta’s and Belnap’s revision theory of definitions and its basic idea is viewing predication (exemplification) as a ‘circular concept’ that can be captured by circular definitions. The paper has the following fourteen sections: (1) Introduction; (2) Formal type-free property theory; (3) Applying RTD [revision theory of definitions] to exemplification; (4) The system P*; (5) Some features of P*; (6) A comparison with Turner’s system; (7) Entailment and P*; (8) P* and natural language semantics; (9) Noun phrases; (10) The need for type-freedom in semantics; (11) Arithmetic in P*; (12) Arithmetic in PN*; (13) Complexity of P*; (14) Conclusion, and acknowledgments. (shrink)

In this paper, an objective conception of contexts based loosely upon situation theory is developed and formalized. Unlike subjective conceptions, which take contexts to be something like sets of beliefs, contexts on the objective conception are taken to be complex, structured pieces of the world that (in general) contain individuals, other contexts, and propositions about them. An extended first-order language for this account is developed. The language contains complex terms for propositions, and the standard predicate "ist" that expresses the relation (...) that holds between a context and a proposition just in case the latter is true in the former. The logic for the objective conception features a global classical predicate calculus, a local logic for reasoning within contexts, and axioms for propositions. The specter of paradox is banished from the logic by allowing "ist" to be nonbivalent in problematic cases: it is not in general the case, for any context c and proposition p, that either ist(c,p) or ist(c, ¬p). An important representational capability of the logic is illustrated by proving an appropriately modified version of an illustrative theorem from McCarthy's classic Blocks World example. (shrink)

In an attempt to accommodate natural language phenomena involving nominalization and self-application, various researchers in formal semantics have proposed abandoning the hierarchical type system which Montague inherited from Russell, in favour of more flexible type regimes. We briefly review the main extant proposals, and then develop a new approach, based semantically on Aczel's notion of Frege structure, which implements a version ofsubsumption polymorphism. Nominalization is achieved by virtue of the fact that the types of predicative and propositional complements are contained (...) in the type of individuals. Russell's paradox is avoided by placing a type-constraint on lambda-abstraction, rather than by restricting comprehension. (shrink)

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...) The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth. (shrink)

In their recent article ‘Resolving Frege’s other Puzzle’ Eric Snyder, Richard Samuels, and Stewart Shapiro defend a semantic type-shifting solution to Frege’s other Puzzle and criticize my own cognitive type-shifting solution. In this article I respond to their criticism and in turn point to several problems with their preferred solution. In particular, I argue that they conflate semantic function and semantic value, and that their proposal is neither based on general semantic type-shifting principles nor adequate to the data.

If I say that Alice is everything Oscar hopes to be, I seem to be quantifying over properties. That suggestion faces an immediate difficulty, however: though Alice may be wise, she surely is not the property of being wise. This problem can be framed in terms of a substitution failure: if a predicate like ‘happy’ denoted a property, we would expect pairs like ‘Oscar is happy’ and ‘Oscar is the property of being happy’ to be equivalent, which they clearly are (...) not. I argue that a Fregean response that draws a distinction between objects and concepts faces serious difficulties, and that a syntactic solution to the substitution problem likewise fails. I propose to account for the substitution failure by instead distinguishing different ways that expressions can stand for properties: whereas ‘the property of being happy’ refers to a property, ‘happy’ expresses or ascribes that property. I go on to compare this view to proposals made by Wright and Liebesman, and end by drawing out a consequence my proposal has for a debate about the ontological commitments of predicatively quantified sentences. (shrink)

We may wonder about the status of logical accounts of the meaning of language. When does a particular proposal count as a theory? How do we judge a theory to be correct? What criteria can we use to decide whether one theory is “better” than another? Implicitly, many accounts attribute a foundational status to set theory, and set-theoretic characterisations of possible worlds in particular. The goal of a semantic theory is then to find a translation of the phenomena of interest (...) into a set-theoretic model. Such theories may be deemed to have “explanatory” or “predictive” power if a mapping can found into expressions of set-theory that have the appropriate behaviour by virtue of the rules of set-theory (for example Montague 1973; Montague1974). This can be contrasted with an approach in which we can help ourselves to “new” primitives and ontological categories, and devise logical rules and axioms that capture the appropriate inferential behaviour (as in Turner 1992). In general, this alternative approach can be criticised as being mere “descriptivism”, lacking predictive or explanatory power. Here we will seek to defend the axiomatic approach. Any formal account must assume some normative interpretation, but there is a sense in which such theories can provide a more honest characterisation (cf. Dummett 199). In contrast, the set-theoretic approach tends to conflate distinct ontological notions. Mapping a pattern of semantic behaviour into some pre-existing set-theoretic behaviour may lead to certain aspects of that behaviour being overlooked, or ignored (Chierchia & Turner 1988; Bealer 1982). Arguments about the explanatory and predictive power of set-theoretic interpretations can also be questioned (see Benacerraf 1965, for example). We aim to provide alternative notions for evaluating the quality of a formalisation, and the role of formal theory. Ultimately, claims about the methodological and conceptual inadequacies of axiomatic accounts compared to set-theoretic reductions must rely on criteria and assumptions that lie outside the domain of formal semantics as such. (shrink)

This paper embeds a theory of proper names in a general approach to singular reference based on type‐free property theory. It is proposed that a proper name “N” is a sortal common noun whose meaning is essentially tied to the linguistic type “N”. Moreover, “N” can be singularly referring insofar as it is elliptical for a definite description of the form the “N” Following Montague, the meaning of a definite description is taken to be a property of properties. The proposed (...) theory fulfils the major desiderata stemming from Kripke's works on proper names. (shrink)

Terms such as 'wisdom' or 'happiness' are commonly held to refer to abstract objects that are properties. On the basis of a greater range of linguistic data and with the support of some ancient and medieval philosophical views, I argue that such terms do not stand for objects, but rather for kinds of tropes, entities that do not have the status of objects, but only play a role as semantic values of terms and as arguments of predicates. Such ‘non-objects’ crucially (...) differ from objects in that they are not potential bearers of properties. (shrink)

This volume is about abstract objects and the ways we refer to them in natural language. Asher develops a semantical and metaphysical analysis of these entities in two stages. The first reflects the rich ontology of abstract objects necessitated by the forms of language in which we think and speak. A second level of analysis maps the ontology of natural language metaphysics onto a sparser domain--a more systematic realm of abstract objects that are fully analyzed. This second level reflects the (...) commitments of real metaphysics. The models for these commitments assign truth conditions to natural language discourse. Annotation copyright by Book News, Inc., Portland, OR. (shrink)

Among modal claims, claims that involve the notions of broadly logical possibility and necessity, one that seems almost trivial is this: that if some proposition is possible, then it is possibly true. However, there is an argument, due in its essentials to the medieval philosopher and logician Jean Buridan, to the effect that this seemingly trivial claim is, in fact, untrue. ;Briefly put, the argument is this. Let Q be the proposition that Quine does not exist. Since Quine's existence is (...) contingent, Q is possible. But, propositions are ontologically dependent upon their constituents, and Quine is a constituent of Q. So, necessarily, were Quine not to exist, neither would Q exist. And, a necessary condition of a proposition's being true is that it exist. Hence, there are propositions, such as Q, that are possible, but not possibly true. I call this conclusion, together with certain other similar claims, 'Buridanism'. ;My main topic is the evaluation of the argument for Buridanism, and the exploration of the consequences of Buridanism for modalist theories of possible worlds and for modal logic. I begin by examining the two crucial premises in the argument for Buridanism: N-dependency, according to which propositions expressed by sentences containing proper names are singular propositions that depend ontologically upon the referents of those names, and Buridan's Thesis, according to which a proposition can be neither necessary, nor possible, nor true, unless it exists. ;Robert Adams has argued that accepting Buridanism forces us to revise the modalist conception of possible worlds as maximal and consistent propositions or sets of propositions. I show that this is not the case, and provide an analysis of a proposition's being true relative to a world that allows us to maintain the modalist account while embracing Buridanism. ;Standard systems of quantified modal logic are prone to several related problems that I refer to as the problems of contingency. These systems often include as theorems formulas that seem to presuppose that everything that exists, exists necessarily. I develop a system of modal logic, BML, based upon Buridanism, that is able to overcome these difficulties. (shrink)