According to ontological nihilism there are, fundamentally, no individuals. Both natural languages and standard predicate logic, however, appear to be committed to a picture of the world as containing individual objects. This leads to what I call the \emph{expressibility challenge} for ontological nihilism: what language can the ontological nihilist use to express her account of how matters fundamentally stand? One promising suggestion is for the nihilist to use a form of \emph{predicate functorese}, a language developed by Quine. (...) This proposal faces a difficult objection, according to which any theory in predicate functorese will be a notational variant of the corresponding theory stated in standard predicate logic. Jason Turner (2011) has provided the most detailed and convincing version of this objection. In the present paper, I argue that Turner's case for the notational variance thesis relies on a faulty metasemantic principle and, consequently, that an objection long thought devastating is in fact misguided. (shrink)

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His book will be (...) of great interest to philosophers of language, linguists, metaphysicians, and logicians. (shrink)

Chapter Introduction. Syntactic focus theory and the phenomenon of secondary predication The primary goal of this monograph is to examine the interaction of ...

P.F. Strawson's essay traces some formal characteristics of logic and grammar to their roots in general features of thought and experience.

This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle (...) of compositionality, a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (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.

Whether a predicate is a referential expression depends upon what reference is conceived to be. Even if it is granted that reference is a relation between words and worldly items, the referents of expressions being the items to which they are so related, this still leaves considerable scope for disagreement about whether predicates refer. One of Frege's great contributions to the philosophy of language was to introduce an especially liberal conception of reference relative to which it is unproblematic to (...) suppose that predicates are referring expressions. According to this liberal conception, each significant expression in a language has its own distinctive semantic role or power, a power to effect the truth-value of the sentences in which it occurs. (shrink)

We discuss the challenge to truth-conditional semantics presented by apparent shifts in extension of predicates such as ‘red’. We propose an explicit indexical semantics for ‘red’ and argue that our account is preferable to the alternatives on conceptual and empirical grounds.

I argue that maps do not feature predication, as analyzed by Frege and Tarski. I take as my foil (Casati and Varzi, Parts and places, 1999), which attributes predication to maps. I argue that the details of Casati and Varzi’s own semantics militate against this attribution. Casati and Varzi emphasize what I call the Absence Intuition: if a marker representing some property (such as mountainous terrain) appears on a map, then absence of that marker from a map coordinate signifies absence (...) of the corresponding property from the corresponding location. Predication elicits nothing like the Absence Intuition. “F(a)” does not, in general, signify that objects other than a lack property F. On the basis of this asymmetry, I argue that attaching a marker to map coordinates is a different mode of semantic composition than attaching a predicate to a singular term. (shrink)

According to indexical contextualism, the perspectival element of taste predicates and epistemic modals is part of the content expressed. According to nonindexicalism, the perspectival element must be conceived as a parameter in the circumstance of evaluation, which engenders “thin” or perspective-neutral semantic contents. Echoing Evans, thin contents have frequently been criticized. It is doubtful whether such coarse-grained quasi-propositions can do any meaningful work as objects of propositional attitudes. In this paper, I assess recent responses by Recanati, Kölbel, Lasersohn and MacFarlane (...) to the “incompleteness worry”. None of them manages to convince. Particular attention is devoted to an argument by John MacFarlane, which states that if perspectives must be part of the content, so must worlds, which would make intuitively contingent propositions necessary. I demonstrate that this attempt to defend thin content views such as nonindexical contextualism and relativism conflates two distinct notions of necessity, and that radical indexicalist accounts of semantics, such as Schaffer’s necessitarianism, are in fact quite plausible. (shrink)

According to contextualism, the extension of claims of personal taste is dependent on the context of utterance. According to truth relativism, their extension depends on the context of assessment. On this view, when the tastes of a speaker change, so does the truth value of a previously uttered taste claim, and if it is false, the speaker is required to retract it. Both views make strong empirical assumptions, which are here put to the test for the first time in three (...) experiments with over 740 participants. It turns out that the linguistic behaviour of ordinary English speakers is consistent with contextualist predictions and inconsistent with the predictions of the most widely discussed form of truth relativism advocated by John MacFarlane. (shrink)

Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clarification of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predica-tivity have since taken a life of their own, (...) but have also produced a deeper understanding of the notion of predicativity, therefore witnessing the " light logic throws on problems in the foundations of mathematics. " (Feferman 1998, p. vii) Predicativity has been at the center of a considerable part of Feferman's work: over the years he has explored alternative ways of explicating and analyzing this notion and has shown that predicative mathematics extends much further than expected within ordinary mathematics. The aim of this note is to outline the principal features of predicativity, from its original motivations at the start of the past century to its logical analysis in the 1950-60's. The hope is to convey why predicativity is a fascinating subject, which has attracted Feferman's attention over the years. (shrink)

Several philosophers have recently appealed to predication in developing their theories of cognitive representation and propositions. One central point of difference between them is whether they take predication to be forceful or neutral and whether they take the most basic cognitive representational act to be judging or entertaining. Both views are supported by powerful reasons and both face problems. Many think that predication must be forceful if it is to explain representation. However, the standard ways of implementing the idea give (...) rise to the Frege-Geach problem. Others think that predication must be neutral, if we’re to avoid the Frege-Geach problem. However, it looks like nothing neutral can explain representation. In this paper I present a third view, one which respects the powerful reasons while avoiding the problems. On this view predication is forceful and can thus explain representation, but the idea is implemented in a novel way, avoiding the Frege-Geach problem. The key is to make sense of the notion of grasping a proposition as an objectual act where the object is a proposition. (shrink)

In this article I present a disagreement between classical and constructive approaches to predicativity regarding the predicative status of so-called generalised inductive definitions. I begin by offering some motivation for an enquiry in the predicative foundations of constructive mathematics, by looking at contemporary work at the intersection between mathematics and computer science. I then review the background notions and spell out the above-mentioned disagreement between classical and constructive approaches to predicativity. Finally, I look at possible ways of defending the constructive (...) predicativity of inductive definitions. (shrink)

What is predicativity? While the term suggests that there is a single idea involved, what the history will show is that there are a number of ideas of predicativity which may lead to different logical analyses, and I shall uncover these only gradually. A central question will then be what, if anything, unifies them. Though early discussions are often muddy on the concepts and their employment, in a number of important respects they set the stage for the further developments, and (...) so I shall give them special attention. NB. Ahistorically, modern logical and set-theoretical notation will be used throughout, as long as it does not conflict with original intentions. (shrink)

The implicit content indicating location associated with “raining” and other weather predicates is a definite description meaning “the location occupied by x,” where the individual variable “x” can be referential or bound. This position has deleterious consequences for certain varieties of radical contextualism.

The Millian view that the meaning of a proper name is simply its referent has long been popular among philosophers of language. It might even be deemed the orthodox view, despite its well-known difficulties. Fregean and Russellian alternatives, though widely discussed, are much less popular. The Predicate View has not even been taken seriously, at least until fairly recently, but finally, it is receiving the attention it deserves. It says that a name expresses the property of bearing that name. (...) Despite its apparent shortcomings, it has a distinct virtue: It straightforwardly reckons with the fact that proper names generally have multiple bearers and are sometimes used to ascribe the property of bearing a name rather than to refer to a particular bearer of the name. It holds that proper names are much the same as common nouns, both semantically and syntactically, with only superficial differences. They both can be quantified and modified. The main difference, at least in English, is that when used to refer a proper name, unlike a common noun, is not preceded by the definite article. The Predicate View accounts for manifestly predicative uses, but to be vindicated, it needs to do justice to the fact that the main use of proper names is to refer. (shrink)

Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...) investigates how much of Frege’s Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are (...) predicates in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

In the sentence “Tom sits,” the name distinguishes Tom from anyone else, whereas the predicate assimilates Tom, Theaetetus, and anyone else to whom the predicate applies. The name marks out its bearer and the predicate groups together what it applies to. On that ground, his name is used to trace back Tom, and the predi- cate is used to describe and classify what it applies to. In both cases, the semantic link is a direct link between expressions (...) and particulars. Here, I will explore the workings of predicative names along the direction just hinted at. The analysis of predication has been less central to philosophical investigation than that of referen- tial expressions. Some problems have concerned the unity of the sentence—what makes us understand “The baby cries” as a sentence rather than a list of words? Other problems have been what a predicate was taken to stand for, properties and relations, and the understanding of either at the ontological level. If a predicate refers to a property or a relation, yet predication, which is central to our understand- ing of predicates, applies it to one or more particulars. On the background hinted at, these problems might be differently viewed. (shrink)

What in Aristotle corresponds, in whole or (more likely) in part, to our contemporary notion of predication? This paper sketches counterparts in Aristotle's text to our theories of expression and of truth, and on this basis inquires into his treatment of sentences assigning an individual to its kinds. In some recent accounts, the Metaphysics offers a fresh look at such sentences in terms of matter and form, in contrast to the simpler theory on offer in the Categories . I argue (...) that the Metaphysics initiates no change in this regard over the Categories . The point that form is (metaphysically) predicated of matter is a contribution, not to the account of statement predication, but to the analysis of compound material substances. Otherwise put, in our terms Aristotelian form is not - in particular, is not also - a propositional function, but a function from matter to compound material substances. (shrink)

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting (...) them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

In “Properties and the Interpretation of Second-Order Logic” Bob Hale develops and defends a deflationary conception of properties where a property with particular satisfaction conditions actually exists if and only if it is possible that a predicate with those same satisfaction conditions exists. He argues further that, since our languages are finitary, there are at most countably infinitely many properties and, as a result, the account fails to underwrite the standard semantics for second-order logic. Here a more lenient version (...) of the view is explored, which allows for the possibility of countably infinite predicates understood as the product of linguistic supertasks. This enriched deflationist account of properties—the Infinitary Deflationary Conception of Existence—supports the standard semantics for models with countable first-order domains, and allows one to prove the categoricity of the second-order Peano axioms. (shrink)

Kant said that existence is not a predicate and Russell agreed, arguing that a sentence such as ‘The king of France exists’, which seems to attribute existence to the king of France, really has a logical form that is not reflected in the surface structure of the sentence at all. While the surface form of the sentence consists of a subject and a predicate, the underlying logical form, according to Russell, is the formula given in. This formula obviously (...) has no subjectpredicate form and in fact has no single constituent that corresponds to the verb phrase ‘exists’ in the surface sentence. ∃x∀y The importance of Russell’s analysis becomes clear when we consider ‘The king of France does not exist’. If this sentence would attribute non-existence to the king it should entail that there is someone who does not exist, just as ‘Mary doesn’t like bananas’ entails that there is someone who doesn’t like bananas. Thus the idea that all sentences have subject-predicate form has led some philosophers to the view that there are objects that lack existence. This embarrassing position can be avoided once Russell’s analysis is accepted: if ‘The king of France does not exist’ is formalised as the negation of formula, no unwanted consequences follow. (shrink)

In “Value Ascriptions: Rethinking Cognitivism,” Sigrún Svavarsdóttir offers a novel account of the semantic function of evaluative predication, according to which such predicates function as “linguistically encoded classificatory devices.” This short paper raises three questions about Svavarsdóttir’s account: how it relates to familiar sorts of projects in and about semantics, how to understand the nature of “linguistic encoding,” and how to understand the significance of the account’s central use of sets.

In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices (...) as multiple indexing or quantification over times. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...) of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

The-Predicativism is the view that names are count nouns. For example, the meaning of the name ‘Louise’ is roughly the property of being called Louise. Moreover, proponents of this view maintain that names that are ostensibly in argument position of a predicate are covert definite descriptions. In recent years, The-Predicativism has acquired a number of new supporters, mainly Elbourne (), Matushansky (), and Fara (). And while it was pointed out by Kripke () that these kinds of views generally (...) struggle with capturing the rigidity of proper names, these new views are alleged to solve this problem. In this paper I argue that the more recent versions of the view continue to struggle. In particular, I show that the views fail to provide an explanatory and/or empirically adequate analysis of rigidity. My discussions of these views are then supplemented with a general diagnosis of the problem and an explanation of why it is unlikely to be solved by The-Predicativism. (shrink)

In this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. -/- The book discusses the philosophical interpretation of these modal paradoxes and argues that any satisfactory approach (...) to modality will have to face the paradoxes independently of the grammatical category of the modal notion. By systematizing modal principles with respect to their joint consistency and inconsistency, Stern provides an overview of the options and limitations of the predicate approach to modality that may serve as a useful starting point for future work on predicate approaches to modality. Stern also develops a general strategy for constructing philosophically attractive theories of modal notions conceived as predicates. The idea is to characterize the modal predicate by appeal to its interaction with the truth predicate. This strategy is put to use by developing the modal theories Modal Friedman-Sheard and Modal Kripke-Feferman. (shrink)

Over the course of the past ten-plus years, Peter Hanks and Scott Soames have developed detailed versions of Act-Based views of propositions which operate with the notions of reference to objects, indicating properties, predication, and judgment (or entertaining). In this paper I discuss certain foundational aspects of the Act-Based approach having to do with the relations between these notions. In particular, I argue for the following three points. First, that the approach needs both an atomistically understood thin notion of reference, (...) a bare act of thinking of o, as well as a more involved notion, something like making o a target of predication. Second, that the acts of thinking of o and indication of the property of being F are in no sense parts of the acts of predication of being F of o and judgment that o is F. Rather, the former are simply necessary preconditions for the performance of the latter. The acts of predication or judgment are emphatically not structured sequences of separate acts but unities in and of themselves. Finally, that we should understand the Act-Based theorists’ claim that to predicate is to judge as the claim that judgment can be reductively analyzed in terms of predication. Furthermore, while predication is metaphysically a multiple relation between a predicator, a target, and the property predicated, judgment is a monadic property, just one that has propositional content. (shrink)

An exploration of why and how the human competence for predication came to be.

Simple sentences containing predicates like "tasty" and "beautiful" typically suggest that the speaker has first-hand knowledge of the item being evaluated. I consider two explanations of this acquaintance inference: a presuppositional approach and a pragmatic-epistemic approach. The presuppositional approach has a number of virtues, but runs into trouble because the acquaintance inference has a very different projection pattern from that of standard presuppositions. The pragmatic-epistemic approach accounts for the main data discussed in the paper, but faces challenges of its own.

In his 2000 book Logical Properties Colin McGinn argues that predicates denote properties rather than sets or individuals. I support the thesis, but show that it is vulnerable to a type-incongruity objection, if properties are (modelled as) functions, unless a device for extensionalizing properties is added. Alternatively, properties may be construed as primitive intensional entities, as in George Bealer. However, I object to Bealer’s construal of predication as a primitive operation inputting two primitive entities and outputting a third primitive entity. (...) Instead I recommend we follow Pavel Tichý in construing both predication and extensionalization as instances of the primitive operation of functional application. (shrink)

Recently, there’s been a lot of interest in a research program that tries to understand propositional representation in terms of the subject’s performance of sub-propositional mental acts like reference and predication (e. g. Burge 2010, Hanks 2015, Soames 2010, 2015). For example, on one version of the view, for a subject to predicate the property of being a composer of Arvo just is what it is to perform the to the basic propositional act of judging that Arvo is a (...) composer (e. g. Hanks 2015). In this paper I first present my own version of this view and contrast it with alternatives. I then argue that we must clearly separate the thin predication-resultant notion of judging (S(emantic)-judgment) from a much richer notion used in epistemology (E(pistemic)-judgment). The former is just the act of thinking a forceful thought. The latter is the act of making up one’s mind about how things are, a way of concluding theoretical or doxastic deliberation. I argue that these two acts differ in three ways: levels of propositional attitude, objective vs. subjective norms, and the possibility of sub-personal occurrence. (shrink)

This book claims that Aristotle followed an aspect theory of predication.

In this paper, the predicate counterparts, defined both axiomatically and semantically by means of Kripke frames, of the modal propositional logics $\textbf {GL}$, $\textbf {Grz}$, $\textbf {wGrz}$ and their extensions are considered. It is proved that the set of semantical consequences on Kripke frames of every logic between $\textbf {QwGrz}$ and $\textbf {QGL.3}$ or between $\textbf {QwGrz}$ and $\textbf {QGrz.3}$ is $\Pi ^1_1$-hard even in languages with three (sometimes, two) individual variables, two (sometimes, one) unary predicate letters, and (...) a single proposition letter. As a corollary, it is proved that infinite families of modal predicate axiomatic systems, based on the classical first-order logic and the modal propositional logics $\textbf {GL}$, $\textbf {Grz}$, $\textbf {wGrz}$ are not Kripke complete. Both $\Pi ^1_1$-hardness and Kripke incompleteness results of the paper do not depend on whether the logics contain the Barcan formula. (shrink)

Prominent constructive theories of sets as Martin-Löf type theory and Aczel and Myhill constructive set theory, feature a distinctive form of constructivity: predicativity. This may be phrased as a constructibility requirement for sets, which ought to be finitely specifiable in terms of some uncontroversial initial “objects” and simple operations over them. Predicativity emerged at the beginning of the 20th century as a fundamental component of an influential analysis of the paradoxes by Poincaré and Russell. According to this analysis the paradoxes (...) are caused by a vicious circularity in definitions; adherence to predicativity was therefore proposed as a systematic method for preventing such problematic circularity. In the following, I sketch the origins of predicativity, review the fundamental contributions by Russell and Weyl and look at modern incarnations of this notion. (shrink)