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)
This paper explores the possibility of developing a hybrid version of dispositional theories of aesthetic values. On such a theory, uses of aesthetic predicates express relational second-order dispositional properties. If the theory is not absolutist, it allows for the relativity of aesthetic values. But it may be objected to on the grounds that it fails to explain disagreement among subjects who are not disposed alike. This paper explores the possibility of adapting recent proposals of hybrid expressivist theories for moral (...)predicates to the case of aesthetic predicates. Hybrid expressivist theories make no explicit commitment about the kind of property expressed by the predicate, but make explicit commitments to implicated (or presupposed)expressive content. It is argued that dispositionalism about the properties expressed by aesthetic predicates, combined with expressive implicatures (or presuppositions), can account for aesthetic disagreements even in cases where subjects are not relevantly alike. (shrink)
Predicates such as tall or to know Latin, which intuitively denote permanent properties, are called individual-level predicates. Many peculiar properties of this class of predicates have been noted in the literature. One such property is that we cannot say #John is sometimes tall. Here is a way to account for this property: this sentence sounds odd because it triggers the scalar implicature that the alternative John is always tall is false, which cannot be, given that, if John (...) is sometimes tall, then he always is. This intuition faces two challenges. First: this scalar implicature has a weird nature, since it must be surprisingly robust (otherwise, it could be cancelled and the sentence rescued) and furthermore blind to the common knowledge that tallness is a permanent property (since this piece of common knowledge makes the two alternatives equivalent). Second: it is not clear how this intuition could be extended to other, more complicated properties of individual-level predicates. The goal of this paper is to defend the idea of an implicature-based theory of individual-level predicates by facing these two challenges. In the first part of the paper, I try to make sense of the weird nature of these special mismatching implicatures within the recent grammatical framework for scalar implicatures of Chierchia (Structures and beyond, 2004) and Fox (2007). In the second part of the paper, I show how this implicature-based line of reasoning can be extended to more complicated properties of individual-level predicates, such as restrictions on the interpretation of their bare plural subjects, noted in Carlson (Reference to kinds in English. Doctoral dissertation, University of Massachusetts at Amherst, 1977), Milsark (Linguistic Analysis 3.1: 1–29, 1977), and Fox (Natural Language Semantics 3: 283–341, 1995); restrictions on German word order, noted in Diesing (Indefinites, 1992); and restrictions on Q-adverbs, noted in Kratzer (The Generic Book, ed. Carlson and Pelletier, 125–175, 1995). (shrink)
In this paper we discuss a phenomenon we call perspectival plurality, which has gone largely unnoticed in the current debate between relativism and contextualism about predicates of personal taste (PPTs). According to perspectival plurality, the truth value of a sentence containing more than one PPT may depend on more than one perspective (subjects, experiencers or judges). Prima facie, the phenomenon engenders a problem for relativism and can be shaped into an argument in favor of contextualism. We explore the consequences (...) of perspectival plurality in depth and assess several possible responses on behalf of advocates of relativism. (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.
In the debate between contextualism and relativism about predicates of taste, the challenge from disagreement (the objection that contextualism cannot account for disagreement in ordinary exchanges involving such predicates) has played a central role. This paper investigates one way of answering the challenge consisting on appeal to certain, less focused on, uses of predicates of taste. It argues that the said thread is unsatisfactory, in that it downplays certain exchanges that constitute the core disagreement data. Additionally, several (...) arguments to the effect that the exchanges in question don’t amount to disagreement are considered and rejected. (shrink)
One question of the bounds of cognition is that of which things have it. A scientifically relevant debate on this question must explain the persistent and selective use of psychological predicates to report findings throughout biology: for example, that neurons prefer, fruit flies and plants decide, and bacteria communicate linguistically. This paper argues that these claims should enjoy default literal interpretation. An epistemic consequence is that these findings can contribute directly to understanding the nature of psychological capacities.
Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the semantic differences between (...) nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (shrink)
This paper presents a precise semantics for incomplete predicates such as “ready”. Incomplete predicates have distinctive logical properties that a semantic theory needs to accommodate. For instance, “Tipper is ready” logically implies “Tipper is ready for something”, but “Tipper is ready for something” does not imply “Tipper is ready”. It is shown that several approaches to the semantics of incomplete predicates fail to accommodate these logical properties. The account offered here defines contexts as structures containing an element (...) called a proposition set, which contains atomic propositions and negations of atomic propositions. The condition under which “Tipper is ready” is true in a context is defined in terms of the contents of the proposition set for the context. On this account, the content of the context pertinent to a conversation must be determined not by what speakers have in mind but by relations of objective relevance. (shrink)
In the debate between relativism and contextualism about various expressions, the Operator Argument, initially proposed by Kaplan , has been taken to support relativism. However, one widespread reaction against the argument has taken the form of arguing against one assumption made by Kaplan: namely, that certain natural language expressions are best treated as sentential operators. Focusing on the only extant version of the Operator Argument proposed in connection to predicates of personal taste such as “tasty” and experiencer phrases such (...) as “for Anna” ), in this paper I investigate whetherthe reasons offered by Cappelen and Hawthorne against various assumptions of the argument failing in the case of modal, temporal, locationaland precisional expressions transfer to the case of experiencer phrases to undercut support for relativism about predicates of personal taste. My aim is to show that they don’t. Thus, I first show that their considerations against experiencer phrases such as “for Anna” being sentential operators are not decisive. Second, I show that even if granting that such experiencer phrases are not sentential operators, a suitably modified version of the Operator Argument can be defended from the objections they raise. (shrink)
Abstract: There are many examples offered as evidence that proper names are predicates. Not all of these cases speak to a name’s semantic content, but many of them do. These include attribution, quantificational, and disambiguation cases. We will explore those cases here, and we will see that none of them conclusively show that names are predicates. In fact, all of these constructions can be given alternative analyses that eliminate the predicative characteristics of names they feature. These analyses do (...) not involve having names functioning as predicates in any way whatsoever. In attribution cases, the names within them are to be understood as occurring in a comparative construction, not an attributive construction. In the last two kinds of cases, the names that occur are analyzed as part of a more complex name for a specific domain, rather than functioning as predicates. Both paraphrases can be given plausible semantic treatments that have significant advantages over their competitors. For this reason, there is less motivation to focus on predicative views of proper names. The alternative semantic treatments are tailored to the different cases, and are therefore different from another, but the treatments do not entail an ambiguity hypothesis, since the second of them is not a semantic treatment of the specific proper names occurring within them, but instead of a more complex phrase that only mentions specific proper names that is not itself understood as structured. (shrink)
According to the simple proposal, a predicate is rigid iff it signifies the same property across the different possible worlds. The simple proposal has been claimed to suffer from an over-generalization problem. Assume that one can make sense of predicates signifying properties, and assume that trivialization concerns, to the effect that the notion would cover any predicate whatsoever, can be overcome. Still, the proposal would over-generalize, the worry has it, by covering predicates for artifactual, social, or evaluative properties, (...) such as 'is a knife,' 'is a bachelor,' or 'is funny.' In defense, it is argued that rigidity for predicates as characterized plays the appropriate theoretical role, and that the contention that "unnatural" properties are not to be rigidly signified is ungrounded. (shrink)
Despite the wide acceptance of standard modal logic, there has always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators. The aim of the formal model outlined in this paper is to capture what I take to be the only plausible sense in which ‘possible’ and ‘necessary’ can be treated as predicates. The model is built by enriching the language of standard (...) modal logic with a quantificational apparatus that is “substitutional” rather than “objectual”, and by obtaining from the language so enriched another language in which constants for such predicates apply to singular terms that stand for propositions. (shrink)
Two cases are distinguished. In one case two predicates belong to distinct languages. A straight-forward argument is presented that the predicates might be synonymous without being coextensive. In the second case the predicates belong to the same language. Here the issue is more involved, but the same conclusion is reached.
Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of (...) counting, to them is associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described. (shrink)
In this paper I put forward and substantiate a possible defensive move on behalf of the relativist about predicates of personal taste that can be used to block a recent contextualist argument raised against the view: the ‘argument from binding’ proposed in Schaffer (). The move consists in adopting Recanati's “variadic functions” apparatus and applying it to predicates of personal taste like ‘tasty’ and experiencer phrases like ‘for John’. I substantiate the account in a basic relativistic framework and (...) reply to several objections to the variadic-functions approach in general and to its application to the expressions at hand. (shrink)
Elizabeth Prior claims that dispositional predicates are incomplete in the sense that they have more than one argument place. To back up this claim, she offers a number of arguments that involve such ordinary dispositional predicates as ‘fragile’, ‘soluble’, and so on. In this paper, I will first demonstrate that one of Prior’s arguments that ‘is fragile’ is an incomplete predicate is mistaken. This, however, does not immediately mean that Prior is wrong that ‘fragile’ is an incomplete predicate. (...) On the contrary, I maintain that she has offered another valid argument that does indeed establish the claim that ‘fragile’ is an incomplete predicate. I will argue further that Prior is right that ‘soluble’ is an incomplete predicate. Then does this mean that all dispositional predicates are incomplete? I don’t think so. I will suggest that there are complete dispositional predicates that have no more than one argument place. Finally, by relying on my discussion of the incompleteness of dispositional predicates, I will attempt to provide a better understanding of the context-dependence and intrinsic nature of dispositional ascriptions. (shrink)
The aim of this paper is (i) to defend Frege's view that the referents of predicates are certain kinds of functions, or "concepts", i.e. incomplete entities, and not their extensions (i.e. sets of objects described by those predicates); and (ii) to justify, by a natural augmentation of Frege's semantic theory with modal ingredients, Frege's position that the sameness between concepts, or property-sharing, turns only on the sameness of extensions. Several problems with the doctrine that a predicate's extension is (...) its referent are presented, including the regress argument and an argument from the modern philosophy of language related to natural kind terms. In this connection, it is also pointed out that all referential expressions are in a sense rigid. (shrink)
The paper examines the Cartesian and the Strawsonian answers to the question of why self-applied and other-applied mental predicates mean the same. While these answers relate to different, complementary aspects of this question, they seem and are usually considered as incompatible. Indeed, their apparent incompatibility constitutes a major objection to the Cartesian answer. A primary aim of the paper is to show that the Strawsonian answer does not pose a real problem to the Cartesian answer. Unlike other attempts to (...) show this, the paper does not seek to undermine the Strawsonian answer. Indeed, its second aim is to defend this answer against these other attempts. The paper’s strategy in defending the Cartesian answer is to show that the framework underlying this answer can — indeed, for internal reasons, must — accommodate the Strawsonian answer. By showing this, the paper also shows that a Cartesian framework can provide a comprehensive answer to the aforementioned question, which is its third aim. (shrink)
This paper argues that truth values of sentences containing predicates of “personal taste” such as fun or tasty must be relativized to individuals. This relativization is of truth value only, and does not involve a relativization of semantic content: If you say roller coasters are fun, and I say they are not, I am negating the same content which you assert, and directly contradicting you. Nonetheless, both our utterances can be true (relative to their separate contexts). A formal semantic (...) theory is presented which gives this result by introducing an individual index, analogous to the world and time indices commonly used, and by treating the pragmatic context as supplying a particular value for this index. The context supplies this value in the derivation of truth values from content, not in the derivation of content from character. Predicates of personal taste therefore display a kind of contextual variation in interpretation which is unlike the familiar variation exhibited by pronouns and other indexicals. (shrink)
Predicates of taste, such as?fun? and?tasty?, have received considerable attention in recent debates between contextualists and relativists, with considerations involving disagreement playing a central role. Considerations involving disagreement have been taken to present a problem for contextualist treatments of predicates of taste. My goal is to argue that considerations involving disagreement do not undermine contextualism. To the extent that relativism was supposed to be motivated by contextualists being unable to deal with disagreement, this motivation is lacking. The argument (...) against contextualism rests on a too simple and narrow conception of disagreement that turns out to be problematic once we consider a wider range of cases. If we reject the assumptions about disagreement that the argument rests on, it no longer poses a threat to contextualism. (shrink)
Predicates of personal taste (fun, tasty) and epistemic modals (might, must) share a similar analytical difficulty in determining whose taste or knowledge is being expressed. Accordingly, they have parallel behavior in attitude reports and in a certain kind of disagreement. On the other hand, they differ in how freely they can be linked to a contextually salient individual, with epistemic modals being much more restricted in this respect. I propose an account of both classes using Lasersohn’s (Linguistics and Philosophy (...) 28: 643–686, 2005) “judge” parameter, at the same time arguing for crucial changes to Lasersohn’s view in order to allow the extension to epistemic modals and address empirical problems faced by his account. (shrink)
The article discusses an idea of how to extend the notion of rigidity to predicates, namely the idea that predicates stand in a certain systematic semantic relation to properties, such that this relation may hold rigidly or nonrigidly. The relation (which I call signification) can be characterised by recourse to canonical property designators which are derived from predicates (or general terms) by means of nominalization: a predicate signifies that property which the derived property designator designates. Whether signification (...) divides into rigid and non-rigid cases will then depend uponwhether canonical property designators divide into rigid and non-rigid ones. But, I shall argue, they do not, and so the only notion of rigidity gained this way is trivial. To show this, I first focus on the kind of canonical property designators which could be thought to be nonrigid, canonical designators such as having the colour of ripe tomatoes which themselves contain non-rigid property designators. An argument to the effect that such complex canonical designators are non-rigid is rebutted, five arguments to the effect that they are rigid are formulated, and finally an explanation of their rigidity based on the general nature of canonical property designators is presented. (shrink)
The history of the idea of predicate is the history of its emancipation. The lesson of this paper is that there are two more steps to take. The first is to recognize that predicates need not have a fixed degree, the second that they can combine with plural terms. We begin by articulating the notion of a multigrade predicate: one that takes variably many arguments. We counter objections to the very idea posed by Peirce, Dummett's Frege, and Strawson. We (...) show that the arguments of a multigrade predicate must be grouped into places, with perhaps several arguments occupying positions at a place. Variability may relate to places or positions. Russell's multiple judgement predicate turns out to be just one example of a family-'is necessarily true of', 'is said of', 'is instantiated by' and so on-of predicates with variably many places. Our main concern, however, is lists. Any adequate account of lists must include plural as well as singular terms. On one account, lists are mere strings of separate arguments, which occupy variably many positions within a place of a multigrade predicate. A quite different account takes the list itself to be a compound plural term. We compare these rival conceptions, and reach some surprising conclusions. As a coda, we deploy the conceptual apparatus developed in the paper to assess Morton's pioneer system of multigrade logic. (shrink)
We offer a new account of the semantics of predicates of personal taste (PPTs) like tasty and fun which, unlike recent proposals (Lasersohn 2005; Stephenson 2007a, 2007b), does not appeal to a judge parameter as a component of the evaluation index. We identify empirical shortcomings of previous proposals, arguing that PPTs have a first-person-oriented meaning component even in cases that seem to involve an exocentric interpretation. We propose that the interpretation of PPTs involves first-person-oriented genericity in the sense of (...) Moltmann (2006, 2010a). When I say This cake is tasty, I say roughly that for all worlds w and all individuals x such that x is relevant in w and I identify with x, the cake is tasty to x in w. We explain the shifting of the first person orientation from speaker to attitude holder in attitude reports by taking both matrix and embedded sentences to express properties rather than propositions (Stojanovic 2011). In both cases, an abstraction operator in the left periphery of the clause binds the variable responsible for the first-person-oriented interpretation of the sentence. The paper closes with a comparison with a similar proposal by Moltmann (2010b, forthcoming) and a discussion of the implications of our semantics for the analysis of attitudes de se. (shrink)
In reply to Geach's objection against expressivism, some have claimed that there is a plurality of truth predicates. I raise a difficulty for this claim: valid inferences can involve sentences assessable by any truth predicate, corresponding to 'lightweight' truth as well as to 'heavyweight' truth. To account for this, some unique truth predicate must apply to all sentences that can appear in inferences. Mixed inferences remind us of a central platitude about truth: truth is what is preserved in valid (...) inferences. The question is why we should postulate truth predicates that do not satisfy this platitude. (shrink)
I argue for two major claims in this paper. First, I argue that the linguistic evidence best supports a certain form of contextualism about predicates of personal taste (PPTs) like ?fun? and ?tasty?. In particular, I argue that these adjectives are both individual-level predicates (ILPs) and anaphoric implicit argument taking predicates (IATPs). As ILPs, these naturally form generics. As anaphoric IATPs, PPTs show the same dependencies on context and distributional behavior as more familiar anaphoric IATPs, for example, (...) ?local? and ?apply?. Moreover, they are subject to important binding-related phenomena, for example, various kinds of anaphora, binding arguments, and strict-sloppy ambiguities. The latter are particularly problematic for relativism, contextualism's major competitor. I argue that relativism cannot account for these binding facts in a non-ad hoc manner. Second, I argue that disagreement is a predictable feature of dialogues involving PPTs in conjunction with the contextualist semantics defended. Appealing to ?off the shelf? analyses of genericity, I show how disagreement arises in just the cases we would expect, licensing just the kinds of responses we would expect. They also suggest promising explanations, unavailable to relativists, of various otherwise puzzling features of disagreements involving PPTs. (shrink)
This takes a closer look at the actual semantic behavior of apparent truth predicates in English and re-evaluates the way they could motivate particular philosophical views regarding the formal status of 'truth predicates' and their semantics. The paper distinguishes two types of 'truth predicates' and proposes semantic analyses that better reflect the linguistic facts. These analyses match particular independently motivated philosophical views.
If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates (...) of sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (shrink)
It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regulated by what Kit (...) Fine calls penumbral connections, including a principle of tolerance. As I see it, vague predicates are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning how one reasons with such predicates. In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning, even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context , Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated. (shrink)
The most common philosophical view of existence is that existence amounts to existential quantification or is a second-order concept. A less common philosophical view is that existence is a first-order property distinguishing between nonexistent (past, possible, or merely intentional) objects and existing objects. An even less common philosophical view is that existence divides into different ‘modes of being’ for different kinds of entities. The aim of the present paper is to take a closer look at how the notion of existence (...) is in fact expressed in natural language. In natural language, it appears, existence is not so much expressed by quantification, which can be shown to be neutral as regards any distinction between existent and nonexistent objects that one might draw. Rather existence is expressed by predicates, and that is, first-order predicates, such as in English 'exist', 'occur', and 'obtain'. The semantic behavior of such existence predicates reveals a notion of existence that divides into at least three different kinds of modes being, reflecting the distinction between endurance and perdurance, as well as their space-related analogues, but also the particular mode of being of such entities as states, facts, conditions, and laws. (shrink)
I propose a semantics for a class of English predicates characteristically associated with possibility. The central idea is that such predicates are typically associated with an ordering source, and that differences among them are due to differences in their ordering sources. The ‘dispositional predicates’ that have been central to philosophical discussions are shown to be derivable as a special case from this more general class.
Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. (...) This is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields real-valued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense. (shrink)
Most speakers experience unclarity about the application of predicates like tall and red to liminal cases. We formulate alternative psychological hypotheses about the nature of this unclarity, and report experiments that provide a partial test of them. A psychologized version of the ‘vagueness-as-ignorance’ theory is then advanced and defended.
The focus of this article is on the pragmatic presuppositions involved in the use of general terms in inductive practices. The main thesis is that the problem of characterizing the assumptions underlying the projection of predicates in inductive practices and the ones underlying the classification of crtain general terms as «natural kind terms» coincide to a good extent. The reason for this, it is argued, is that both classifications, «projectibility» and «natural kind term», are attempts to answer to the (...) same semantico-epistemological phenomenon, viz. underdertermination. It is proposed a «deflationary» reading of the so-called «theory of direct reference» as to enable an evaluation of its contribution to epistemological problems associated with this kind of phenomena, as well as it is argued that a purely de facto account of projectibility is not viable. The resulting hypothesis is that the conception of «natural kind terms» is only interesting insofar as they are seen as a kind of projectible general terms and thus as parts of classifications used in natural science, more generally, in inductive practices, and that this is a perspective that makes undue metaphysical readings avoidable. (shrink)
Minimal predicates P satisfying a given first-order description φ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order ‘PIA conditions’ φ(P) which guarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of ‘predicate intersection’. Next, we show how iterated predicate minimization on PIA-conditions yields a language (...) MIN(FO) equal in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. (shrink)
In this paper a connection between intentionality, intensionality, language and emotion will be drawn up through a demonstration of an intimate relationship between the intentionality of emotion and intensionality in language. What will be shown is that the intentionality of emotion can ultimately be traced to the intensionality of emotional contexts. For this purpose, emotive predicates will be categorized in terms of their intensional behavior and regularities. They will then be brought forward for an explication of why and how (...) far the intentionality of emotion is unique. The insights derived from the relevant analyses will then be employed for the implications and ramifications that might be thrown upon the fabric of emotion and language within the space of cognition. (shrink)
This paper introduces an interesting class of predicates that come in pairs, so-called total and partial predicates. It will be shown that such predicates contribute to an explanation for the weak and strong interpretations of donkey sentences. This paper proposes that the phenomenon of weak and strong interpretations is real, and that whether a sentence receives the weak or the strong interpretation depends on the predicate in the nuclear scope of the sentence. It also proposes that sum (...) individuals are calculated at some level before the nuclear scope of the sentence is processed. Once the sum individuals are calculated, it will be decided whether the nuclear scope is true of at least one element of the sum individual (weak interpretation) or true of all elements of the sum individual (strong interpretation). (shrink)
A theory of higher-order vagueness for partially-defined, context-sensitive predicates like is blue is offered. According to the theory, the predicate is determinately blue means roughly is an object o such that the claim that o is blue is a necessary consequence of the rules of the language plus the underlying non-linguistic facts in the world. Because the question of which rules count as rules of the language is itself vague, the predicate is determinately blue is both vague and partial (...) in a sense analogous (though not completely identical) to the sense in which is blue is vague and partial. However, higher-order vagueness stops there. Although the anti-extension of is determinately blue differs from that of is blue, further iterations of determinately have no semantic effect. -/- The paper closes with a discussion of the need to posit sharp and precise lines dividing the range of potential application of a vague predicate into semantically distinct categories. It is argued that this is less of a problem for the present theory than for many others, because the categories into which the range is divided by the present theory -- like the category of counting as blue because the rules of the language offer speakers no discretion, as opposed to the category of counting as blue because speakers have invoked an absolute minimum of discretion in adjusting the contextually sensitive boundaries of the predicate -- are not those that the linguistic competence of ordinary speakers equips them to make highly accurate and reliable judgments about. (shrink)
According to the simple proposal about rigidity for predicates, a predicate is rigid (roughly) if it signifies the same property across the relevant worlds. Recent critics claim that this suffers from a trivialization problem: any predicate whatsoever would turn out to be trivially rigid, according to the proposal. In this paper a corresponding "problem" for ordinary singular terms is considered. A natural solution is provided by intuitions concerning the actual truth-value of identity statements involving them. The simple proposal for (...)predicates is then defended, by exploiting corresponding intuitions concerning statements involving their nominalizations, in an analogous manner. (shrink)
PA is Peano Arithmetic. Pr(x) is the usual Σ1-formula representing provability in PA. A strong provability predicate is a formula which has the same properties as Pr(·) but is not Σ1. An example: Q is ω-provable if PA + ¬ Q is ω-inconsistent (Boolos ). In  Dzhaparidze introduced a joint provability logic for iterated ω-provability and obtained its arithmetical completeness. In this paper we prove some further modal properties of Dzhaparidze's logic, e.g., the fixed point property and the Craig (...) interpolation lemma. We also consider other examples of the strong provability predicates and their applications. (shrink)
The „Paradox of the Concept Horse" arises on the assumption of the Reference Principle: that co-referential expressions should be cross-substitutable salva veritate in extensional contexts and salva congruitate in all. Accordingly no singular term can co-refer with an unsaturated expression. The paper outlines a number of desiderata for a satisfactory response to the problem and argues that recent treatments by Dummett and Wiggins fall short by their lights. It is then pointed out that a more consistent perception of the requirements (...) of the Reference Principle leads not to the Paradox but to the result that Frege had no business extending the notion of Bedeutung to unsaturated expressions in the first place. Rather the relation between, e.g., predicates and the entities that comprise the range of higher-order logical variables must be logically unlike that between singular terms and their referents; the way is therefore opened for singular terms to refer to entities of the former kind after all. The Concept Horse is a concept. (shrink)
Minimal predicates P satisfying a given first-order description ϕ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order 'PIA conditions' ϕ(P) which quarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of 'predicate intersection'. Next, we show how iterated predicate minimization on PIA-conditions yields a language (...) MIN(FO) equal in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. (shrink)
A subset A $\subseteq$ M of a totally ordered structure M is said to be convex, if for any a, b $\in A: [a . A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some $\emptyset$ -definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a weakly o-minimal theory (...) T, any expansion M + of M by a family of unary predicates has a weakly o-minimal theory iff the set of all realizations of each predicate is a union of a finite number of convex sets (Theorem 63), that solves the Problem of Cherlin-Macpherson-Marker-Steinhorn [MMS] for the class of weakly o-minimal theories. (shrink)
The most common philosophical view about the notion of existence is that it is a second-order property or existential quantification. A less common view is that existence is a (first-order) property of 'existent' as opposed to 'nonexistent' (past or merely intentional) objects. An even less common view is that existence divides into different 'modes of being' for different sorts of entities. In this paper I will take a closer look at the semantic behavior of existence predicates in natural language, (...) such as exist, occur, and obtain, arguing that existence predicates in natural language support the two less common philosophical views. I will develop explicit analyses of existence predicates in their time-relative and space-relative uses which will explain why they apply to some kinds of entities, but not others. (shrink)
We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of (...) Whitehead (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)
Indexicality is a feature of predicates and predicate components (verbs, adjectives, adverbs and the like) as well as of referring expressions. With classic referring indexicals such as 'I' or 'that' a distinctive rule takes us from token and context to some item present in the content which is the semantic correlate of the token. Predicates and predicate components may function in an analogous fashion. For example 'thus' is an indexical adverb which latches onto some manner of performance present (...) in its context. 'John sang thus', said while indicating someone singing discordantly, claims that John sang discordantly. The phenomenon of predicatival indexicality is widespread in English and is expressed in a variety of idioms. Indexical predication plays important epistemological and psychological roles and the notion may have other interesting philosophical applications. (shrink)