Predicates

Hurford argues that propositions of the form PREDICATE(x) represent conceptual structures that predate language and that can be explicated in terms of neural structure. I disagree, arguing that such predicates are descriptions of limited aspects of brain function, not available as representations in the brain to be exploited in the frog or monkey brain and turned into language in the human.

I have attempted to show that many attributive adjectives can be dealt with within the framework of first-order predicate calculus by the method suggested in this paper. I've also supplied independent reasons for the claim that attributive adjectives that are not responsive to this method require a formal treatment different from the one that the adjectives successfully dealt with by that method require. Thus, if the method I've argued for is sound, then the scope of first-order predicate calculus was shown (...) to be wider than assumed by several logicians. This I take to be of interest from a logical point of view. (shrink)

The paper presents both new data and a new analysis of the semantic and pragmatic properties of the class of absolute scalar adjectives within an extension of a well-known logical framework for the analysis of gradable predicates: the delineation semantics framework . It has been long observed that the context-sensitivity, vagueness and gradability features of absolute scalar predicates give rise to certain puzzles for their analysis within most, if not all, modern formal semantic frameworks. While there exist proposals for solving (...) these puzzles within other major frameworks , it has been argued that some of their aspects are particularly challenging for the analysis of absolute scalar predicates within the delineation approach. By combining insights into the relationship between context-sensitivity and scalarity from the DelS framework with insights into the relationship between tolerance/similarity relations and the Sorites paradox from Cobreros et al.’s Tolerant, Classical, Strict framework, I propose a new logical system, called Delineation TCS , in which to set analyses of four classes of adjectival predicates. I argue that this new framework allows for an analysis of absolute scalar adjectives that answers these challenges for delineation-based frameworks, while still preserving the heart of the Klein-ian approach. (shrink)

This volume offers an unusual variety of topics presented during the sixth annual Oberlin Colloquium in Philosophy.

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)

This paper addresses a dilemma arising from the linguistic behaviour of arithmetical expressions in two basic ways: they occur, either as singular terms in identity statements or as predicates of concepts in adjectival statements. However, those forms of syntactical behaviour give rise to opposite accounts of the ontological status of natural numbers. The substantival use of arithmetical expressions is associated with the interpretation of natural numbers as abstract particulars while the adjectival use of arithmetical expressions ordinarily supports the interpretation of (...) natural numbers either as properties of physical collections or as properties of sortal concepts, i.e. as second-order properties. Both types of interpretation are taken under consideration and the special difficulties of each position are sketched, in view of recently discussed aspects of the ‘arithmetical platonism’ issue. The interpretation of numbers as abstract particulars by the neo-Fregean program presupposes the discrimination of singular terms from other categories of expressions. However, to achieve the alleged syntactical distinction by means of an appropriate set of criteria is considered as a very ambitious task which has not yet been met in an adequate way. On the other hand, interpretations of natural numbers as (1st or 2nd-order) properties face difficulties which, to a large extent, are taken to arise from the fact that those interpretations do not offer a satisfactory account of arithmetical identities. In particular, the paper takes in account Maddy’s approach according to which natural numbers are properties of sets. Then it investigates the reasons why interpretations of numbers as properties often result in an extensional treatment of those properties. Then the paper tries out a reduction strategy to investigate the relationship between the substantival form ‘ ’ and the adjectival form ‘ ’ and determine, if possible, the most fundamental of the two accounts. Hence, it presents three options. The first option is to examine whether the substantival form is reducible to the adjectival form, by an attempt to undermine the semantic role of arithmetical terms as genuine singular terms. The second option is to apply the converse reduction strategy. The third option is to take the substantival form to be equivalent to the adjectival form. In particular, the paper focuses its attention on the third option. To articulate the proposal about the alleged equivalence between the two forms of syntactical behaviour of numbers, it embarks on a discussion of Ramsey’s argument that no essential difference between particulars and universals can be asserted at least on syntactical grounds. Then the paper moves on to present the reasons why the third option appears to be the most prevalent of the three. To highlight this claim, it presents an account of how an equivalence principle can actually be settled among the two forms of arithmetical syntactical behaviour. The paper concludes with suggestions about possible ways by which we can construe the alleged equivalence, considering the substantival and the adjectival account as the two sides of the same coin. (shrink)

In earlier work, we developed an composition in which predicates can be composed with arguments by operations other than Function Application, and it makes a difference which composition operation is employed. Here we take our approach further by examining two nonsaturating operations that combine property contents: Restrict, which composes a predicate with the property content of an indefinite; and Modify, which is involved in predicate modification. Nonsaturating operations that combine property contents are often formalized in terms of predicate intersection, which (...) is commutative. Using Austronesian language Chamorro, we argue that Restrict and Modify are not ‘commutative’, but instead incorporate an asymmetry: they take one content to supply a domain that is narrowed further by combination with the other content. Syntactically, it is transparent which category’s content supplies the domain. But semantically, this information can be recovered only from the way in which the composition operation affects the contents that it composes, since—as we show—the same contents can be composed with distinct results. (shrink)

Conceptual realism begins with a conceptualist theory of the nexus of predication in our speech and mental acts, a theory that explains the unity of those acts in terms of their referential and predicable aspects. This theory also contains as an integral part an intensional realism based on predicate nominalization and a reflexive abstraction in which the intensional contents of our concepts are “object”-ified, and by which an analysis of predication with intensional verbs can be given. Through a second nominalization (...) of the common names that are part of conceptual realism’s theory of reference (via quantifier phrases), the theory also accounts for both plural reference and predication and mass noun reference and predication. Finally, a separate nexus of predication based on natural kinds and the natural properties and relations nomologically related to those natural kinds, is also an integral part of the framework of conceptual realism. (shrink)

A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing to Aristotle the (...) view that subjects and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle's core semantic notion is not identity but the weaker relation of constitution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle's view, just in case the mereological sum of humans is a part of the mereological sum of mortals. (shrink)

Predicates involved in language and reasoning are claimed to radically differ from categories applied to objects. Human predicates are the cognitive result of a contrast between perceived objects. Object recognition alone cannot generate such operations as modification and explicit negation. The mechanism studied by Hurford constitutes at best an evolutionary prerequisite of human predication ability.

Although in every inductive inference, an act of invention is requisite, the act soon slips out of notice. Although we bind together facts by superinducing upon them a new Conception, this Conception, once introduced and applied, is looked upon as inseparably connected with the facts, and necessarily implied in them. Having once had the phenomena bound together in their minds in virtue of the Conception men can no longer easily restore them back to the detached and incoherent condition in which (...) they were before they were thus combined. The pearls once strung, they seem to form a chain by their nature. Induction has given them unity which it is so far from costing us an effort to preserve, that it requires an effort to imagine it dissolved — William Whewell, 1858. (Quoted from Butts (ed.), 1989, p. 143). (shrink)

In his article ‘Names, Verbs and Quantification’ Nicholas Denyer argues that a previous attempt of mine, on behalf of realism, to play down the ontological importance of the distinction between grammatical names and verbs ignores some striking logical differences between them. I concede the differences Denyer alludes to, but argue that they do not assist the orthodox nominalist, since if anything they point to a position according to which relations, but not monadic properties, are unreal. But this position is, I (...) claim, as implausible as nominalism itself is. (shrink)

In this article we give a detailed presentation of state event logic which is a modal logic for reasoning about concurrent events and causality between events [8] State event logic differs from previous approaches in the following directions: First, events enjoy the same attention as states. In the same way as states can be viewed as models of the formulae describing the facts that hold in them we think of events as models of the formulae describing the subevents. Second, instead (...) of postulating just one set of states as primitive objects we use two sets, a set of states and a set of events In terms of modal logic, the universe then becomes a set of pairsin which the first component is a state and the second is an event following the state. The connection between two subsequent pairs is expressed by an accessibility relation.Propositional and first-order state event logic are formulated and illustrated with examplese.From these examples we can immediately infer that state event logic can also be applied for the representation of real world scenarios. Finally we added a thorough discussion on related approaches. (shrink)

In this article I contrast in two ways those conceptions of semantic theory deriving from Richard Montague's Intensional Logic (IL) and later developments with conceptions that stick pretty closely to a far weaker semantic apparatus for human first languages. IL is a higher-order language incorporating the simple theory of types. As such, it endows predicates with a reference. Its intensional features yield a conception of propositional identity (namely necessary equivalence) that has seemed to many to be too coarse to be (...) acceptable. In the most usual expositions, it takes the object of linguistic explication to be the sentence in a context, as in Kaplan, 1977. This last has led to recent speculations about 'shifted' contexts. IL may be contrasted with a more linguistically (representationally) bound conception of propositions and interpretation of their predicational and functional parts, and with the explication, not of sentences in contexts, but of potential utterances, relative to the antecedent referential intentions of their speakers. We may then advance, as an empirical hypothesis about all human languages, that contexts never shift, and propose that apparent counterexamples stem from the misconstrual of linguistically coded anaphoric relations, relations that are wanted independently anyway. Donald Davidson's posthumous volume Truth and Predication mounts a sustained criticism of the notion of predicate reference. This criticism is not decisive. However, it may put the ball in the other court, insofar as it asks for a justification of what IL takes as given. Elaborations of IL using structured propositions, recently defended in King, 2007, recognize the problem of predicate reference, and the correlative issue of the 'unity of the proposition'; but I do not see that they can do better than bite the bullet already bitten in IL. I agree with Frege's insight that full justification of predicate reference pushes the boundaries of natural language, and to that extent may not be found within the semantic (as opposed to general scientific) enterprise. (shrink)

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)

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)

The distinction between telic and atelic predicates has been described in terms of the algebraic properties of their meaning since the early days of model-theoretic semantics. This perspective was inspired by Aristotle’s discussion of types of actions that do or do not take time to be completed1 which was taken up and turned into a linguistic discussion of action-denoting predicates by Vendler (1957). The algebraic notion that seemed to be most conducive to express the Aristotelian distinction appeared to be the (...) mereological notion of a part, applied to the time at which these predicates hold: atelic predicates, like push a cart, have the subinterval property, that is, whenever they are true at a time interval, then they are true at any part of that interval; this does not hold for telic predicates, like eat an apple, cf. Bennett & Partee (1972), Taylor (1977), and Dowty (1979)2. Bach (1986) integrated these insights into a semantics based on events. (shrink)

The paper discusses the structure of non-verbal predication, with particular reference to the role of the copula. Differently from the main tenets of contemporary logico-philosophical and linguistic theories, a model of predication is proposed where the verbal component (specifically, tense information) is regarded as central in establishing the syntactic and semantic relation between a predicate and its subject. It is thus possible to recover some of the insights of the pre-Fregean analysis of predication. The proposed solution has a number of (...) significant consequences for the structure to be assigned to non-verbal predication, in particular for the semantics of small clause constituents, where the predication is established without the copula. (shrink)

The present paper is an attempt at the investigation of the nature of polarity contrast in natural languages. Truth conditions for natural language sentences are incomplete unless they include a proper definition of the conditions under which they are false. It is argued that the tertium non datur principle of classical bivalent logical systems is empirically invalid for natural languages: falsity cannot be equated with non-truth. Lacking a direct intuition about the conditions under which a sentence is false, we need (...) an independent foundation of the concept of falsity. The solution I offer is a definition of falsity in terms of the truth of a syntactic negation of the sentence. A definition of syntactic negation is proposed for English (Section 1). The considerations are applied to the analysis of definites in non-generic sentences and the analysis of generic indefinites. These two domains are investigated in breadth and some depth and the analyses compared and connected. During the discussion of non-generic predications with definite arguments and their respective negations (Section 2), a theory of predication is developed, basic to which is the distinction between integrative and summative predication. Summative predication, e.g., distributive plural, leads to contrary, all-or-no-thing, polarity contrasts due to the fundamental Presupposition of Indivisibility. Further-more, levels of predication are distinguished that are built up by various processes of constructing macropredications from lexical predicates. Given this analysis, particular (i.e., non-generic) quantification (Section 3) can be reanalyzed as an integrative, first-order form of predication that fills the truth-value gaps created by summative predication. The account comprises both nominal and adverbial quantification and relates quantification to the simpler types of predication discussed in Section 2. (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)

In this paper I want to look at what the evidence from Complex Predicates can tell us about the design parameters of an empirically adequate theory of Universal Grammar (UG). This is a fertile field for investigation because, according to the standard assumptions of the field, complex predicates are monoclausal with respect to some properties and multiclausal with respect to others and this tension can only be resolved by giving up some cherished beliefs. After introducing the problem in Section 1, (...) Sections 2–4 will lay out the basis of the dilemma. Sections 2 and 3 argue that Romance complex predicates have an articulated rightwardbranching phrase structure, and cannot be analyzed as some sort of verb compound or verbal complex while conversely Section 4 shows how in many respects a complex predicate does behave just like a single predicate. Hence we require a notion of monoclausality that these complex predicates satisfy despite their articulated phrase structure. (shrink)

This paper argues that certain complements in philosophically significant constructions, especially predicative and clausal complements and intensional NPs, should not be analysed as providing an argument for a relation expressed by the verb, but rather as forming a complex predicate together with the verb. Apparent evidence for the traditional relational analyses, namely the possibility of replacing the complement by quantifiers such as 'something', will be shown to be misguided. Quantifiers like 'something' rather act as nominalizing expressions introducing ‘new’, derived objects (...) into the semantic structure of a sentence. The resulting analyses will have several philosophical ramifications. (shrink)

The most common analyses of comparatives make use of degrees, abstract objects that form a total ordering. In this paper, I will explore a novel analysis of comparatives in which the central notion is not the notion of a degree, but rather the notion of a concrete property manifestation, a particularized property, or a trope, as it is most commonly called in contemporary metaphysics. This trope-based analysis, I argue, has some major conceptual and empirical advantages over a degree-based account. A (...) degree-based analysis of (1a) looks as in (1b) (Cresswell 1976, von Stechow 1984) or (1c) (Pinkal 1989, Moltmann 1992), with the adjective being taken to express a relation between objects and degrees. (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)

The semantic function of the modifier 'together' in adnominal position has generally been considered to be that of preventing a distributive reading of the predicate. This paper will argue that this view is mistaken. The semantic function of adnominal 'together' rather is that of inducing a cumulative measurement of the group that together is associated with. The measurement-based analysis of adnominal together that I propose can also, with some modifications, be extended to adverbial occurrences of together.

In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally distinguishing between (...) natural colour predicates and Goodmanian predicates like grue and bleen. Moreover the problem of characterizing natural predicates is reformulated in such a way that its connection with the classical problem of geometric conventionalism becomes manifest. This can be used to shed some new light on Goodman's remarks on the relative entrenchment of predicates as a criterion of projectibility. (shrink)

On any speedometer, there are two kinds of what might very loosely be called ‘zones of indifference’. The first kind is found between any two marked speeds. If your speed is in fact 61 mph, it probably falls in one kind of zone of indifference. A normal speedometer is simply not designed to distinguish speeds between 60 and 65 mph, and if asked, we would probably report such a speed as ‘about 60’. There is, however, another kind of zone of (...) indifference. It is the one that extends beyond the highest marked speed, and includes all speeds that are too fast for the speedometer to register them—all the speeds that are literally off the scale. The big-picture theoretical aim of this paper is to explore the possibility that natural languages work in more or less the same way, with both kinds of zones of indifference. (shrink)

This paper explores the similarities between the conceptual structure of quantum theory and relational biology as developed within the Rashevsky-Rosen-Louie school of theoretical biology. With this aim, generalized quantum theory and the abstract formalism of (M,R)-systems are briefly presented. In particular, the notion of organizational invariance and relational identity are formalized mathematically and a particular example is given. Several quantum-like attributes of Rosen’s complex systems such as complementarity and nonseparability are discussed. Taken together, this work emphasizes the possible role of (...) self-referentiality and impredicativity in quantum theory. (shrink)