Predicates in perspective

A familiar strategy of argument to the effect that natural-language predicates are semantically context dependent rests on constructing what I term Travis cases: different contexts for the use of a predicate are imagined in which its semantic (typically, truth-conditional) properties are claimed to differ. I propose an account of the semantic properties of predicates that give rise to Travis cases; I then argue that the account underwrites a genuine alternative to the standard explanations of Travis cases to be found in the literature; I close with a brief sketch of the connections, required by a fuller development of my account, among the semantic notion of a predicate??s content, the metaphysical notion of a property??s instantiation, and the cognitive notion of a language user??s perspective in using a predicate.     

Descriptions as Predicates

Philosophical Studies -     

Reasoning with Slippery Predicates

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.     

Suppes Predicates for Space-Time

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.     

Suppes Predicates for Meta-Ranking Structures

In this paper the general notion of Bourbaki structures, interpreted in terms of Suppes predicates, will be used to axiomatize a system of meta-rankings in the sense introduced by A. K. Sen. It will be argued that this axiomatization must take place in a Kantian-ruled world in order to provide a link between meta-rankings and individual actions.Dedicated to Prof. Francisco A. Doria on his 50th birthday.     

Property Designators,Predicates, and Rigidity

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.     

Complex Predicates and Logics for Properties and Relations

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

On Mixed Inferences and Pluralism about Truth Predicates

A familiar view concerning sentences about the ethical or comical is that they are not truth-apt – not capable of being true or false. Against this view Peter Geach famously noted that such sentences may figure in true (or false) conditionals and so must thereby be truth-apt. In response to Geach's argument, Crispin Wright proposed a pluralism about truth predicates, a pluralism which sees Geach's conditional clauses as being true in a sense that avoids realism about the entities involved. I defend Wright's proposal against an interesting recent attack by Christine Tappolet, and show that, pace Tappolet, Wright's proposed pluralism is compatible with the Tarskian idea that validity is necessary truth-preservation.     

Partially Interpreted Relations and Partially Interpreted Quantifiers

Logics in which a relation R is semantically incomplete in a particular universe E, i.e. the union of the extension of R with its anti-extension does not exhaust the whole universe E, have been studied quite extensively in the last years. (Cf. van Benthem (1985), Blamey (1986), and Langholm (1988), for partial predicate logic; Muskens (1996), for the applications of partial predicates to formal semantics, and Doherty (1996) for applications to modal logic.) This is not so with semantically incomplete generalized quantifiers which constitute the subject of the present paper. The only systematic study of these quantifiers from a purely logical point of view, is, to the best of my knowledge, that by van Eijck (1995). We shall take here a different approach than that of van Eijck and mention some of the abstract properties of the resulting logic. Finally we shall prove that the two approaches are interdefinable.     

Russell’s Paradox of Predicates

Russell’s letter to Frege of June 16, 1902 contains the famous paradox of the class of all classes which are not members of themselves as well as a second paradox of the predicates that cannot be predicated of themselves. The latter paradox arises out of Russell’s theory of classes and class concepts in Principles of Mathematics.     

Possible-Worlds Semantics for Modal Notions Conceived as Predicates

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 A holds at a world wW if and only if A holds at every world vW such that wRv. 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 -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.     

Semantic Normativity and Semantic Causality

Semantic normativism, which is the view that semantic properties/concepts are some kind of normative properties/concepts, has become increasingly influential in contemporary meta‐semantics. In this paper, I aim to argue that semantic normativism has difficulty accommodating the causal efficacy of semantic properties. In specific, I raise an exclusion problem for semantic normativism, inspired by the exclusion problem in the philosophy of mind. Moreover, I attempt to show that the exclusion problem for semantic normativism is peculiarly troublesome: while we can solve (or dissolve) mental‐physical exclusion by adopting the so‐called ‘autonomy approach’, a similar autonomy solution to semantic exclusion is implausible if semantic properties are understood as normative properties.     

On Conservative Extensions in Logics with Infinitary Predicates

If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for an extension to be conservative. The origin of the results is algebraic logic. Presented by Daniele Mundici Supported by grant OTKA T43242.     

Elementary Particles,Hidden Variables,And Hidden Predicates

We recently showed that it is possible to deal withcollections of indistinguishable elementary particles (in thecontext of quantum mechanics) in a set-theoretical framework, byusing hidden variables. We propose in the presentpaper another axiomatics for collections of indiscernibleswithout hidden variables, where hidden predicates are implicitlyassumed. We also discuss the possibility of a quasi-settheoretical picture for quantum theory. Quasi-set theory, basedon Zermelo-Fraenkel set theory, was developed for dealing withcollections of indistinguishable, but, not identical objects.