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 present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of (...) quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of settheoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items. (shrink)

The essays in this companion volume prefigure, elaborate, or defend the proposals put forward in that landmark work.

This thesis investigates the distinction, or distinctions, between response-dependent and response-independent concepts or subject matters. I present and discuss the three most influential versions of the distinction: Crispin Wright’s, Mark Johnston’s, and Philip Pettit’s. I argue that the versions do not compete for a single job, but that they can supplement each other, and that a system of different distinctions is more useful than a single distinction. I distinguish two main paradigms of response-dependence: response-dependence of subject matter, and response-dependence of (...) concepts only. I develop Pettit’s ‘ethocentric’ story of concept acquisition into an account of concept evolution that suggests answers to a range of hard questions about language, reality, and the relation between them. I argue that while response-dependence theses of subject matter can be motivated in very different ways, the resulting theses are less different than they might seem. I suggest that the traditional ways of distinguishing response-dependent subject matters from response-independent ones – in terms of a priori biconditionals connecting facts of the disputed class with responses in subjects in favourable conditions, and fulfilling some further conditions such as non-triviality and sometimes necessity – may not be the best approach. I also discuss two general problems for response-dependence theses: the problem of ‘finkish’ counterexamples, and the problem of specifying the ‘favourable conditions’ a priori, yet in a non-trivial way. The discussion of response-dependence is informed by a framework based on the idea that some realism disputes can be viewed as location disputes: disputes over the correct location of the disputed properties among several levels of candidate properties. The approach taken in this work is a charitable one: I try to make sense of response-dependence. The conclusion is the correspondingly optimistic one that the idea of response-dependence makes sense. (shrink)