Jeffrey C. King

In The Principles of Mathematics, Bertrand Russell famously puzzled over something he called the unity of the proposition. Echoing Russell, many philosophers have talked over the years about the question or problem of the unity of the proposition. In fact, I believe that there are a number of quite distinct though related questions all of which can plausibly be taken to be questions regarding the unity of propositions. I state three such questions and show how the theory of propositions defended in my recent book The Nature and Structure of Content answers them.

At least since Russell’s influential discussion in The Principles of Mathematics, many philosophers have held there is a problem that they call the problem of the unity of the proposition. In a recent paper, I argued that there is no single problem that alone deserves the epithet the problem of the unity of the proposition. I there distinguished three problems or questions, each of which had some right to be called a problem regarding the unity of the proposition; and I showed how the account of propositions formulated in my book The Nature and Structure of Content [2007 Oxford University Press] solves each of these problems. In the present paper, I take up two of these problems/questions yet again. For I want to consider other accounts of propositions and compare their solutions to these problems, or lack thereof, to mine. I argue that my account provides the best solutions to the unity problems.

Like many, though of course not all, philosophers, I believe in propositions. I take propositions to be structured, sentence-like entities whose structures are identical to the syntactic structures of the sentences that express them; and I have defended a particular version of such a view of propositions elsewhere. In the present work, I shall assume that the structures of propositions are at least very similar to the structures of the sentences that express them. Further, I shall assume that ordinary names are devices of direct reference and contribute only their bearers to propositions, that n-place predicates contribute n-place properties or relations to propositions, and that verbs of propositional attitude contribute to propositions two-place relations between individuals and propositions. The broad outline of a framework that includes these assumptions is one that I think many, though again not all, philosophers of language find congenial. I am concerned here to investigate and explain, from the standpoint of this framework, a puzzling phenomenon. The explanation I give of the phenomenon could be adapted to fit with frameworks somewhat different from the one adopted here. I adopt the present framework in part simply for definiteness.

The dissertation is an attempt to provide a formal semantics for occurrences of anaphoric pronouns and definite descriptions whose quantifier antecedents occur in sentences other than those in which the anaphoric pronouns and descriptions themselves occur, . The predominant view of anaphoric pronouns whose quantifier antecedents occur in the same sentence as they do is that they function as bound variables . Chapter 1 of this dissertation is constituted by a series of arguments against a bound variable treatment of q - terms and the observation that the semantic behavior of q - terms is similar to that of certain singular terms in English arguments. Given the similarity of semantic behavior between the latter and q - terms, it seems plausible to suppose that a theory of the semantic behavior of these singular terms in English arguments would provide a model for the eventual production of a semantic theory of q - terms. In Chapter 2, a formal semantics for these singular terms in arguments is produced. In Chapter 3, a formal semantics for q - terms is produced, on the model of the semantics in Chapter 2. Finally, in Chapter 4 it is shown that the formal semantics of Chapter 3 can be extended to handle pronouns in discourses containing verbs of propositional attitudes such as 'wants', 'dreams' etc. It is also shown that some occurrences of sentences containing q - terms have truth conditions not expressible by any quantified first order sentence. One must use finite partially ordered quantifiers to express the truth conditions of such occurrences of sentences. ;The dissertation contains two appendices: the first is a technical discussion of the formal semantics of Hans Kamp which shows that his theory cannot accomodate the linguistic data mine is designed to handle. The second examines the views of Gareth Evans, Charles Chastain and Keith Donnellan on certain anaphoric pronouns

A central job for propositions is to be the objects of the attitudes. Propositions are the things we doubt, believe and suppose. Some philosophers have thought that propositions are sets of possible worlds. But many have become convinced that such an account individuates propositions too coarsely. This raises the question of how finely propositions should be individuated. An account of how finely propositions should be individuated on which they are individuated very finely is sketched. Objections to the effect that the account individuates propositions too finely are raised and responses to the objections are provided. It is also shown that theories that try to individuate propositions less finely have serious problems.

Though these expressions are often called “names of months”, there is good reason to hold that they are not names at all. Syntactically, these words behave as count nouns. They combine with determiners such as ‘every’, ‘many’, ‘exactly three’ etc. to form restricted quantifiers:3 (1) Every January I go skiing. (2) I spent many Januarys at Squaw Valley. (3) I wasted exactly three Januarys in Bakersfield. Like other count nouns, they can take relative clauses in constructions such as (1)-(3): (1a) Every January that you visited we went skiing. (2a) I spent many Januarys that I will never forget at Squaw Valley. (3a) I wasted three Januarys that seemed interminable in Bakersfield. They also combine with the copula, indefinite article and adjectival modifiers to form predicates in the way that other count nouns do: (4) The first full month I lived in Northern California was a pleasant July. Further, it is generally held that only constituents of the same syntactic category can be conjoined. And as the following example shows, ‘January’ can be conjoined with other count nouns:4 (5) All Januarys and funerals last too long. Thus distributional evidence strongly suggests that ‘January’, ‘February’, etc. are count nouns. Since in general we take count nouns to express properties, we ought to take ‘January’, ‘February’ etc. to express properties as well.5 We shall return to the question of what properties such words express below. For now, we shall stick with syntax

Semantics is the discipline that studies linguistic meaning generally, and the qualification ‘formal’ indicates something about the sorts of techniques used in investigating linguistic meaning. More specifically, formal semantics is the discipline that employs techniques from symbolic logic, mathematics, and mathematical logic to produce precisely characterized theories of meaning for natural languages or artificial languages. Formal semantics as we know it first arose in the twentieth century. It was made possible by certain developments in logic during that period. This article chronicles those developments and how they led to the development of formal semantics.