This philosophical treatise on the foundations of semantics is a systematic effort to clarify, deepen, and defend the classical doctrine that words are conventional signs of mental states, principally thoughts and ideas, and that meaning consists in their expression. This expression theory of meaning is developed by carrying out the Gricean program, explaining what it is for words to have meaning in terms of speaker meaning, and what it is for a speaker to mean something in terms of intention. But (...) Grice's own formulations are rejected and alternatives developed. The foundations of the expression theory are explored at length, and the author develops the theory of thought as a fundamental cognitive phenomenon distinct from belief and desire, argues for the thesis that thoughts have parts, and identifies ideas or concepts with parts of thoughts. This book will appeal to students and professionals interested in the philosophy of language. (shrink)

Belief in propositions has had a long and distinguished history in analytic philosophy. Three of the founding fathers of analytic philosophy, Gottlob Frege, Bertrand Russell, and G. E. Moore, believed in propositions. Many philosophers since then have shared this belief; and the belief is widely, though certainly not universally, accepted among philosophers today. Among contemporary philosophers who believe in propositions, many, and perhaps even most, take them to be structured entities with individuals, properties, and relations as constituents. For example, the (...) proposition that Glenn loves Tracy has Glenn, the loving relation, and Tracy as constituents. What is it, then, that binds these constituents together and imposes structure on them? And if the proposition that Glenn loves Tracy is distinct from the proposition that Tracy loves Glenn yet both have the same constituents, what is about the way these constituents are structured or bound together that makes them two different propositions? In The Nature and Structure of Content, Jeffrey C. King formulates a detailed account of the metaphysical nature of propositions, and provides fresh answers to the above questions. In addition to explaining what it is that binds together the constituents of structured propositions and imposes structure on them, King deals with some of the standard objections to accounts of propositions: he shows that there is no mystery about what propositions are; that given certain minimal assumptions, it follows that they exist; and that on his approach, we can see how and why propositions manage to have truth conditions and represent the world as being a certain way. The Nature and Structure of Content also contains a detailed account of the nature of tense and modality, and provides a solution to the paradox of analysis. Scholars and students working in the philosophy of mind and language will find this book rewarding reading. (shrink)

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, (...) and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

What counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of (...) set theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to the iterative concept of set and/or to overall methodological principles, like unify and maximize, and investigate the relation of the latter to success in mathematics. (shrink)

First published in 1937. Routledge is an imprint of Taylor & Francis, an informa company.

The tradition descending from Frege and Russell has typically treated theories of meaning either as theories of meanings, or as theories of truth conditions. However, propositions of the classical sort don't exist, and truth conditions can't provide all the information required by a theory of meaning. In this book, one of the world's leading philosophers of language offers a way out of this dilemma. Traditionally conceived, propositions are denizens of a "third realm" beyond mind and matter, "grasped" by mysterious Platonic (...) intuition. As conceived here, they are cognitive-event types in which agents predicate properties and relations of things--in using language, in perception, and in nonlinguistic thought. Because of this, one's acquaintance with, and knowledge of, propositions is acquaintance with, and knowledge of, events of one's cognitive life. This view also solves the problem of "the unity of the proposition" by explaining how propositions can be genuinely representational, and therefore bearers of truth. The problem, in the traditional conception, is that sentences, utterances, and mental states are representational because of the relations they bear to inherently representational Platonic complexes of universals and particulars. Since we have no way of understanding how such structures can be representational, independent of interpretations placed on them by agents, the problem is unsolvable when so conceived. However, when propositions are taken to be cognitive-event types, the order of explanation is reversed and a natural solution emerges. Propositions are representational because they are constitutively related to inherently representational cognitive acts. Strikingly original, What Is Meaning? is a major advance. (shrink)

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox, a challenge to 'classical' mathematics from a world-famous mathematician, a new foundational school, and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection (...) brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

The book also sheds new light on the nature of metaphysical theorizing by exploring the interaction of semantic and metaphysical issues, the connections between different metaphysical issues, and the nature of ontological commitment.

In this book, Scott Soames argues that the revolution in the study of language and mind that has taken place since the late nineteenth century must be rethought. The central insight in the reigning tradition is that propositions are representational. To know the meaning of a sentence or the content of a belief requires knowing which things it represents as being which ways, and therefore knowing what the world must be like if it is to conform to how the sentence (...) or belief represents it. These are truth conditions of the sentence or belief. But meanings and representational contents are not truth conditions, and there is more to propositions than representational content. In addition to imposing conditions the world must satisfy if it is to be true, a proposition may also impose conditions on minds that entertain it. The study of mind and language cannot advance further without a conception of propositions that allows them to have contents of both of these sorts. Soames provides it. He does so by arguing that propositions are repeatable, purely representational cognitive acts or operations that represent the world as being a certain way, while requiring minds that perform them to satisfy certain cognitive conditions. Because they have these two types of content—one facing the world and one facing the mind—pairs of propositions can be representationally identical but cognitively distinct. Using this breakthrough, Soames offers new solutions to several of the most perplexing problems in the philosophy of language and mind. (shrink)

Propositional attitudes, like believing and asserting, are relations between agents and propositions. Agents are individuals who do the believing and asserting; propositions are things that are believed and asserted. Propositional attitude ascriptions are sentences that ascribe propositional attitudes to agents. For example, a propositional attitude ascription α believes, or asserts, that S is true iff the referent of a bears the relation of believing, or asserting, to the proposition expressed by s. The questions I will address have to do with (...) the precise nature of propositions, and the attitudes, like belief, that we bear to them.I will assume both that propositions are the semantic contents of sentences, and that the proposition expressed by a sentence is a structured complex made up of the semantic contents of the parts of the sentences that express it. (shrink)

(2013). What are Propositions? Canadian Journal of Philosophy: Vol. 43, Essays on the Nature of Propositions, pp. 702-719.

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. (shrink)

In this paper I defend an account of the nature of propositional content according to which the proposition expressed by a declarative sentence is a certain type of action a speaker performs in uttering that sentence. On this view, the semantic contents of proper names turn out to be types of reference acts. By carefully individuating these types, it is possible to provide new solutions to Frege’s puzzles about names in identity- and belief-sentences.

Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining what (...) is meant by definability and by “arbitrariness,” a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds to offer an elementary discussion of how far the Zermelo—Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect. (shrink)

Geometrical and physical intuition, both untutored andcultivated, is ubiquitous in the research, teaching,and development of mathematics. A number ofmathematical ``monsters'', or pathological objects, havebeen produced which – according to somemathematicians – seriously challenge the reliability ofintuition. We examine several famous geometrical,topological and set-theoretical examples of suchmonsters in order to see to what extent, if at all,intuition is undermined in its everyday roles.

This philosophical treatise on the foundations of semantics is a systematic effort to clarify, deepen and defend the classical doctrine that words are conventional signs of mental states, principally thoughts and ideas, and that meaning consists in their expression. This expression theory of meaning is developed by carrying out the Gricean programme, explaining what it is for words to have meaning in terms of speaker meaning, and what it is for a speaker to mean something in terms of intention. But (...) Grice's own formulations are rejected and alternatives developed. The foundations of the expression theory are explored at length, and the author develops the theory of thought as a fundamental cognitive phenomenon distinct from belief and desire, argues for the thesis that thoughts have parts, and identifies ideas or concepts with parts of thoughts. This book will appeal to students and professionals interested in the philosophy of language. (shrink)

Philosophy, science, and common sense all refer to propositions--things we believe and say, and things which are true or false. But there is no consensus on what sorts of things these entities are. Jeffrey C. King, Scott Soames, and Jeff Speaks argue that commitment to propositions is indispensable, and each defend their own views on the debate.

This book critically examines some widespread views about the semantic phenomenon of reference and the cognitive phenomenon of singular thought. It begins with a defense of the view that neither is tied to a special relation of causal or epistemic acquaintance. It then challenges the alleged semantic rift between definite and indefinite descriptions on the one hand, and names and demonstratives on the other—a division that has been motivated in part by appeals to considerations of acquaintance. Drawing on recent work (...) in semantics, the book explores a more unified account of all four types of expression, according to which none of them paradigmatically fits the profile of a referential term. On the proposed framework, all four involve existential quantification but admit of uses that exhibit many of the traits associated with reference—a phenomenon that is due to the presence of what we call a ‘singular restriction’ on the existentially quantified domain. The book concludes by drawing out some implications of the proposed semantic picture for the traditional categories of reference and singular thought. (shrink)

Leading experts in the field contributing to this volume make the case for the singularity of thought and debate a broad spectrum of issues it raises, including ...

Constructive and intuitionistic Zermelo-Fraenkel set theories are axiomatic theories of sets in the style of Zermelo-Fraenkel set theory (ZF) which are based on intuitionistic logic. They were introduced in the 1970's and they represent a formal context within which to codify mathematics based on intuitionistic logic. They are formulated on the basis of the standard first order language of Zermelo-Fraenkel set theory and make no direct use of inherently constructive ideas. In working in constructive and intuitionistic ZF we can thus (...) to some extent rely on our familiarity with ZF and its heuristics. -/- Notwithstanding the similarities with classical set theory, the concepts of set defined by constructive and intuitionistic set theories differ considerably from that of the classical tradition; they also differ from each other. The techniques utilised to work within them, as well as to obtain metamathematical results about them, also diverge in some respects from the classical tradition because of their commitment to intuitionistic logic. In fact, as is common in intuitionistic settings, a plethora of semantic and proof-theoretic methods are available for the study of constructive and intuitionistic set theories. -/- The entry introduces the main features of Constructive and Intuitionistic ZF and offers links to the relevant bibliography. (shrink)

The principle of set theory known as the Axiom of Choice (AC) has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s axiom of parallels which was introduced more than two thousand years ago”1 It has been employed in countless mathematical papers, a number of monographs have been exclusively devoted to it, and it has long played a prominently role in discussions on the foundations of (...) mathematics. (shrink)