Several of these essays have been printed whole in journals; others are in varying degrees new. Two main themes run through them. One is the problem of meaning, particularly as involved in the notion of an analytic statement. The other is the notion of ontological, commitment, particularly as involved in the problem of universals.

Divided into two parts, the first concentrates on the logical properties of propositions, their relation to facts and sentences, and the parallel objects of commands and questions. The second part examines theories of intentionality and discusses the relationship between different theories of naming and different accounts of belief.

Truth and Meaning is a classic collection of original essays on fundamental questions in the philosophy of language.

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)

There is little doubt that a second-order axiomatization of Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) is desirable. One advantage of such an axiomatization is that it permits us to express the principles underlying the first-order schemata of separation and replacement. Another is its almost-categoricity: M is a model of second-order ZFC if and only if it is isomorphic to a model of the form Vκ, ∈ ∩ (Vκ × Vκ) , for κ a strongly inaccessible ordinal.

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...) modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (shrink)

The aim of this essay is to show that the subject-matter of ontology is richer than one might have thought. Our route will be indirect. We will argue that there are circumstances under which standard first-order regimentation is unacceptable, and that more appropriate varieties of regimentation lead to unexpected kinds of ontological commitment.

In his groundbreaking Grundlagen, Frege (1884) pointed out that number words like ‘four’ occur in ordinary language in two quite different ways and that this gives rise to a philosophical puzzle. On the one hand ‘four’ occurs as an adjective, which is to say that it occurs grammatically in sentences in a position that is commonly occupied by adjectives. Frege’s example was (1) Jupiter has four moons, where the occurrence of ‘four’ seems to be just like that of ‘green’ in (...) (2) Jupiter has green moons. On the other hand, ‘four’ occurs as a singular term, which is to say that it occurs in a position that is commonly occupied by paradigmatic cases of singular terms, like proper names: (3) The number of moons of Jupiter is four. Here ‘four’ seems to be just like ‘Wagner’ in (4) The composer of Tannhäuser is Wagner, and both of these statements seem to be identity statements, ones with which we claim that what two singular terms stand for is identical. But that number words can occur both as singular terms and as adjectives is puzzling. Usually adjectives cannot occur in a position occupied by a singular term, and the other way round, without resulting in ungrammaticality and nonsense. To give just one example, it would be ungrammatical to replace ‘four’ with ‘the number of moons of Jupiter’ in (1): (5) *Jupiter has the number of moons of Jupiter moons. This ungrammaticality results even though ‘four’ and ‘the number of moons of Jupiter’ are both apparently singular terms standing for the same object in (3). So, how can it be that number words can occur both as singular terms and as adjectives, while other adjectives cannot occur as singular terms, and other singular terms cannot occur as adjectives? (shrink)

In this paper I outline an alternative to hermeneutic fictionalism, an alternative I call indifferentism, with the same advantages as hermeneutic fictionalism with respect to ontological issues but avoiding some of the problems that face fictionalism. The difference between indifferentism and fictionalism is this. The fictionalist about ordinary utterances of a sentence S holds, with more orthodox views, that the speaker in some sense commits herself to the truth of S. It is only that for the fictionalist this is truth (...) in the relevant fiction. According to the indifferentist, by contrast, we are simply non-committal – or indifferent – with respect to some aspects of what is literally said in our assertive utterances. (shrink)

(1) The average Mum has 2.4 children. (2) The number of Argle’s fingers equals the number of Bargle’s toes. (3) There are two possible ways in which Joe could win this chess game. In the right contexts, and outside the philosophy room, all the above sentences may be completely uncontroversial. For instance, if we know that Joe could win either by exchanging queens and entering an endgame, or by initiating a kingside attack then, if ignorant of Quine’s work on ontology, (...) we would take (3) to be uncontroversially true. (shrink)

All sides in the recent debates over the Quine‐Putnam Indispensability thesis presuppose Quine's criterion for determining what a discourse is ontologically committed to. I subject the criterion to scrutiny, especially in regard to the available competitor‐criteria, asking what means of evaluation there are for comparing alternative criteria against each other. Finding none, the paper concludes that ontological questions, in a certain sense, are philosophically indeterminate.

Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.

If we must take mathematical statements to be true, must we also believe in the existence of abstract eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant Realism which forces our commitment to anything (...) that our theories quantify. Escaping metaphysical straitjackets, while retaining the insight that some truths are about objects that do exist, Azzouni says that we can sort scientifically-given objects into two categories: ones which exist, and to which we forge instrumental access in order to learn their properties, and ones which do not, that is, which are made up in exactly the same sense that fictional objects are. He offers as a case study a small portion of Newtonian physics, and one result of his classification of its ontological commitments, is that it does not commit us to absolute space and time. (shrink)

Richard Cartwright is one of the most clearheaded, astute, and penetrating philosophers in this country. Because of his own strict standards, however, his work has been published only sparingly and is not as well known as he himself is. Philosophical Essays is a welcome first collection. It includes fifteen essays spanning three decades of Cartwright's thought and focusing on central problems in the philosophy of logic, the philosophy of language, and metaphysics. The introduction offers an excellent guide to Cartwright's mode (...) of thought and pedagogical style. Some of these essays are now regarded as classics; six others are published here for the first time. Each of them, from "Macbeth's Dagger" to "Negative Existentials" and "Propositions of Pure Logic" is a model of craftsmanship and clarity of thought. They span a variety of topics, including identity, truths, essence, implication, and philosophical method. Richard Cartwright is Professor of Philosophy and Head of the Department of Linguistics and Philosophy at MIT. (shrink)

Graham Priest presents a ground-breaking account of the semantics of intentional language--verbs such as "believes," "fears," "seeks," or "imagines." Towards Non-Being proceeds in terms of objects that may be either existent or non-existent, at worlds that may be either possible or impossible. The book will be of central interest to anyone who is concerned with intentionality in the philosophy of mind or philosophy of language, the metaphysics of existence and identity, the philosophy of fiction, the philosophy of mathematics, or cognitive (...) representation in AI. (shrink)

This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.

[Stephen Yablo] The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association, to become the distinction between statements made within make-believe games and those made outside them-or, rather, a special case of it with some claim to be called the metaphorical/literal distinction. Not even Quine considers figurative speech committal, so this turns the tables somewhat. To determine our ontological commitments, we have to ferret out all traces of (...) nonliterality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology. /// [Andre Gallois] I discuss Steve Yablo's defence of Carnap's distinction between internal and external questions. In the first section I set out what I take that distinction, as Carnap draws it, to be, and spell out a central motivation Carnap has for invoking it. In the second section I endorse, and augment, Yablo's response to Quine's arguments against Carnap. In the third section I say why Carnap's application of the distinction between internal and external questions runs into trouble. In the fourth section I spell out what I take to be Yablo's version of Carnap. In the last I say why that version is especially vulnerable to the objection raised in the second. (shrink)

With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar-but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.

When I first began to take an interest in the debate over nominalism in philosophy of mathematics, some twenty-odd years ago, the issue had already been under discussion for about a half-century. The terms of the debate had been set: W. V. Quine and others had given “abstract,” “nominalism,” “ontology,” and “Platonism” their modern meanings. Nelson Goodman had launched the project of the nominalistic reconstruction of science, or of the mathematics used in science, in which Quine for a time had (...) joined him before turning against him. William Alston, Rudolf Carnap, and Michael Dummett had raised doubts about what the point of Goodman’s exercise could be, and though they had unfortunately been largely ignored, Quine’s contention that the exercise cannot be successfully completed had gained wide publicity as the so-called “indispensability” argument against nominalism. By contrast, two subtle discussions of Paul Benacerraf had been appropriated by nominalists and turned into the so-called “multiple reductions” and “epistemological” arguments for nominalism. (shrink)

This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...

I argue against the standard view that ontological debates can be fully described as disagreements about what we should believe to exist. The central thesis of the paper is that believing in Fs in the ontologically relevant sense requires more than merely believing that Fs exist. Believing in Fs is not even a propositional attitude; it is rather an attitude one bears to the term expressed by 'Fs'. The representational correctness of such a belief requires not only that there be (...) Fs, but also that the term expressed by 'Fs' should not misrepresent them. In certain cases we might believe that there are Fs without believing our conception of Fs applies to them. This may well be the situation we are in with regard to abstract entities of various sorts. (shrink)

In a number of essays published over the last decade or so, W. V. Quine has made some interesting suggestions concerning the ontology of theories. If I understand him correctly, one of his principal objects has been to formulate a criterion by means of which one can correctly decide what are the ontological commitments of any given theory. My aim in this paper is to reveal what I think are inadequacies in Quine's criterion and to indicate the direction in which (...) a proper formulation lies. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...) that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...) and science, and two smaller sections on the relationship of ethics and language, and on the philosophy of logic and aesthetics. (shrink)

It is persons who are ontologically committed. But a person is not ontologically committed by virtue of his character, his height, his social standing or whatever, but by virtue of the sentences he assents to. Hence we should look to sentences for a criterion of ontological commitment. This is precisely what is done by advocates of what I will call the Referential theory. In this paper I argue that the Referential theory faces serious objections related to the role paraphrase must (...) play in it. I then present a modified Referential theory and go on to discuss certain implications of the modified theory. More precisely, the paper divides up as follows. In §1 I present the Referential theory. In §2 I argue that it is in trouble over paraphrase. In §3 I consider a general objection to the arguments of §2. In §4 I present the modified theory. In §5 I consider the implications of the modified theory for polemic over what there is and for the existence of properties or universals. (shrink)