Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s

As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing the development of his views in the forties have recently begun to be published, as well as careful philosophical studies of, for instance, the evolution of his key doctrine that mathematical and logical truth are continuous with, not divorced from, the truths of natural science. But one central text has remained unexplored: Quine's Portuguese-language book on logic, his 'farewell for now' to the discipline as he embarked on an assignment in the Navy in WWII. Anglophone philosophers have neglected this book because they could not read it. Jointly with colleagues, I have completed the first full English translation of this book. In this accompanying paper I draw out the main philosophical contributions Quine made in the book, placing them in their historical context and relating them to Quine's overall philosophical development during the period. Besides significant developments in the evolution of Quine's views on meaning and analyticity, I argue, this book is also driven by Quine's indebtedness to Russell and Whitehead, Tarski, and Frege, and contains crucial developments in his thinking on philosophy of logic and ontology. This includes early versions of some arguments from 'On What There Is', four-dimensionalism, and virtual set theory

Existence, knowledge & truth in mathematics

This thesis offers an overview of some current work in the philosophy of mathematics, in particular of work on the metaphysical, epistemological, and semantic problems associated with mathematics, and it also offers a theory about what type of entities numbers are. Starting with a brief look at the historical and philosophical background to the problems of knowledge of mathematical facts and entities, the thesis then tackles in depth, and ultimately rejects as flawed, the work in this area of Hartry Field, Penelope Maddy, Jonathan Lowe, John Bigelow, and also some aspects of the work of Philip Kitcher and David Armstrong. Rejecting both nominalism and physicalism, but accepting accounts from Bigelow and Armstrong that numbers can be construed as relations, the view taken in this work is that mathematical objects, numbers in particular, are universals, and as such are mind dependent entities. It is important to the arguments leading to this conception of mathematical objects, that there is a notion of aspectual seeing involved in mathematical conception. Another important feature incorporated is the notion, derived from Anscombe, of an intentional object. This study finishes by sketching what appears to be a fruitful line of enquiry with some significant advantages over the other accounts discussed. The line taken is that the natural numbers are mind dependent intentional relations holding between intentional individuals, and that other classes of number - the rationals, the reals, and so on - are mind dependent intentional relations holding between other intentional relations. The distinction in type between the natural numbers and the rest, is the intuitive one that is drawn naturally in language between the objects referred to by the so-called count nouns, and the objects referred to by the so-called mass nouns

Philosophy of mathematics education

PHILOSOPHY OF MATHEMATICS EDUCATION\ud This thesis supports the view that mathematics teachers should be aware of differing views of the nature of mathematics and of a range of teaching perspectives. The first part of the thesis discusses differing ways in which the subject 'mathematics' can be identified, by relying on existing philosophy of mathematics. The thesis describes three traditionally recognised philosophies of mathematics: logicism, formalism and intuitionism. A fourth philosophy is constructed, the hypothetical, bringing together the ideas of Peirce and of Lakatos, in particular. The second part of the thesis introduces differing ways of teaching mathematics, and identifies the logical and sometimes contingent connections that exist between the philosophies of mathematics discussed in part 1, and the philosophies of mathematics teaching that arise in part 2. Four teaching perspectives are outlined: the teaching of mathematics as aestheticallyorientated, the teaching of mathematics as a game, the teaching of mathematics as a member of the natural sciences, and the teaching of mathematics as technology-orientated. It is argued that a possible fifth perspective, the teaching of mathematics as a language, is not a distinctive approach. A further approach, the Inter-disciplinary perspective, is recognised as a valid alternative within previously identified philosophical constraints. Thus parts 1 and 2 clarify the range of interpretations found in both the philosophy of mathematics and of mathematics teaching and show that they present realistic choices for the mathematics teacher. The foundations are thereby laid for the arguments generated in part 3, that any mathematics teacher ought to appreciate the full range of teaching 4 perspectives which may be chosen and how these link to views of the nature of mathematics. This would hopefully reverse 'the trend at the moment... towards excessively narrow interpretation of the subject' as reported by Her Majesty's Inspectorate (Aspects of Secondary Education in England, 7.6.20, H. M. S. O., 1979). While the thesis does not contain infallible prescriptions it is concluded that the technology-orientated perspective supported by the hypothetical philosophy of mathematics facilitates the aims of those educators who show concern for the recognition of mathematics in the curriculum, both for its intrinsic and extrinsic value. But the main thrust of the thesis is that the training of future mathematics educators must include opportunities for gaining awareness of the diversity of teaching perspectives and the influence on them of philosophies of mathematics

A pragmatic theory of truth and ontology

At the heart of my pragmatic theory of truth and ontology is a view of the relation between language and reality which I term internal justification: a way of explaining how sentences may have truth-values which we cannot discover without invoking the need for the mystery of a correspondence relation. The epistemology upon which the theory depend~ is fallibilist and holistic (chapter 2); places heavy reliance on modal idioms (chapter 4); and leads to the conclusion that current versions of realism and anti-realism are deficient (chapter 5). Just as my theory avoids the need for an epistemic 'given', it avoids the need for a metaphysical 'given' or 'joints'. I offer a view of the nature of philosophy and what it can properly achieve with respect to ontological questions (chapter 3); since those views lead me to believe that philosophical discussion about what exists should be restricted to 'entities' discussed in non-philosophical contexts, my views on how we should understand claims made about the existence of middle-sized physical objects (chapters 2 and 6), theoretical entities in science (chapter 6), and abstract entities in mathematics (chapter 7), give the thesis a schematic completeness. My theory leads me to a conception of inquiry which defends the cognitive status of moral statements whilst being critical of Kantian and utilitarian approaches to morality (chapter 8). Chapter 1 explores the views of my closest philosophical allies: William James and Nelson Goodman

Inquiries into the status of truth-claims in religious discourse: some interpretations of the philosophical system of Donald Davidson

This work reflects its title in that it is in two parts. The first two chapters attempt to show that truth is not the property of statements or propositions alone but is directly related to the beliefs or intentions (or other dispositions) which they encode. The role of Christian expectation as a truth-bearer is given some prominence. The third chapter begins the interpretative aspect of the analysis. The truth-theory of Donald Davidson is outlined against the background of his whole philosophical system. This leads to a new understanding of propositional attitudes, for they are now seen to express a causal relationship with the reality which underlies them. Davidson's method of seeking a correspondence with that reality via a coherence theory of truth is then analysed. This relies upon a so-called 'Convention of Charity' embodying a holistic agreement about what it is to call a thing 'real'. Considerable attention is given to the way that Davidson is continually developing his philosophy in this respect. The fourth chapter discusses the ways in which the truth-conditional theory of Davidson could be applied to religious discourse. The problems of religious divergence and of figurative or metaphorical language are singled out for special attention. The final chapter attempts to unite the study by evaluating this interpretation in the light of the claims for truth which theologians might make. This involves outlining the form which a new non-foundationalist theological epistemology might take, given the application of a Davidsonian philosophical system. This study is seen as particularly fruitful in generating areas for future research. A secondary aim of this analysis has been to investigate what sort of realism is possible for religious discourse

With reference to truth : studies in referential semantics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1982.MICROFICHE COPY AVAILABLE IN ARCHIVES AND HUMANITIESVita.Includes bibliographical references.by Douglas Fillmore Cannon.Ph.D

Plural predication

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, February 2001.Includes bibliographical references (p. 87-89).My thesis consists of three self-contained but interconnected papers. In the first one, 'Word and Objects', I assume that it is possible to quantify over absolutely everything, and show that certain English sentences containing collective predicates resist paraphrase in first-order languages and even in first-order languages enriched with plural quantifiers. To capture such sentences I develop a language containing plural predicates. The introduction of plural predicates leads to an extension of Quine's criterion of ontological commitment. I argue that theories containing plural predicates can have plural ontological commitments in addition to singular ones. In this sense, I argue that the subject-matter of ontology is richer than one might have thought. Plural predicates turn out to be tremendously fruitful. For example, they provide us with natural formalizations for English plural definite descriptions and generalized quantifiers. They also allow us to state important set theoretic propositions, and give a formal semantics for second-order languages. Such a formal semantics is developed in the second paper, 'Toward a Theory of Second-Order Consequence', which is a collaboration with Gabriel Uzquiano. In the third paper, 'Frege's Unofficial Arithmetic', I consider an application of plural predicates to the philosophy of mathematics. By developing a suggestion of the later Frege, I show that any arithmetical predicate can be transformed into a plural predicate in such a way that the arithmetical predicate is true of the number of the Fs just in case the plural predicate is true of the Fs themselves. The transformation is important both because it can be put to use by nominalists about arithmetic and neo-Fregeans, and because it provides the foundations for an account of applied arithmetic.by Agustín Rayo.Words and objects -- Toward a theory of second-order consequence -- Fregg's unofficial arithmetic.Ph.D

An Observation about Truth

Tarski's analysis of the concept of truth gives rise to a hierarchy of languages. Does this fragment the concept all the way to philosophical unacceptability? I argue it doesn't, drawing on a modification of Kaplan's theory of indexicals

Meaning theory and the problem of the acquisition of a first language.

The thesis begins by making two distinctions which are\ud central to its methodology. The first is that between valid\ud and invalid criticism, the second between philosophy of\ud language and meaning theory. These distinctions combine to\ud produce the methodology which informs the thesis, namely\ud that a theory of meaning can be validly criticised in terms\ud of its account, implicit or explicit, of first language\ud acquisition and, conversely, an account of first language\ud acquisition can be validly criticised in terms of its\ud theory, implicit or explicit, of meaning. The thesis\ud continues by testing the appropriateness of the methodology\ud against the classical empiricist and rationalist accounts of\ud meaning expressed in terms of Ideas, arguing that the\ud majority of criticisms of these accounts misfire as they do\ud not operate within the framework of the positions they\ud purport to criticise. Such invalid criticism is replaced\ud with that argued for here, the conclusion being that the\ud classical accounts of meaning are to be rejected on the\ud grounds that they make use of a phenomenon, language, whose\ud acquisition they cannot, within the terms of their own\ud position, explain. Modern, post-Fregean, empiricist and\ud rationalist positions, those of Quine and Chomsky\ud respectively, are then subjected to similar treatment. Both\ud of these positions have explicit accounts of first language acquisition and so the conclusion to this section of the\ud thesis reverses that reached when discussing the classical\ud positions, in that the explanations of first language\ud acquisition given by modern empiricists and rationalists are\ud based on meaning theories which, for a variety of reasons,\ud do not justify their explanations of the phenomenon of first\ud language acquisition.\ud In an attempt to move towards a more positive position two\ud alternative accounts of meaning theory, the formal and the\ud descriptive, are then examined. The formal account,\ud Davidson's, is defended against those critics who produce\ud attacks centering upon its meaning theory as being, in the\ud sense described above, invalid. However, as it is then\ud shown not to be able to account for first language\ud acquisition, it is eventually rejected. The descriptivist\ud account is identified by tracing the development of\ud Wittgenstein's philosophy to support a particular\ud interpretation of his later account of meaning as being a\ud descriptive one and a defence is offered to a number of\ud criticisms of that position. A poorly worked out\ud experiential account of first language acquisition is then\ud identified, and this is developed further by introducing the\ud area of non-linguistics, where meaning can be given without\ud words. The thesis concludes by suggesting that this area's\ud account of first language acquisition, although having a\ud number of difficulties with its implied meaning theory, can be combined with the later work of Wittgenstein to produce\ud what is at least a descriptively adequate account of both\ud meaning and first language acquisition. Moreover, it points\ud to an area of enquiry where philosophical techniques can be\ud utilised to great effect so as to add new dimensions t