Jaakko Hintikka

On Godel

Vincent F. Hendricks

John Symons

Knowledge and Belief - An Introduction to the Logic of the Two Notions

Merrill B. Hintikka

Investigating Wittgenstein

On Wittgenstein

Patrick Suppes

J.M.E. Moravcsik

The papers and comments published in the present volume represent the proceedings of a research workshop on the grammar and semantics of natural languages held at Stanford University in the fall of 1970. The workshop met first for three days in September and then for a period of two days in November for extended discussion and analysis. The workshop was sponsored by the Committee on Basic Research in Education, which has been funded by the United States Office of Education through a grant to the National Academy of Education and the National Academy of Sciences - National Research Council. We acknowledge with pleasure the sponsorship which made possible a series oflively and stimulating meetings that were both enjoyable and instructive for the three of us, and, we hope, for most of the participants, including a number of local linguists and philosophers who did not contribute papers but actively joined in the discussion. One of the central participants in the workshop was Richard Montague. We record our sense of loss at his tragic death early in 1971, and we dedicate this volume to his memory. None of the papers in the present volume discusses explicitly problems of education. In our view such a discussion is neither necessary nor sufficient for a contribution to basic research in education. There are in fact good reasons why the kind of work reported in the present volume constitutes an important aspect of basic research in education.

Proceedings of the 1970 Stanford Workshop on Grammar and Semantics

Approaches to Natural Language

I. Niiniluoto

Esa. Saarinen

The Fourth Scandinavian Logic Symposium and the First Soviet-Finnish Logic Conference were held in JyvaskyIa, Finland, June 29-July 6, 1976. The Conferences were organized by a committee which consisted of the editors of the present volume. The Conferences were supported financially by the Ministry of Education of Finland, by the Academy of Finland, and by the Division of Logic, Methodology, and Philosophy of Science of the International Union of History of Science. The Philosophical Society of Finland and the Jyvaskyla Summer Festival gave valuable help in various practicalities. 35 papers by authors representing 10 countries were presented at the two meetings. Of those papers 24 appear here. THE EDITORS v TABLE OF CONTENTS PREFACE v PART 1/ PROOF THEORY GEORG KREISEL / Some Facts from the Theory of Proofs and Some Fictions from General Proof Theory 3 DAG PRAWITZ / Proofs and the Meaning and Completeness of the Logical Constants 25 v. A. SMIRNOV / Theory of Quantification and tff-calculi 41 LARS SVENONIUS/Two Kinds of Extensions of Primitive Recursive Arithmetic 49 DIRK VAN DALEN and R. STATMAN / Equality in the Presence of Apartness 95 PART II / INFINITARY LANGUAGES VEIKKO RANTALA / Game-Theoretical Semantics and Back-and- Forth 119 MAARET KAR TTUNEN / Infinitary Languages N oo~.

Proceedings of the Fourth Scandinavian Logic Symposium and of the First Soviet-Finnish Logic Conference, Jyväskylä, Finland, June 29–July 6, 1976

Essays on Mathematical and Philosophical Logic

Päämäärä, sattuma ja välttämättömyys

IF WITI'GENSTEIN COULD TALK, COULD WE UNDERSTAND HIM? Perusing the secondary literature on Wittgenstein, I have frequently experienced a perfect Brechtean Entfremdungseffekt. This is interesting, I have felt like saying when reading books and papers on Wittgenstein, but who is the writer talking about? Certainly not Ludwig Wittgenstein the actual person who wrote his books and notebooks and whom I happened to meet. Why is there this strange gap between the ideas of the actual philosopher and the musings of his interpreters? Wittgenstein is talking to us through the posthumous publication of his writings. Why don't philosophers understand what he is saying? A partial reason is outlined in the first essay of this volume. Wittgenstein was far too impatient to explain in his books and book drafts what his problems were, what it was that he was trying to get clear about. He was even too impatient to explain in full his earlier solutions, often merely referring to them casually as it were in a shorthand notation. For one important instance, in The Brown Book, Wittgenstein had explained in some detail what name-object relationships amount to in his view. There he offers both an explanation of what his problem is and an account of his own view illustrated by means of specific examples of language-games. But when he raises the same question again in Philosophical Investigations I, sec.

Ludwig Wittgenstein: Half-Truths and One-and-a-Half-Truths

D. Davidson

It is gratifying to see that philosophers' continued interest in Words and Objections has been so strong as to motivate a paperback edition. This is gratifying because it vindicates the editors' belief in the permanent im portance of Quine's philosophy and in the value of the papers com menting on it which were collected in our volume. Apart from a couple of small corrections, only one change has been made. The list of Professor Quine's writings has been brought up to date. The editors cannot claim any credit for this improvement, however. We have not tried to imitate the Library of Living Philosophers volumes and to include Professor Quine's autobiography in this volume, but we are fortunate to publish here his brand-new auto bibliography. 1975 THE EDITORS TABLE OF CONTENTS V PREFACE 1 EDITORIAL INTRODUCTION 1. 1. C. SMAR T / Quine's Philosophy of Science 3 GILBERT HARMAN / An Introduction to 'Translation and Meaning', Chapter Two of Word and Object 14 ERIK STENIUS / Beginning with Ordinary Things 27 NOAM CHOMSKY / Quine's Empirical Assumptions 53 1AAKKO HINTIKKA / Behavioral Criteria of Radical Translation 69 BARRY STROUD / Conventionalism and the Indeterminacy of Translation 82 P. F. STRA WSON / Singular Terms and Predication 97 118 H. P. GRICE / Vacuous Names P. T.

Essays on the Work of W.V. Quine

Words and Objections

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general.

Selected Essays

Models for Modalities

Les quatre études qui composent le présent recueil témoignent de la variété des intérêts de l'auteur. Les questions que posent le statut du langage et ses liens avec ce que nous appelons ordinairement le réel ne sont pas fondamentalement ni forcément étrangères aux interrogations ou aux visées qui animent la création artistique. Assurément, les propos des peintres sont rarement immédiatement compréhensibles au philosophe ; ceux des écrivains peuvent l'être davantage. Pourtant, à la lumière de leurs oeuvres, ils révèlent de singulières convergences, des parallèles ou des complicités croisant les voies dans lesquelles la philosophie se fraye un chemin, de façon tout aussi problématique, quoique plus consciente en apparence. Des réflexions qui concernent ici la vérité à celles qui s'étendent à Picasso et Braque, puis à Virginia Woolf, jusqu'au sens de la phénoménologie chez Wittgenstein, un fil court dont Hintikka tente de suivre les méandres : celui de la poursuite du réel.

et autres essais

La vérité est-elle ineffable ?

Metaphor is one of the most frequently evoked but at the same time most poorly understood concepts in philosophy and literary theory. In recent years, several interesting approaches to metaphor have been presented or outlined. In this volume, authors of some of the most important new approaches re-present their views or illustrate them by means of applications, thus allowing the reader to survey some of the prominent ongoing developments in this field. These authors include Robert Fogelin, Susan Haack, Jaakko Hintikka (with Gabriel Sandu), Bipin Indurkhya and Eva Kittay (with Eric Steinhart). Their stance is in the main constructive rather than critical; but frequent comparisons of different views further facilitate the reader's overview. In the other contributions, metaphor is related to the problems of visual representation (Noël Carroll), to the open class test (Avishai Margalit and Naomi Goldblum) as well as to Wittgenstein's idea of 'a way of life' (E.M. Zemach).

Aspects of Metaphor

Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.

Essays on the Development of the Foundations of Mathematics

From Dedekind to Gödel

Aspects of Inductive Logic

The Intentions of Intentionality and Ather New Models for Modalities

Most of the papers appearing in volume 87 numbers, 1-2 are based on papers presented at the Colloquium on the Philosophy of Ludwig Wittgenstein held at the Department of Philosophy at Florida State University on 7-8 April 1989. We owe warm thanks to Florida State University for generously supporting this colloquium. The English translation of the chapter entitled 'Philosophie', from Wittgenstein's typescript number 213 (von Wright), appears here with permission of Wittgenstein's literary heirs, without affecting existing copyrights. The original German version of this chapter was edited by Heikki Nyman and appeared in Revue Internationale de Philosophie 43 (1989), pp. 175-203. Jaakko Hintikka's article (87, No.2) first appeared in a shorter form in The Times Literary Supplement No. 4565 (28 September to 4 October 1990, p. 1030). The present version appears with the permis sion of The Times Literary Supplement, which is gratefully acknowl edged. Our thanks are due to all the participants of the colloquium and the contributors to these special numbers.

Proceedings of the Colloquium on the Philosophy of Ludwig Wittgenstein, Florida State University, 7–8 August 1989

Wittgenstein in Florida

Kaarlo Jaakko Juhani Hintikka

Fernand Vandamme

Logic of Discovery and Logic of Discourse

One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.

Jaakko Hintikka

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