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."

The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know weIl, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science."

The two volumes to which this is a preface consist of the Proceedings of the Second International Conference on History and Philosophy of Science. The Conference was organized by the Joint Commission of the International Union of History and Philosophy of Science (IUHPS) of the IUHPS, the Italian Society for Logic and under the auspices Philosophy of Science, and the Domus Galilaeana of Pisa, headed by Professor Vincenzo Cappelletti. Domus GaIilaeana also served as the host institution, with some help from the University of Pisa. The Conference took place in Pisa, Italy, on September 4-8, 1978. The editors of these two volumes of the Proceedings of the Pisa Conference acknowledge with gratitude the help by the different sponsoring organizations, and in the first place that by both, Divisions of the IUHPS, which made the Conference possible.' A special recognition is due to Professor Evandro Agazzi, President of the Italian Society for Logic and Philosophy of Science, who was co opted as an additional member of the Organizing Committee. This committee was otherwise identical with the Joint Commission, whose members were initially John Murdoch, John North, Arpad Szab6, Robert Butts, Jaakko Hintikka, and Vadim Sadovsky. Later, Erwin Hiebert and Lubos Novy were appointed as additional members."

A word of warning concerning the aims of this volume is in order. Other wise some readers might be unpleasantly surprised by the fact that two of the chapters of an ostensibly historical book are largely topical rather than historical. They are Chapters 7 and 9, respectively entitled 'Are Logical Truths Analytic?' and 'A Priori Truths and Things-In-Them selves'. Moreover, the history dealt with in Chapter 11 is so recent as to have more critical than antiquarian interest. This mixture of materials may seem all the more surprising as I shall myself criticize (in Chapter I) too facile assimilations of earlier thinkers' concepts and problems to later ones. There is no inconsistency here, it seems to me. The aims of the present volume are historical, and for that very purpose, for the purpose of understanding and evaluating earlier thinkers it is vital to know the conceptual landscape in which they were moving. A crude analogy may be helpful here. No military historian can afford to neglect the topo graphy of the battles he is studying. If he does not know in some detail what kind of pass Thermopylae is or on what sort of ridge the battle of Bussaco was fought, he has no business of discussing these battles, even if this topographical information alone does not yet amount to historical knowledge."

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 .

cake, even though it is typically given the pride of place in expositions in Frege's semantics. As a part of this attempted reversal of emphasis, Jaakko Hintikka has also called attention to the role Frege played in convincing almost everyone that verbs for being had to be treated as multiply ambiguous between the "is" of identity, the "is" of predication, the "is" of existence, and the "is" of class-inclusion - a view that had been embraced by few major figures (if any) before Frege, with the exception of John Stuart Mill and Augustus De Morgan. Hintikka has gone on to challenge this ambiguity thesis. At the same time, Frege's role in the genesis of another major twentieth-century philosophical movement, the phenomenological one, has become an important issue. Even the translation of Frege's key term "Bedeutung" as "reference" has become controversial. The interpretation of Frege is thus thrown largely back in the melting pot. In editing this volume, we have not tried to publish the last word on Frege. Even though we may harbor such ambitions ourselves, they are not what has led to the present editorial enterprise. What we have tried to do is to bring together some of the best ongoing work on Frege. Even though the ultimate judgment on our success lies with out readers, we want to register our satisfaction with all the contributions.

The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science."

The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science."

The two volumes to which this is apreface consist of the Proceedings of the Second International Conference on History and Philosophy of Science. The Conference was organized by the Joint Commission of the International Union of History and Philosophy of Science (IUHPS) under the auspices of the IUHPS, the Italian Society for Logic and Philosophy of Science, and the Domus Galilaeana of Pisa, headed by Professor Vincenzo Cappelletti. Domus Galilaeana also served as the host institution, with some help from the University of Pisa. The Conference took place in Pisa, Italy, on September 4-8, 1978. The editors of these two volumes of the Proceedings of the Pisa Conference acknowledge with gratitude the help by the different sponsoring organizations, and in the first place that by both Divisions of the IUHPS, which made the Conference possible. A special recognition is due to Professor Evandro Agazzi, President of the Italian Society for Logic and Philosophy of Science, who was co opted as an additional member of the Organizing Committee. This committee was otherwise identical with the Joint Commission, whose members were initially John Murdoch, John North, Arpad Szab6, Robert Butts, Jaakko Hintikka, and Vadim Sadovsky. Later, Erwin Hiebert and Lubos Novy were appointed as additional members."

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 (Noel 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).

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.

Several of the basic ideas of current language theory are subjected to critical scrutiny and found wanting, including the concept of scope, the hegemony of generative syntax, the Frege-Russell claim that verbs like is' are ambiguous, and the assumptions underlying the so-called New Theory of Reference. In their stead, new constructive ideas are proposed.

R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however.

This volume contains papers on truth, logic, semantics, and history of logic and philosophy. These papers are dedicated to Jan Wolenski to honor his 60th birthday. Jan Wolenski is professor of philosophy at the Department of Philosophy of the Jagiellonian University in Cracow, Poland. He is likely to be the most well-known Polish philosopher of this time, best known for his work on the history of the philosophy and logic of the Lvov-Warsaw School.

Is a genuine logic of scientific discovery possible? In the essays collected here, Hintikka not only defends an affirmative answer; he also outlines such a logic. It is the logic of questions and answers. Thus inquiry in the sense of knowledge-seeking becomes inquiry in the sense of interrogation. Using this new logic, Hintikka establishes a result that will undoubtedly be considered the fundamental theorem of all epistemology, viz., the virtual identity of optimal strategies of pure discovery with optimal deductive strategies. Questions to Nature, of course, must include observations and experiments. Hintikka shows, in fact, how the logic of experimental inquiry can be understood from the interrogative vantage point. Other important topics examined include induction (in a forgotten sense that has nevertheless played a role in science), explanation, the incommensurability of theories, theory-ladenness of observations, and identifiability.

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 Goedel: 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 Goedel 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.

Aristotle thought of his logic and methodology as applications of the Socratic questioning method. In particular, logic was originally a study of answers necessitated by earlier answers. For Aristotle, thought-experiments were real experiments in the sense that by realizing forms in one's mind, one can read off their properties and interrelations. Treating forms as independent entities, knowable one by one, committed Aristotle to his mode of syllogistic explanation. He did not think of existence, predication and identity as separate senses of estin. Aristotle thus serves as an example of a thinker who did not rely on the distinction between the allegedly different Fregean senses, thereby shedding new light on our own conceptual presuppositions.
This collection comprises several striking interpretations that Jaakko Hintikka has put forward over the years, constituting a challenge not only to Aristotelian scholars and historians of ideas, but to everyone interested in logic, epistemology or metaphysics and in their history.

This volume contains papers on truth, logic, semantics, and history of logic and philosophy. These papers are dedicated to Jan Wolenski to honor his 60th birthday. Jan Wolenski is professor of philosophy at the Department of Philosophy of the Jagiellonian University in Cracow, Poland. He is likely to be the most well-known Polish philosopher of this time, best known for his work on the history of the philosophy and logic of the Lvov-Warsaw School.

Is a genuine logic of scientific discovery possible? In the essays collected here, Hintikka not only defends an affirmative answer; he also outlines such a logic. It is the logic of questions and answers. Thus inquiry in the sense of knowledge-seeking becomes inquiry in the sense of interrogation. Using this new logic, Hintikka establishes a result that will undoubtedly be considered the fundamental theorem of all epistemology, viz., the virtual identity of optimal strategies of pure discovery with optimal deductive strategies. Questions to Nature, of course, must include observations and experiments. Hintikka shows, in fact, how the logic of experimental inquiry can be understood from the interrogative vantage point. Other important topics examined include induction (in a forgotten sense that has nevertheless played a role in science), explanation, the incommensurability of theories, theory-ladenness of observations, and identifiability.

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.

Several of the basic ideas of current language theory are subjected to critical scrutiny and found wanting, including the concept of scope, the hegemony of generative syntax, the Frege-Russell claim that verbs like is' are ambiguous, and the assumptions underlying the so-called New Theory of Reference. In their stead, new constructive ideas are proposed.

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.

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.

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 GAdel: 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 GAdel 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.