Jaakko Hintikka was born on January 12th, 1929. He received his doctorate from the University of Helsinki under the supervision of Professor G. H. von Wright at the age of 24 in 1953. Hintikka was appointed Professor of philosophy at the University of Helsinki in 1959. Since the late 50s, he has shared his time between Finland and the U.S.A. He was appointed Professor of philosophy at Stanford University in 1964. As from 1970 Hintikka has been permanent research professor of the Academy of Finland. He has published 13 books and about 200 articles, not to mention the various editorial and organizational activities he has played an active role in. The present collection of essays has been edited to honour Jaakko Hintikka on the occasion of his fiftieth birthday. By dedicating a Festschrift to Jaakko Hintikka, the contributors wish to pay homage to this remarkable man whom they see not only as a scholar of prodigious energy and insight, but as a friend, colleague and former teacher. The contributors hope the essays collected here will bring pleasure to the man they are intended to honour. All of the essays touch upon topics Hintikka has taken an direct or indirect interest in, ranging from technical problems of mathematical logic and applications of formal methods through philosophical logic, philosophy of language, epistemology and history of philosophy to philosophical aesthetics.

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 .

SECTION I In 1972, Donald Davison and Gilbert Hannan wrote in the introduction to the volume Semantics of Natural Language: "The success of linguistics in treating natural languages as formal ~yntactic systems has aroused the interest of a number of linguists in a parallel or related development of semantics. For the most part quite independently, many philosophers and logicians have recently been applying formal semantic methods to structures increasingly like natural languages. While differences in training, method and vocabulary tend to veil the fact, philosophers and linguists are converging, it seems, on a common set of interrelated problems. " Davidson and Harman called for an interdisciplinary dialogue of linguists, philosophers and logicians on the semantics of natural language, and during the last ten years such an enterprise has proved extremely fruitful. Thanks to the cooperative effort in these several fields, the last decade has brought about striking progress in our understanding of the semantics of natural language. This work on semantics has typically paid little attention to psychological aspects of meaning. Thus, psychologists or computer scientists working on artificial intelligence were not invited to join the forces in the influential introduction of Semantics of Natural Language. No doubt it was felt that while psychological aspects of language are important in their own right, they are not relevant to our immediate semantic concerns. In the last few years, several linguists and logicians have come to question the fundamental anti-psychological assumptions underlying their theorizing.

This book is a collection of studies applying game-theoretical concepts and ideas to analysing the semantics of natural language and some formal languages. The bulk of the book consists of several papers by Hintikka, Carlson and Saarinen and discusses several of the central problems of the semantics of natural language.

The topics covered are the semantics of natural language quantifiers, conditionals, pronouns and anaphora more generally. Hintikkaa (TM)s famous essay presenting examples of "branching quantifier structures" in English, as well as one formulating his "any-every thesis," are included. The book also includes Hintikkaa (TM)s closely argued philosophical discussion of the relationships between the new semantical games with the language games of Wittgenstein. Other papers apply the game-theoretical approach to formal languages including tense logics and tense anaphora (Saarinen), deontic logic and Rossa (TM) paradox (Hintikka), and usual predicate logic (Rantala). The latter amounts to an explication of the "impossible possible" worlds as is shown in Hintikkaa (TM)s concluding paper.

In this collection of essays, some of the leading ecologists and philosophers discuss the foundations of ecology and evolutionary biology. While large scale philosophical convictions and attitudes often direct the theorist's line of concrete action in data collection and in theory information, the founda tional convictions typically remain tacit, and are seldom argued for. The present collection aims to remedy this situation. It brings together scholars representing different approaches in a joint effort to explicate and analyse some of the key issues underlying ecological theorizing, be they conceptual, epistemological or ontological. The bulk of the present collection is reprinted from Synthese 43 (1980). William C. Wimsatt's paper 'Reductionistic Research Strategies and Their Biases in the Units of Selection Controversy' is in turn reprinted from T. Nickles (ed.) Scientific Discovery: Case Studies (D. Reidel, 1980). It appears here with the kind permission of Prof. Nickles. The publisher's consent for the reprints has been in each case automatic. The essays of Y rjo Haila and Olli Jarvinen, and of Leigh M. Van Valen appear here for the first time. In bringing the present collection together, as well as in editing the Synthese symposium on which it is based, I have greatly benefited from the suggestions of Professors Marjorie Grene, Olli J iirvinen and Daniel Simberloff. In addition to them, I wish to thank all the contributors for their interest in this project."

SECTION I In 1972, Donald Davison and Gilbert Hannan wrote in the introduction to the volume Semantics of Natural Language: "The success of linguistics in treating natural languages as formal ~yntactic systems has aroused the interest of a number of linguists in a parallel or related development of semantics. For the most part quite independently, many philosophers and logicians have recently been applying formal semantic methods to structures increasingly like natural languages. While differences in training, method and vocabulary tend to veil the fact, philosophers and linguists are converging, it seems, on a common set of interrelated problems. " Davidson and Harman called for an interdisciplinary dialogue of linguists, philosophers and logicians on the semantics of natural language, and during the last ten years such an enterprise has proved extremely fruitful. Thanks to the cooperative effort in these several fields, the last decade has brought about striking progress in our understanding of the semantics of natural language. This work on semantics has typically paid little attention to psychological aspects of meaning. Thus, psychologists or computer scientists working on artificial intelligence were not invited to join the forces in the influential introduction of Semantics of Natural Language. No doubt it was felt that while psychological aspects of language are important in their own right, they are not relevant to our immediate semantic concerns. In the last few years, several linguists and logicians have come to question the fundamental anti-psychological assumptions underlying their theorizing.

This book is a collection of studies applying game-theoretical concepts and ideas to analysing the semantics of natural language and some formal languages. The bulk of the book consists of several papers by Hintikka, Carlson and Saarinen and discusses several of the central problems of the semantics of natural language.

The topics covered are the semantics of natural language quantifiers, conditionals, pronouns and anaphora more generally. Hintikkaa (TM)s famous essay presenting examples of a ~branching quantifier structuresa (TM) in English, as well as one formulating his a ~any-every thesisa (TM), are included. The book also includes Hintikkaa (TM)s closely argued philosophical discussion of the relationships between the new semantical games with the language games of Wittgenstein. Other papers apply the game-theoretical approach to formal languages including tense logics and tense anaphora (Saarinen), deontic logic and Rossa (TM) paradox (Hintikka), and usual predicate logic (Rantala). The latter amounts to an explication of the a ~impossible possiblea (TM) worlds as is shown in Hintikkaa (TM)s concluding paper.

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 .