Epistemology or theory of knowledge has always been one of the most important -if not the most important -field of philosophy. New arguments are constantly brought to bear on old views, new variants are marshalled to revive ancient stands, new concepts and distinctions increase the sophistication of epistemogical theories. There are a great many excellent textbooks, monographs as well as anthologies consisting of articles in epistemology. Similarly, there are useful philosophical dictionaries which contain a great number of relatively short entries, and general philosophical handbooks which also touch epistemological issues. This volume of 27 essays grew out from the interest to see a handbook which is devoted entirely to the historical roots and systematic development of theory of knowledge. It is not intended to compete but to supplement the already existing literature. It aims at giving both beginners and more advanced students as well as professionals in epistemology and other areas of philosophy an overview of the central problems and solutions of epistemology. The essays are self-contained and stil often rather extensive discussions of the chosen aspects of knowledge. The contributions presuppose very little familiarity with previous literature and only a few of them require the mastery of even elementary logical notation. This, we hope, makes the volume also accessible to the philosophically interested wider audience. The contributors were asked to provide substantial, up-to-date, self-contained and balanced surveys of the various subareas and more specific topics of epistemology, with reference to literature.

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 .

The modern discussion on the concept of truthlikeness was started in 1960. In his influential Word and Object, W. V. O. Quine argued that Charles Peirce's definition of truth as the limit of inquiry is faulty for the reason that the notion 'nearer than' is only "defined for numbers and not for theories." In his contribution to the 1960 International Congress for Logic, Methodology, and Philosophy of Science at Stan ford, Karl Popper defended the opposite view by defining a compara tive notion of verisimilitude for theories. was originally introduced by the The concept of verisimilitude Ancient sceptics to moderate their radical thesis of the inaccessibility of truth. But soon verisimilitudo, indicating likeness to the truth, was confused with probabilitas, which expresses an opiniotative attitude weaker than full certainty. The idea of truthlikeness fell in disrepute also as a result of the careless, often confused and metaphysically loaded way in which many philosophers used - and still use - such concepts as 'degree of truth', 'approximate truth', 'partial truth', and 'approach to the truth'. Popper's great achievement was his insight that the criticism against truthlikeness - by those who urge that it is meaningless to speak about 'closeness to truth' - is more based on prejudice than argument."

This collection brings together several essays which have been written between the years 197 5 and 1983. During that period I have been occupied with the attempt to find a satisfactory explicate for the notion of tnithlike ness or verisimilitude. The technical results of this search have partly appeared elsewhere, and I am also working on a systematic presentation of them in a companion volume to this book: Truthlikeness (forthcoming hopefully in 1985). The essays collected in this book are less formal and more philos ophical: they all explore various aspects of the idea that progress in science is associated with an increase in the truthlikeness of its results. Even though they do not exhaust the problem area of scientific change, together they constitute a step in the direction which I find most promising in the defence of critical scientific realism. * Chapter 1 appeared originally in Finnish as the opening article of a new journal Tiede 2000 (no. 1 I 1980) - a Finnish counterpart to journals such as Science and Scientific American. This explains its programmatic character. It tries to give a compact answer to the question 'What is science?', and serves therefore as an introduction to the problem area of the later chapters. Chapter 2 is a revised translation of my inaugural lecture for the chair of Theoretical Philosophy in the University of Helsinki on April 8, 1981. It appeared in Finnish inParnasso 31 (1981), pp."

Epistemology or theory of knowledge has always been one of the most important -if not the most important -field of philosophy. New arguments are constantly brought to bear on old views, new variants are marshalled to revive ancient stands, new concepts and distinctions increase the sophistication of epistemogical theories. There are a great many excellent textbooks, monographs as well as anthologies consisting of articles in epistemology. Similarly, there are useful philosophical dictionaries which contain a great number of relatively short entries, and general philosophical handbooks which also touch epistemological issues. This volume of 27 essays grew out from the interest to see a handbook which is devoted entirely to the historical roots and systematic development of theory of knowledge. It is not intended to compete but to supplement the already existing literature. It aims at giving both beginners and more advanced students as well as professionals in epistemology and other areas of philosophy an overview of the central problems and solutions of epistemology. The essays are self-contained and stil often rather extensive discussions of the chosen aspects of knowledge. The contributions presuppose very little familiarity with previous literature and only a few of them require the mastery of even elementary logical notation. This, we hope, makes the volume also accessible to the philosophically interested wider audience. The contributors were asked to provide substantial, up-to-date, self-contained and balanced surveys of the various subareas and more specific topics of epistemology, with reference to literature.

The modern discussion on the concept of truthlikeness was started in 1960. In his influential Word and Object, W. V. O. Quine argued that Charles Peirce's definition of truth as the limit of inquiry is faulty for the reason that the notion 'nearer than' is only "defined for numbers and not for theories." In his contribution to the 1960 International Congress for Logic, Methodology, and Philosophy of Science at Stan ford, Karl Popper defended the opposite view by defining a compara tive notion of verisimilitude for theories. was originally introduced by the The concept of verisimilitude Ancient sceptics to moderate their radical thesis of the inaccessibility of truth. But soon verisimilitudo, indicating likeness to the truth, was confused with probabilitas, which expresses an opiniotative attitude weaker than full certainty. The idea of truthlikeness fell in disrepute also as a result of the careless, often confused and metaphysically loaded way in which many philosophers used - and still use - such concepts as 'degree of truth', 'approximate truth', 'partial truth', and 'approach to the truth'. Popper's great achievement was his insight that the criticism against truthlikeness - by those who urge that it is meaningless to speak about 'closeness to truth' - is more based on prejudice than argument."

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.

Conceptual change and its connection to the development of new seien tific theories has reeently beeome an intensively discussed topic in philo sophieal literature. Even if the inductive aspects related to conceptual change have already been discussed to some extent, there has so far existed no systematic treatment of inductive change due to conceptual enrichment. This is what we attempt to accomplish in this work, al though most of our technical results are restricted to the framework of monadic languages. We extend Hintikka's system of inductive logic to apply to situations in which new concepts are introduced to the original language. By interpreting them as theoretica1 concepts, it is possible to discuss a number of currently debated philosophical and methodological problems which have previously escaped systematic and exact treatment. For instance, the role which seientific theories employing theoretical con cepts may play within inductive inference can be studied within this framework. From the viewpoint of seientific realism, sueh a study gives outlines for a theory of what we call hypothetico-induetive inference. Some parts of this work which are based on Hintikka's system of in ductive logic are fairly technical. However, no previous knowledge of this system is required, but, in general, acquaintance with the basic ideas of elementary logic and probability theory is suffieient. This work is part of a project, originated by Professors Jaakko Hintikka and Raimo Tuomela, concerning the role of theoretical concepts in science."

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 .

This collection brings together several essays which have been written between the years 197 5 and 1983. During that period I have been occupied with the attempt to find a satisfactory explicate for the notion of tnithlike ness or verisimilitude. The technical results of this search have partly appeared elsewhere, and I am also working on a systematic presentation of them in a companion volume to this book: Truthlikeness (forthcoming hopefully in 1985). The essays collected in this book are less formal and more philos ophical: they all explore various aspects of the idea that progress in science is associated with an increase in the truthlikeness of its results. Even though they do not exhaust the problem area of scientific change, together they constitute a step in the direction which I find most promising in the defence of critical scientific realism. * Chapter 1 appeared originally in Finnish as the opening article of a new journal Tiede 2000 (no. 1 I 1980) - a Finnish counterpart to journals such as Science and Scientific American. This explains its programmatic character. It tries to give a compact answer to the question 'What is science?', and serves therefore as an introduction to the problem area of the later chapters. Chapter 2 is a revised translation of my inaugural lecture for the chair of Theoretical Philosophy in the University of Helsinki on April 8, 1981. It appeared in Finnish inParnasso 31 (1981), pp."