Jaakko Hintikka

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

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.

Truthlikeness

Jan Wolenski

Matti Sintonen

The twenty-eight essays in this Handbook, all by leading experts in the field, provide the most extensive treatment of various epistemological problems, supplemented by a historical account of this field. The entries are self-contained and substantial contributions to topics such as the sources of knowledge and belief, knowledge acquisition, and truth and justification. There are extensive essays on knowledge in specific fields: the sciences, mathematics, the humanities and the social sciences, religion, and language. Special attention is paid to current discussions on evolutionary epistemology, relativism, the relation between epistemology and cognitive science, sociology of knowledge, epistemic logic, knowledge and art, and feminist epistemology. This collection is a must-have for anybody interested in human knowledge, and its fortunes and misfortunes.

I. Niiniluoto

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