Book 23

Models for Modalities

by Jaakko Hintikka

Published 30 April 1975
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.

Book 90

The leisure to do the thinking whose results are gathered here has largely been provided by the Academy of Finland, whose support has also made possible the help and co-operation of a group of younger logicians and philosophers. Less tangible support and help is unfortunately harder to record and to thank for. Once again, in working on the many themes I have tried to weave together in this book I have incurred more intellectual and moral debts I can in so many words acknowledge here. Let me only say that the closer to home I get the greater they become. I have especially in mind my colleagues and students at Stanford; my colleagues in Helsinki; the past and present members of my research group in Helsinki; and incom parably more than anybody else my wife Soili. Helsinki, April 1975 JAAKKO HINTIKKA INTRODUCTION A literal-minded reader might easily object to the (sub)title of this volume. What is to be found here, he might allege, are neither models, nor modalities stricto sensu, nor yet any completely new applications of modal logic. Even though the purpose of the title is only to signal the con tinuity between the present volume and its predecessor, Models for Modalities (D. Reidel Publishing Co., Dordrecht, 1969), the objection is sufficiently well taken to serve as an excuse for an attempt to put my enterprise in a wider perspective.

Book 200

somewhat like Henkin's nonstandard interpretation of higher-order logics, while the right semantics [or logical modalities is an analogue to the standard of type theory in Henkin's sense. interpretation Another possibility would be to follow W.V. Quine's advice to give up logi- cal modalities as being beyond repair. Or we could also try to develop a logic of conceptual possibility, restricting the range of our "possible worlds" to those compatible with the transcendental presuppositions of our own conceptual sys- tem. This looks in fact like one of the most interesting possible theories I have dreamt of developing but undoubtedly never will. Its kinship with Kant's way of thinking should be obvious. Besides putting the entire enterprise of possible-worlds semantics into a perspective, we can also see that the actual history of possible-worlds seman- tics is more complicated than it might first appear to be. For the standard in- terpretation of modal logics has reared its beautiful head repeatedly in the writings of Stig Kanger, Richard Montague the pre-Montague-semantics theorist, and Nino Cocchiarella.