REFORGING THE GREAT CHAIN OF BEING SYNTHESE HISTORICAL LIBRARY TEXTS AND STUDIES IN THE HISTOR Y OF LOGIC AND PHILOSOPHY Editors: N. KRETZMANN, Cornell University G. NUCHELMANS, University of Leyden L. M. DE RIIK, University of Leyden Editorial Board: J. BERG, Munich Institute of Technology F. DEL PUNT A, Linacre College, Oxford D. P. HENR Y, University of Manchester J. HINTIKKA B. MATES, University of California, Berkeley J. E. MURDOCH, Harvard University G. PAT Z IG, University of Gottingen VOLUME 20 REFORGING THE GREAT CHAIN OF BEING Studies of the History ofModal Theories Edited by SIMO KNUUTTILA University of Helsinki, Dept. of Philosophy, Helsinki, Finland SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. Library of Congress Cataloging in Publication Data Main entry under title: Reforging the great chain of being. (Synthese historicallibrary ; v. 20) lncludes bibliographies. 1. Modality (Logic)-Addresses, essays, lectures. 2. Modality (Theory of knowledge)-Addresses, essays, lectures. 1. Knuuttila, Simo,1946- II. Series. BC199.M6R36 160 80-19869 ISBN 978-90-481-8360-9 ISBN 978-94-015-7662-8 (eBook) DOI 10.1007/978-94-015-7662-8 Ali Rights Reserved Copyright © 1981 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1981 Softcover reprint of the hardcover 1st edition 1981 and copyright holders as specified on the appropriate pages within. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording or by any informational storage and retrieval system, without written permission from the copyright owner T ABLE OF CONTENTS INTRODUCTION vii JAAKKO HINTIKKA I Gaps in the Great Chain of Being: An Exer­ cise in the Methodology of the History of Ideas MICHAEL DAVID ROHR I Empty Forms in Plato 19 JAAKKO HINTIKKA I Aristotle on the Realization of Possibilities in Time 57 R. M. DANCY I Aristotle and the Priority of Actuality 73 EILEEN F. SERENE I Anselm's Modal Conceptions 117 SIMO KNUUTTILA I Time and Modality in Scholasticism 163 JAAKKO HINTIKKA I Leibniz on Plenitude, Relations, and the 'Reign of Law' 259 JAAKKO HINTIKKA and HEIKKI KANNISTO I Kant on 'The Great Chain of Being' or the Eventual Realization of All Possi- bilities: A Comparative Study 287 INDEX OF NAMES 309 INDEX OF SUBJECTS 315 INTRODUCTION A sports reporter might say that in a competition all the participants realize their potentialities or possibilities. When an athlete performs far below his usual standard, it can be said that it was possible for him to do better. But the idea of fair play requires that this use of 'possible' refers to another com­ petition. It is presumed that the best athlete wins and that no real possibility of doing better is left unrealized in a competition. Here we have a use of language, a language game, in which modal notions are used so as to imply that if something is possible, it is realized. This idea does not belong to the general presuppositions of current ordinary usage. It is, nevertheless, not difficult to fmd other similar examples outside of the language of sports. It may be that such a use of modal notions is sometimes calculated to express that in the context in question there are no real alternative courses of events in contradistinction to other cases in which some possible alternatives remain unrealized. Even though modal notions are currently interpreted without the presup­ position that each genuine possibility should be realized at some moment of the actual history, there are contemporary philosophical models of modalities which incorporate this presupposition. In his book Untersuchungen tiber den Modalkalkiil (Anton Hain, Meisenheim am Glan 1952, pp. 16-36), Oscar Becker presents a statistical interpretation of modal calculi. The basic defmi­ tions are as follows: (1) op = (x)P(x) == ~(Ex)~P(x) (2) ~Op =~(Ex)P(x) == (x)~P(x) (3) Op = (Ex)P(x) == ~(x)~P(x) (4) ~o p = ~(x)P(x) == (Ex)~P(x) (0 stands for necessity, 0 for possibility). In this interpretation it is pre­ supposed that there is a variable element in modal propositions. 'Necessity' and 'possibility' are captured by the universal operator and the existential operator, respectively. They operate on propositional functions, of which those are necessarily true that are satisfied by all values of the bound variable 'x'. Those propositional functions are possible that are satisfied by some value vii S. Knuuttila (ed.), Reforging the Great Chain ofBeing, vii-xiv. Copyright © 1980 by D. Reidel Publishing Company. viii INTRODUCTION of 'x'. If the bound variable 'x' ranges over moments of time, then we have the presupposition mentioned. According to Becker, this is one possible way of understanding the statis­ tical interpretation of modal notions, and he refers to the following passage in Kant: "The Schema of possibility .... is the determination of the re­ presentation of a thing at any time whatsoever. The schema of reality is the existence at a given time. The schema of necessity is the existence of an object at all times." (Immanuel Kant, Critique of Pure Reason, transl. by F. Max Miiller, Doubleday, Garden City, N.Y. 1966, p. 125). This is not the only explication Becker offers to his statistical interpreta­ tion of modal calculi. But on this interpretation modal notions are reduced to extensional terms, and hence similar ideas were not uncommon among the logical positivists. (For some examples see H. Poser, 'Das Scheitern des logischen Positivismus an modaltheoretischen Problemen', Studium Generale 24 (1971), pp. 1522-1535). Other examples of this line of thought can be easily found in the works of Bertrand Russell. In 'The Philosophy of Logical Atomism' (1918) he writes: "One may call a propositional function necessary when it is always true; possible, when it is sometimes true; impossible, when it is never true." (See Bertrand Russell, Logic and Knowledge. Essays 1901-1950, edited by R. C. Marsh, Allen & Unwin, London 1956, p. 231). Russell says that he gets the notion of existence out of the notion of sometimes "which is the same as the notion of possible". So by saying that unicorns exist one means that "x is a unicorn" is possible i.e., there is at least one value of x for which this is true. If there is no such value, then the propositional function is impossible. (Op. cit. pp. 231-233). It is then contended that ordinary uses of the word 'possible' are derived from the idea that a propositional function is possible, when there are cases in which it is true. This is elucidated by discussing the (rather ambiguous) sentence "It is possible it may rain to-morrow". According to Russell this means that "It will rain to-morrow" belongs to "the class of propositions 'It rains at time t', where t is different times. We mean partly that we do not know whether it will rain or whether it will not, but also that that is the sort of proposition that is quite apt to be true, that it is a value of a propositional function of which we know some value to be true." (Op. cit. pp. 254-255. For Russell's views, see also G. H. von Wright, 'Diachronic and Synchronic Modalities', Teorama IX (I979), pp. 231-245.) It is easy to see why Russell must say that modal notions are attributes of propositional functions and not of propositions. He trusts in the analogy between modal notions and those expressing historical frequency without INTRODUCTION ix considering the idea of alternatives of a temporally defmite case. On his interpretation the statistically understood modal notions refer to realization in the actual history, and when temporally defmite events or propositions are discussed, they as such seem to have no modal status. It is typical that in the above quotation the focus of attention is changed from the temporally defmite proposition to a form where there is a blank to be filled by a temporal specification. It is clear that the alleged possibility of the latter, i.e. the fact that it is true for some moments of time, does not say anything about the possibilities at the moment to which the original proposi­ tion refers. Contrary to what Russell says, it does not appear to be typical for the contemporary understanding of possibility that it refers to types of states of affairs exemplified in the actual history. The current ordinary understand­ ing of modality is rather codified, for instance, in what is generally known "as possible worlds semantics. According to it the logic of modal notions can be spelled out only by considering several possible worlds and their relations to each other at the same time. For example, Op is true in the actual world if there is a possible world in which p is true. There is no demand that the pos­ sible world in which p holds true should sometime be actual in the real his­ tory. (See, e.g., laakko Hintikka, Models for Modalities, D. Reidel, Dordrech t 1969). Although there are in contemporary philosophy approaches to the logic of modal notions analogous to those mentioned above, they have mainly lost their attraction as theories about modality. It is widely thOUght that when modal notions are reduced to extensional terms which classify events of the actual history, the resulting idiom does not speak about modality at all. Be this as it may, it seems to be a historical fact that certain kinds of reductionistic statistical interpretations of modal terms enjoyed a prominent status among the presuppositions of Western thought from Aristotle until the late thirteenth century. This was realized by C.