Reforging the Great Chain of Being: Studies of the History of Modal Theories

331 Pages·1981·7.572 MB·English

by  Jaakko Hintikka (auth.), Simo Knuuttila (eds.)

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 ofM odal 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 1s t 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 ofB eing, 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. S. Peirce, who wrote in
his article 'Modality' for Baldwin's Dictionary of Philosophy and Psychology
(MacMillan, Gloucester, Mass. 1901) as follows: "The simplest account of
modality is the scholastic, according to which the necessary (or impossible)
proposition is a sort of universal proposition; the possible (or contingent, in
the sense of not necessary) proposition, a sort of particular proposition. That
is to assert 'A must be true' is to assert not only that A is true but that all
propositions analogous to A are true; and to assert 'A may be true' is to assert
only that some proposition analogous to A is true. If it be asked what is there
meant by analogous propositions, the answer is - all those of a certain class
which the conveniences of reasoning establish."
I don't comment here on Peirce's own interpretation of "the scholastic
x INTRODUCTION
account of modality"; it is not scholastic. But it is interesting that he refers
to the scholastic theory in which 'necessity' and 'possibility' were defmed in
terms of "true in every case" and "true in some cases", respectively.
In 1936 Arthur O. Lovejoy published his William James Lectures delivered
at Harvard University in 1933 under the title The Great Chain of Being: A
Study of the History of an Idea, (Harvard University Press, Cambridge, Mass.
1936). In this famous study of the history of certain concepts much attention
is paid to the so-<:alled Principle of Plenitude, according to which no genuine
possibility remains unrealized. Lovejoy treats this principle merely as a
corollary to the idea of the Great Chain of Being, i.e., the idea that the selec
tion of different kinds of individuals as are exemplified in actuality is the
fullest possible one. FollOwing his general methodological guidelines, he also
argues that the Principle of Plenitude is a perennial idea which different
thinkers have built into their systems in different ways. In fact the Principle
of Plenitude, when it is understood as a certain kind of relation between
possibility and actuality, can have many various roles in philosophical argu
mentation. It is, e.g., contained in reductionistic statistical modal theories
described above. It can be shown that Lovejoy's reliance on the assumption
of 'unit ideas' prevented him from realizing the variety of ways in which this
alleged 'unit idea' figures in the history of Western thought.
The methodological shortcomings of Lovejoy's attempt are pointed out in
Jaakko Hintikka's essay 'Gaps in the Great Chain of Being: An Exercise in the
Methodology of the History of Ideas' (below pp. 1-17). It serves as a general
introduction to the topics of this book. Hintikka calls attention to different
traditions and lines of thought which in fact imply the Principle of Plenitude
but which were not dealt with in Lovejoy's study. If the Principle is under
stood as a possible ingredient of a theory of modal notions, we can use it as a
theoretical concept in the study of the history of modal notions. Then we
will fmd instances of it as more as less explicit parts of various doctrines in
the history of thought. Many different starting points may yield the same
opinion that each possibility must ultimately bear fruit.
Perhaps the most important single mistake in Lovejoy's book is his claim
that the Principle of Plenitude was explicitly denied by Aristotle. This view
also made him blind to certain peculiarities of the interpretation of modal
notions in the Aristotelian tradition. In his many studies on Aristotle's theory
of modality Hintikka has maintained that the principle is in fact included in
all of Aristotle's modal paradigms. Some of his evidence against Lovejoy's
view of Aristotle is collected in the article 'Aristotle on the Realization of
Possibilities in Time' included in this volume (pp. 57-72).
INTRODUCTION xi
In his book Lovejoy referred to certain passages in which Aristotle seems
to maintain that some possibilities can remain unrealized. This could be called
the Principle of Scarcity. In his interpretation Hintikka maintains that Scar
city does not pertain to total possibilities in Aristotle. It is trivially true that
there are all sorts of unrealized potentialities according to Aristotle. For
instance, he distinguishes what might be called active potencies from passive
ones. If the former is an efficient cause and the latter a material cause, it is
of course possible that in an individual case the material cause is actual but
that the efficient cause is not present. In this sense there can be unrealized
partial potentialities or partial possibilities. But because neither sort of poten
tiality alone can initiate a change or motion, a partial possibility cannot be
actualized in so far it is only a partial possibility. Because a partial possibility
cannot, as such, be actualized, it cannot be a genuine possibility according
to Aristotle. In his paper 'Aristotle and the Priority of Actuality' R. M. Dancy
discusses the respective roles of the Principles of Plenitude and Scarcity in
Aristotle's metaphysics (pp. 73-115). He shows that, in the argument for the
priority of actuality on which the doctrine of the eternity of the world is
based, Aristotle uses both the Principle of Plenitude as well as the Principle
of Scarcity. They do not contradict each other in Aristotle, Dancy argues,
for all that Scarcity tells us is that a potentiality need not, at any given time,
be actualized. Plenitude tells us that every possibility must sooner or later be
realized. In this form both principles go together with the statistical inter
pretation of modal notions.
In both of the works mentioned Hintikka doubts Lovejoy's claim that
Plato adopted the Principle of Plenitude without qualifications. Many other
scholars have also been skeptical about this view of Lovejoy's. In his paper
'Empty Forms in Plato' Michael Rohr discusses the alleged counter-evidence,
especially the opinion according to which Plato thought that there are empty
forms (pp. 19-56). Rohr argues that in Plato there are no forms which have
only the forms themselves as instances, i.e., that there is no form which is
never instantiated by any particulars. Although some forms may be temporally
empty, all forms have as many instances as they can. His careful argumenta
tion lends interesting support to Lovejoy's somewhat sketchy thesis and
offers challenges to further studies of Plato's modal ideas.
Aristotle regarded the typical form of singular declarative statements as
temporally unqualified. Hintikka has maintained that the statistical model
of modality in Aristotle is connected with his preference for this type of
sentences, which contain a reference to the time of utterance as a part of
their meaning. On the statistical interpretation of modality in Aristotle,