Table Of ContentDESCARTES
HARVESTER READINGS IN THE HISTORY OF
SCIENCE AND PHILOSOPHY
General Editor: Dr. Stephen W. Gaukroger Philosophy, Mathematics
and Physics
Harvester Readings in the History of Science and Philosophy is a new
series of collections of papers dealing with general theoretical problems
in the work of particular philosophers and scientists. One of the main
aims of the series is to avoid restricting discussion of these problems to
what might currently be considered to be properly philosophical or
scientific questions, by placing a strong emphasis on understanding why EDITED BY
problems were often posed in ways which may seem alien to us today. It
is hoped that this will provide a fuller insight into the reasons why STEPHEN GAUKROGER
certain strategies and approaches in the development of philosophy and
science were rejected and why others were taken up, thus providing a Research Fellow in the Philosophy of Science,
firm basis for the assessment of these developments. Clare Hall, Cambridge
Although a significant proportion of the contents will consist of new
material written specially for the series, already published material
which makes a significant contribution to the area will be reprinted, and
some classic papers—and in certain cases monographs—^will appear in
English for the first time.
A colleaion on Galileo is in preparation and collections on Kepler and
Leibniz are planned for the future. Manuscripts and suggestions for
future titles are welcome.
THE HARVESTER PRESS • SUSSEX
BARNES & NOBLE BOOKS • NEW JERSEY
First published in Great Britain in 1980 by
THE HARVESTER PRESS LIMITED
Publishers: John Spiers and Margaret A. Boden
16 Ship Street, Brighton, Sussex
Order is what is needed: all the thoughts that can come into the human
and in the USA by mind must be arranged in an order like the natural order of numbers.
BARNES & NOBLE BOOKS
Descartes to Mersenne, 20 November 1629
81 Adams Drive, Totowa, New Jersey 07512
© This edition, 1980, The Harvester Press Ltd.
British Library Cataloguing in Publication Data
Descartes. - (Harvester readings in the history of science and philosophy; vol. 1).
1. Descartes, Rene
2. Mathematical physics - Philosophy
I. Gaukroger, Stephen
530.1'5'0924 B1878.S3
ISBN 0-85527-798-X
BARNES 8c NOBLE
ISBN 0-389-20084-0
Text set in 10/11 pt Linotron 202 Sabon, printed and bound
in Great Britain at The Pitman Press, Bath
All rights reserved
CONTENTS
Preface
Introduction 1
1 DESCARTES’EMPIRICAL EPISTEMOLOGY 6
Charles Larmore
2 CARTESIAN OPTICS AND THE GEOMETRIZATION
OFNATURE 23
Nancy L. Maull
3 DESCARTES'MATHESIS UNIVERSALIS, 1619-2S 41
John A. Schuster
4 DESCARTES’ PROJECT FOR A MATHEMATICAL
PHYSICS 97
Stephen Gaukroger
5 THE BEGINNINGS OF ALGEBRAIC THOUGHT IN
THE SEVENTEENTH CENTURY 141
Michael S. Mahoney
6 DESCARTES’ UNIFICATION OF ALGEBRA AND
GEOMETRY 156
Emily R. Grosholz
7 PROOF AND ETERNAL TRUTHS; DESCARTES AND
LEIBNIZ 169
Ian Hacking
8 DESCARTES, ETERNAL TRUTHS AND THE DIVINE
OMNIPOTENCE 181
Amos Funkenstein
vii
viii Contents
9 THE METAPHYSICS AND PHYSICS OF FORCE IN
PREFACE
DESCARTES 196
Martial Gueroult 1
1 One of Descartes’ major concerns, perhaps his primary concern, was the
I'l attempt to provide a philosophical foundation for mathematical physics.
10 FORCE AND INERTIA IN THE SEVENTEENTH The papers in this collection are designed to offer some elucidation of
this attempt either by taking up particular issues in Descartes’ physics
CENTURY: DESCARTES AND NEWTON 230
and mathematics or by providing a discussion of related topics in his
Alan Gabbey more general writings. As a result, comparatively little attention has
n been devoted to purely epistemological discussions of the hyperbolic
%
doubt, the cogito and the ‘Cartesian circle’, topics which usually
Notes on Contributors 321
if command the lion’s share of books and papers on Descartes. The
collection is, nevertheless, directed as much to philosophers as to
Index Locorum 323 historians of science. It is designed, not as a supplement to the
1
it mainstream of Descartes studies, but as a reassessment of some central
iA issues in Descartes’ work.
General Index 327
In particular, many of the papers raise problems about the extent to
which modern pre-occupations in epistemology, logic and metaphysics
can be read back into Descartes. We can of course distinguish what, by
current criteria, we would consider to be genuine and well-posed
philosophical questions and determine what contribution, if any,
Descartes’ work makes to answering these questions. But a project of
this kind may obscure important insights and important problems in
Descartes’ work, a grasp of which may contribute not only to our
understanding of seventeenth-century philosophy but also to our under
standing of twentieth-century philosophy. Descartes’ metaphysical,
mathematical, physical and physiological concerns, for example, are so
closely related that there are parts of his work where they are virtually
indistinguishable. We have often found it useful to distinguish between
these kind of concerns in modern philosophy: beciLuse of the use..to
which the sense data theorists of the middle part of this century put
physiological arguments in dealing with sceptical problems about
knowledge, for example, we have often found it necessary to make rigid
distinctions between physiological and epistemological accounts of
perception.
But to read back these distinctions into Descartes may compound
rather than clarify the problems. To approach the subject in this fashion
would, to some extent, have to pre-suppose that the way in which
epistemological problems are posed in contemporary philosophy is
relatively unproblematic, whereas many of the ways in which Descartes
poses epistemological questions will turn out to be problematic because
of their relation to his other concerns. It may well be, however, that the
way in which Descartes sets up particular problems, and the way in
which we set up particular problems in modern philosophy, are both
problematic, albeit in different ways and for different reasons. In this
case, it seems worthwhile to examine the problems that Descartes raises
ix
I
X Preface Preface xi
in the context of his own concerns, rather than singling out some of these Chapter 7 first appeared as ‘Leibniz and Descartes: Proof and Eternal
problems as having a ‘perennial’ value. We are, in general, reticent to do Truths,’ Proceedings of the British Academy, LIX (1973).
this in the case of his natural philosophy and I think the papers in this Chapter 8 first appeared as ‘Descartes, Eternal Truths and the Divine
collection will provide support for the idea that we should be similarly Omnipotence,’ Studies in History and Philosophy of Science, VI (1975).
reticent in epistemology and metaphysics. Chapter 9 is a complete translation of the first part of a paper which
The work on editing this collection and preparing my own contribution originally appeared as ‘Metaphysique et Physique de la Force chez
was done during the tenure of a Visiting Research Fellowship in the Descartes et chez Malebranche,’ Revue de Metaphysique et de Morale,
Department of History and Philosophy of Science at the University of LIX (1954). English translation by the editor.
Melbourne and I should like to register my thanks here for the excellent Chapter 10 is a considerably revised and expanded version of a paper
facilities provided. I have benefited greatly from discussions with my which originally appeared as ‘Force and Inertia in Seventeenth Century
colleagues in this department. I should also like to thank the Master and Dynamics,’ Studies in History and Philosophy of Science, II (1971).
Fellows of Clare Flail, Cambridge, for allowing me to intermit my
Research Fellowship there for a year to prepare this work. Finally, I should
like to thank Hazel Maxian for her help in checking through my
translation of the paper by Gueroult, and Gerd Buchdahl and John
Schuster for first stimulating my interest in the problems with which this
book is concerned.
References to Descartes’ works in this collection are given in the
following way; the name of the work (or, in the case of letters, addressee
and date) is given first, followed by the section and chapter number where
applicable, followed by the reference to the volume and page number of
the Adam and Tannery edition {Oeuvres de Descartes^ 13 Vols, Paris,
1879-1913; abbreviated to AT), followed by a reference to the English
translation, if this is generally available. Three English translations have
been abbreviated throughout the book: HR refers to E. Haldane and G.
Ross, The Philosophical works of Descartes (2 Vols, Cambridge, 1970); PL
refers to A. Kenny, Descartes: Philosophical Letters (Oxford, 1970); CB
refers to J. Cottingham, Descartes’ Conversation with Burman (Oxford,
1976). I have deviated from this practice of citation in the case of the
Principles^ where more specific citations can be provided by simply giving
the Part and article number. Unless otherwise stated all references are to
the Latin edition of the Principles-^ similarly with the Meditations.
Acknowledgements
I wish to thank the authors and publishers who have so generously allowed
the use of copyright material. Acknowledgements are made as follows:
Chapter 2: Review of Metaphysics; Chapter 5: Rete-^ Chapter 7: British
Academy; Chapter 8: Pergamon Press; Chapter 9: A. Colin, Paris; Chapter
10: Alan Gabbey.
Chapters 1, 3, 4 and 6 were written specially for the collection.
Chapter 2 is a revised version of a paper which originally appeared as
‘Cartesian Optics and the Geometrization of Nature,’ The Review of
Metaphysics, XXXII (1978).
Chapter 5 is a complete translation of a paper which originally
appeared as ‘Die Anfange der algebraischen Denkweise im 17. Jahrhun-
dert,’ Rete, I (1971). English translation by the author.
INTRODUCTION
The contributions to this collection form a roughly continuous sequence
starting with Descartes’ general ideas on knowledge and science, and
moving on to the impact of these ideas on his work in physics and
mathematics. My purpose in this short Introduction is to indicate some
of the central themes that dominate the collection.
One of the most important elements in Descartes’ epistemology is his
theory of perception. This is primarily an optico-physiological theory
and other theories of perception are criticized by Descartes on what are
mainly optico-physiological grounds. Chapter 1 by Charles Larmore
emphasises this empirical side of Descartes’ epistemology and defends it
against modern criticisms that would seek to exclude empirical consid
erations from epistemology altogether. Moreover, by comparing
Descartes’ account of perception with previous theories, particularly
those which treated perception in terms of ‘intentional species’, the full
novelty of the Cartesian account can be appreciated: unlike his
predecessors, Descartes does not treat our perceptual faculties in a.
fashion that presupposes that we have these faculties because God gives
them to us for the purpose of understanding nature, because they
naturally display to us the world that we wish to understand. Descartes
shows, not just by counterexample but also by a detailed account of the
mechanism of perception (an account which in essence is the one we still
accept today in physiological optics), that many of our beliefs about
what we see are systematically wrong. In this way, Descartes rids our
conception of perceptual systems from the teleology that had previously
dominated accounts of perception. As Larmore points out, although
seventeenth-century science has often been considered in terms of a
break with teleological explanation, this is an important aspect of the
move away from teleology which has not received the attention it
deserves.
Chapter 2 takes up the details of Descartes’ account of perception—
distinguishing in particular between his treatment of distance percep
tion and his treatment of colour perception—in the context of his
project to provide a geometrical account of nature. It is often assumed
that Descartes’ geometrization problem is a problem about the resem
blance between our mental representations of physical objects and
externally existing physical objects. But Maull shows that, in fact, the
problem concerns one of the central issues in Descartes’ projected
mathematical physics, that of the applicability of an a priori geometry to
In the course of her argument, Maull points out that Berkeley’s
criticisms of Descartes’ account of distance perception are, in the main,
misguided. Nevertheless, his claim that there can be no compelling
physiological or psychological evidence for a necessary connection
between sensation and perceptual judgement, as Descartes supposes,
1
2 Descartes: philosophy, mathematics and physics Introduction 3
holds and this undermines Descartes’ solution to the geometrization account of the shift from geometrical to algebraic modes of thought in
problem. the early seventeenth century, and is particularly concerned with the
In as much as Descartes’ account of perception is part of a general move from non-symbolic to symbolic mathematics. It concentrates on
geometrization problem it is clearly related to his project for a math Descartes’ contribution to this shift and particularly on the question of
ematical physics. Putting the matter more generally, Descartes’ account why ‘analysis’, considered to be a heuristic device by the Greeks, comes
of our knowledge of nature forms an integral part of his theory of to take primacy over ‘synthesis’, which, for the Greeks, is the true
nature. These issues are discussed in Chapters 3 and 4. deductive science. The idea that ‘rigour’ is not necessarily a general
Chapter 3 is concerned with Descartes’ ‘universal mathematics’ and desideratum is traced to Ramus, who had argued that the rigorous
the central argument of the paper is that it is the collapse of a developed synthetic proofs of the ancients did not lead to clarity or insight. This is
programme of universal mathematics in the later Regulae that is the related to Descartes’ claim that he uses analysis, and not synthesis, in his
prime factor in shaping the subsequent form of Descartes’ systematic work.
natural philosophy. It is generally thought that universal mathematics, One of the central topics in Descartes’ mathematics, that of the
developed in the period from 1619 to 1628, is an early model for relation between his algebra and his geometry, is discussed in detail in
Descartes’ more general concept of method, which is seen simply as an Chapter 6. Grosholz argues that, contrary to a very widely held view,
extension and generalization of universal mathematics. But Schuster Descartes does not and could not have subsumed geometry under
argues that at no time during this period was universal mathematics algebra. Rather than seeking to understand the relation between
identified with universal method, analytical geometry or a systematic geometry and algebra in reductionist terms, she poses the problem of
corpuscular-mechanical natural philosophy. There are, in fact, two the unification of mathematical fields in a novel way, by considering the
versions of universal mathematics developed by Descartes. The first, relation between two fields in terms of particular problems which one
developed in 1619, is contained in the oldest part of the Regulae, but it field may give rise to but not be able to solve, whereas the other field,
while it does not generate these problems, is nevertheless able to solve
was rapidly superceded by the idea of a universal method. The second,
them. What results is an interaction between two fields, in this case
developed between 1626 and 1628, and contained in Rules 12 to 21,
Cartesian algebra and Cartesian geometry, which functions in terms of
attempts to construct a universal mathematics in detail, and to legiti
correlations and not in terms of a subsumption of one field under the
mate it on the basis of optical, physiological and psychological consid
other. In the context of a discussion of Descartes’ ideas of ‘intuition’ and
erations.
‘deduction’ in the Regulae, Grosholz shows how Descartes rationalizes
The relation between this latter conception and Descartes’ mature
his commitment to the geometrical diagram and his hesitancy to accord
attempts to provide a basis for a mathematical physics is discussed in
algebra the status of a mathematical discipline in its own right.
detail in Chapter 4. It is argued here that Descartes provides a novel
Descartes’ treatment of intuition and deduction is one of the most
conception of mathematical physics in the Regulae, and that the
puzzling and bizarre aspects of his epistemology, and it is to this
problems that Descartes encounters in realising his original project for a
question that Chapters 7 and 8 are directed. The issues are closely
mathematical physics impose constraints on his writings not only in
related to the analysis/synthesis distinction and the problems of discov
physics but also in epistemology. More particularly, it is argued that the
ery and proof in mathematics and logic. Chapter 7 presents Descartes’
Regulae provides an account of what the mind and the corporeal world
promotion of analysis at the expense of synthesis in its strongest form,
must be like if a mathematical physics is to be possible. In Rules 12 and
arguing that for Descartes proof is irrelevant to truth: we may require
14 an attempt is made to establish that the mind is such that a
proof and deduction to be convinced of the truth of something but the
mathematical physics is possible, but the question of whether the world
ideal circumstance is to be in a position to intuit its truth. Ultimately, it
is of such a charaaer is left an open question. In the Meditations,
does not matter how one gets to the truth; the important point is that
however, Descartes raises and attempts to solve all these questions in
when something is seen with clarity and distinctness there is no other
terms of a series of general metaphysical arguments. Nevertheless,
standard of truth than the natural li^t of reason. Moreover, this natural
despite the apparent coherence and exhaustiveness of his conception of
light of reason must be guaranteed by God, who is not only required to
a mathematical physics, he does not manage to produce such a physics
ensure that eternal truths stay true but also to ensure that there is some
and some of the reasons for this are traced to problems inherent in his
truth to believe in. Chapter 8 examines the basis for Descartes’ thesis
original conception of the scope and structure of physical theory.
that God can invalidate fundamental mathematical truths by consid
As far as Descartes’ project for a mathematical physics is concerned,
ering three options: either God is exempt from the principle of
Cartesian algebra and geometry have an importance equal to that of his
contradiction, or there is a difference between real analyticity (known
work in epistemology and physiological optics. Chapter 5 provides an
4 Descartes: philosophy, mathematics and physics Introduction 5
only to God) and analyticity for us, or Descartes denies mathematical the first law is of a particular geometrical kind, and his supporting
truths the status of logical truths. These three interpretations, which arguments for this are not intrinsically related to the idea of motion as a
seem the only possible ones, are each problematic in terms of both state. The paper also deals, inter alia, with the discrepancy between the
coherence and textual support. Funkenstein opts for the third interpre treatment of rest and motion as modes and the attempt to provide a
tation and finds a material basis, in Descartes’ doctrine of substance, for quantitative account of these in terms of the forces responsible for them.
the existence of eternal truths. This underlines one of the most central problems of Descartes’ physics,
Chapter 9 provides a systematic general philosophical account of that of the intractable difficulties involved in attempting to base physics
Descartes’ notion of force. It is primarily concerned with the ontological on the treatment of questions concerning motion and rest in terms of the
status of force in Cartesian metaphysics and physics. For Descartes, no doctrine of extended substance and its modes, i.e. on the doctrine
body can be deprived of force. A body which is not moving is deprived which, throughout his writings, Descartes tries to establish as the sole
of the force that would make it move, but it is not deprived of force per foundation for physics.
se. It possesses the force of rest, which is expressed in its resistance to
motion. Forces are not modes of extension, as rest and motion are, but
they decide the appearance or disappearance of these modes and are
directly expressive of the Divine creative will. Gueroult shows how
force, duration and existence are one and the same thing, namely
conatus, under three different aspects, and how the three notions are
identified in the instantaneous action by which corporeal substance
exists or endures, that is, possesses the force which puts it into existence
or duration. This raises a whole host of problems: insofar as forces are
equated with God’s activity they are causes, but insofar as they exist in
nature they are the effects of God’s activity; insofar as they are in nature
and are not substances they can only be modes of substance, yet insofar
as they are the causes of the modes of extended substance they cannot
themselves be modes. Gueroult attempts to clarify these issues in terms
of the difference between Descartes’ descriptive and explanatory ac
counts of motion, and thereby to decide in what respects force must be
located at the metaphysical level of God, at the physical level of
extended substance, and at some intermediary level. His arguments
provide one of the clearest and most detailed rejoinders to those who
would see Cartesian physics as pure kinematics.
Chapter 10 gives, perhaps, the definitive account of Descartes’
treatment of force and inertia. It provides a very detailed discussion of
the functioning of the metaphysical concepts of substance and mode in
Cartesian physics and calls for a reassessment of the structure of
Descartes’ physical theory. In particular, Gabbey shows that, contrary to
a very widely held view, Descartes’ first two laws of motion do not
anticipate Newton’s First Law of Motion. Despite the descriptive
equivalence of the two sets of laws, they are fundamentally dissimilar in
aim and structure. Gabbey notes that Descartes requires two laws for
Newton’s one and he argues that the two laws are required because of
Descartes’ peculiar conception of the ontological equivalence of motion
and rest. In a detailed analysis of Descartes’ treatment of motion and
rest Gabbey establishes that the first two laws of motion cannot be
treated merely as parts of the one more general law. Descartes needs a
separate law stating that the persevering state of motion described in
Empirical epistemology 7
1 DESCARTES’ EMPIRICAL would not be as in the first case methodological, but instead substantive.
They would focus upon how we are to understand human knowledge given
EPISTEMOLOGY
what we know about the world.
If with these possibilities of an empirical epistemology in mind we look
Charles Larmore
once again at Descartes’ theory of knowledge, the traditional picture of
Descartes as the founder of a priori epistemology begins to appear
There is something close to a general consensus that Descartes initiated importantly incomplete. As I shall show in this essay, his search for an
a search for incorrigible foundations of knowledge that deeply shaped
incorrigible foundation of empirical knowledge forms but one strand in his
modern philosophy and that we have now learned to reject or even
theory of knowledge. There are other epistemological problems for whose
ignore. Characteristic of the Cartesian search for certainty, as opposed solution he deliberately resorted to the results of empirical inquiry. First, it
for example to some tendencies in Greek thought, was that these might be recalled, in regard to the project of setting out criteria of scientific
foundations must be located in individual subjectivity, in our immediate rationality, that he recommended his idea of scientific method because
awareness of our own mental states. It implied that unless we could he had found it successful. However, 1 shall be concerned with the more
show how our beliefs about the world could be legitimately inferred substantive area of his empirical epistemology, especially as it grows out of
from this basis, they would have no more rightful claim to being his attempt at the mathematization of nature. In the light of these generally
knowledge than would our wildest fantasies. ignored aspects of Cartesian philosophy, we will no longer be able to foist
All the different kinds of errors that lie at the heart of the founda- upon Descartes the onus of having encouraged the idea that an a priori
tionalist enterprise do not need rehearsing once again. More directly of approach is all to which epistemology may aspire. Indeed, for the whole of
interest is the fact that a number of philosophers have taken the demise the seventeenth century the theory of knowledge brought together both a
of this enterprise to mean the end of epistemology itself. What else can priori and empirical perspectives. In Descartes, the relation between these
epistemology be but the search for the incorrigible foundations of strands is governed by a conception of method, whereas in Locke, for
knowledge? If that is so, then epistemology indeed amounts only to a example, the character of their relation is far less clear. The origin of the
subject with a glorious past. But this is not the proper conclusion to idea that epistemology, as a philosophical discipline, must proceed
draw. The rejected forms of epistemology proved barren because they independently of the sciences belongs to a later time. It arises both with
restricted themselves to the search for incorrigible truths, untainted by Kantian transcendentalism and with the more recent wish to analyse ‘the
the revisability of the empirical truths they were meant to support. To meaning of the concept of knowledge’. One aim of this essay is to indicate
discard epistemology as a dead subject no longer of interest to living why we need a more complex picture of the origins of modem
philosophy, for this reason alone, merely continues the original error of epistemology in the seventeenth century. But, more directly, the aspects of
believing that the theory of knowledge must be kept pure of all Descartes’ empirical epistemology which I shall treat will be among those
dependence upon the empirical sciences. that can still interest us today.
There are two areas of inquiry whose pursuit would dissociate It is chiefly in his physiological treatises, such as the Treatise on Man and
epistemology from the ideal of a prima philosophia. First of all, we can the Dioptrics, that we come upon his empirical epistemology. But in order
focus the theory of knowledge upon examples of scientific knowledge in to understand why at a certain point Descartes let his epistemology
order to formulate criteria of scientific rationality. However, if we are to become empirical, we will first have to look at his conception of scientific
escape the ideal of a pure epistemology, we must draw out these criteria method (Part 1). In Part II I shall examine the initial physical
in a dialectical way from the history of science. Crudely put, we must problem—^the mathematization of nature—^with which his empirical
abstract the criteria from some theories in order both to evaluate other epistemology begins, then tracing in Part III the broad implications he drew
theories in terms of them and to test the criteria against other examples from that for an understanding of the place of knowledge within the
of theories. Otherwise we may find ourselves, as indeed has often been natural order.
the case in the philosophy of science, stuck with criteria of scientific
Part I Descartes’ Conception of Scientific Method
rationality that no scientific theory has ever met. Obviously, the
Recently it has become increasingly clear just how erroneous was the
problems facing this kind of empirical epistemology are immensely
traditional view that Descartes thought of physical inquiry as a strictly a
difficult. Secondly, we can allow the theory of knowledge to confront
priori concern. We can find no better proof of the untenability of that view
what scientific theories imply about the status of our perceptual and
than to listen to what Descartes himself had to say in the Discourse on
experiential image of nature and about the relation between nature and
Method about the respective roles of the a priori and experience:
ourselves as knowers. Here the concerns of an empirical epistemology
8 Descartes: philosophy, mathematics and physics Empirical epistemology 9
I have first tried to discover generally the principles or first causes of everything that is or conception of scientific method that orders the a priori and empirical
that can be in the world, without considering anything that might accomplish this end but
parts of the theory of knowledge and the theory of nature into a single
God Himself .... But I must also confess tihat the power of nature is so ample and vast,
enterprise.
and these principles are so simple and general, that I observed hardly any particular effect
as to which I could not at once recognize that it might be deduced from the principles in Now this a priori physics cannot, as we have seen Descartes admit,
many different ways; and my greatest difficulty is usually to discover in which of these yield a complete picture of the physical world. Only the most general
ways the effect does depend on them. As to that, I do not know any other plan but again to features of the world can be ascertained through deduction from the
try to find experiments of such a nature that their result is not the same if it has to be
self-evident first principles. For example, from the three fundamental
explained by one of the methods, as it would be if explained by the other.*
laws of nature he thought he could deduce the laws of impact among
Thus, according to Descartes, an account of the physical make-up of the bodies. In Principles III, art 46 there occurs a passage where Descartes
world falls into two distinct parts: one we can develop a priori, while the lists some of the more particular phenomena that we can uncover only
other makes essential use of experience. The ‘principles or first causes’, through empirical inquiry: the size of the parts into which matter is
that cover the most general features of the world, are something that we divided, the speed with which they move, and what circles their
can attain without appeal to experience or experiment. In this passage movements describe. Clearly, this range of empirical phenomena con
Descartes was referring to what he believed he had already accom sists in the numerical values that in any particular case can be given to
plished in his earlier treatise Le Monde. There, from God’s immutability the variables occuring in the a priori laws of motion and their deductive
alone, he had derived the three fundamental laws of nature: consequences. In the passage cited from the Discourse at the beginning
of this section, he mentions another area of necessarily empirical
1 Every bit of matter continues in the same state until constrained to
inquiry. From the a priori laws alone we cannot determine what, in fact,
change by encountering some other object.
is the mechanical constitution of many of the phenomena we observe.
2 When one body alters the state of another, it cannot give it any
This is the domain of empirical inquiry that will be important in what
movement which it itself does not lose at the same time.
follows. His empirical epistemology will depend upon understanding
3 Every body tends to continue to move in a straight line.^
the operation of the human eye, for which he will appeal to empirical
The same claim, that the validity of these laws has an a priori basis in an physiology as well as to a theory of the mechanical nature of light which
understanding of what it means for there to be a God, reappears in the he found himself forced to justify empirically.
Descartes thus bdieved that scientific inquiry must begin with an a
Discourse and in the Principles as well.^ These laws of nature can be
said to be true a priori, of course, only because Descartes thought that priori demonstration of first principles and then, once the scope of a
priori physics has been exhausted, it must turn to the construction of
he could prove the existence of such a God in a purely a priori fashion,
empirical hypotheses. Since earlier works like the Regulae often suggest
and not by means of some natural theology. Both the causal and the
a thoroughly aprioristic method, it is with his mature conception of
ontolo^cal proof take as a premise that I do have a concept of
scientific method that I shall henceforth be concerned.'^
something than which nothing greater can be conceived. That I do have
Those explanatory propositions belonging to the empirical part of
the ideas that I believe I do, whatever may be their material truth, is a
physical inquiry Descartes himself termed ‘hypotheses’. He said that if
result guaranteed by the indubitability of the cogito. Thus, contrary to
the consequences of an hypothesis agree with experience and, more
what has been sometimes suggested, the cogito does play an essential
particularly, if by way of a crucial experiment they agree with an
role in the foundation of physical science. It lies at the basis, Descartes
experimental phenomenon that the deductive consequences of rival
believed, of the a priori deduction of the three fundamental laws of
hypotheses fail to match, then we have every reason to believe that the
nature.
hypothesis is true.^ (It is to be remembered that the Cartesian idea of
It is important to notice how this a priori part of Cartesian physics lies
deduction is broader than the logical concept of deduction—^it covers
on a continuum with a priori epistemology. For Descartes, a priori
any sequence of propositions where we perceive ‘clearly and distinctly’
epistemology does not issue simply in a prescription for the kinds of
that the conclusion follows from the premises.)
propositions that should serve as foundations (that, of course, is the role
The hypothetico-deductive method, for Descartes, belongs only to the
that more recent phenomenalist epistemologies have taken on). Instead,
empirical part of physical theory; it does not touch the fundamental
the cogito and the proofs of God’s existence imply, so he believed, the
laws of nature and their deductive consequences. There is, of course,
fundamental principles of physical science themselves. This continuity
the famous passage at the close of the Principles (IV, art 204) where
between a priori epistemology and a priori physics should be borne in
Descartes refers to the whole of his physical theory as an hypothesis
mind when we come to consider the continuity between physical theory
whose truth can be guaranteed only by the match between its deductive
and Descartes’ empirical epistemology. It will become clear that it is his
