Through a careful and rigorous examination of Descartes’s scattered remarks on his method and its application in his scientific and mathematical works, Daniel E. Flage and Clarence A. Bonnen develop a systematic account of his method and its role in the Meditations.
In the first part of Descartes and Method, Flage and Bonnen interpret the Cartesian search for essences as a search for both laws and conceptual elucidation. In the second half of the book each Meditation is examined in light of the interpretation of method. The interplay between the search for general principles and the clarification of ideas looms large in the discussions of Meditations Two and Three. The book explains how Descartes’s last three Meditations do nothing less than reveal the implications of God’s non-deceptiveness. We see that in the end Descartes, the great rationalist, specifies the scope and limits of empiricism.
Unparalleled in any other work, Descartes and Method delineates the role of the method of analysis in the Meditations. Anyone wishing to gain a new understanding of Descartes’s Meditations should read this book.
Daniel E. Flage is an Associate Professor of Philosophy at James Madison University. He is the author of Berkeley’s Doctrine of Notions, Understanding Logic, and David Hume’s Theory of Mind (Routledge).
Clarence A. Bonnen taught philosophy at Penn State Erie until 1995. He is currently a computer programmer in Austin, Texas.
Routledge Studies in Seventeenth-Century Philosophy
1 The Soft Underbelly of Reason The passions in the seventeenth century Edited by Stephen Gaukroger
2 Descartes and Method A search for a method in Meditations Daniel E. Flage and Clarence A. Bonnen
Descartes and
Method
A search for a method in
Meditations
Daniel E. Flage and
Clarence A. Bonnen
by Routledge
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Routledge is an imprint of the Taylor & Francis Group
This edition published in the Taylor & Francis e-Library, 2001. © 1999 Daniel E. Flage and Clarence A. Bonnen
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Library of Congress Cataloguing in Publication Data
Descartes and Method: a search for a method in Meditations/Daniel E. Flage and Clarence A. Bonnen
p. 13.8 x 21.6 cm
Includes bibliographical references and index
1. Descartes, René. 1596–1650. Meditationes de prima philosophia. I. Bonnen, Clarence A., 1958– II. Flage, Daniel E., 1951–
B1854.F57 1999
194—dc21 98–45328 CIP ISBN 0-415-19250-1 (Print Edition)
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and
you’re making a building, or you’re making a part, an actor’s part – that there’s something about submitting to the logic of the thing you’re building that’s consistent between the two. There’s something about understanding how it works before you set out to use it. There’s something about knowing that one brick goes on top of another and that there’s a purpose for the foundation – to spread the weight. . . . But basically I think it’s just about a method of work. Not expecting a result, but starting out knowing that it needs this for the bottom.
List of figures x
Acknowledgements xi
Abbreviations xiii
Introduction 1
Whither a Cartesian method 1
An outline for a search for a method in the Meditations 4 Method and metaphor 6
PART I
Descartes’s method 11
1 Analysis: the search for laws 13
Analysis 13
Material and formal truth 23 Intuition and the natural light 27 Types of certainty 29
The rules in the Discourse 32 Analysis and the best explanation 43
2 Analysis: the clarification of ideas 45
Are all innate ideas materially true? 45
Clarifying ideas and the four rules of the Discourse 56 Descartes's idea of light 58
3 Causation 72
Caterus on the problem of God’s self-causation 73 Formal and efficient causes 75
Arnauld on the problem of God's self-causation 77 Cartesian essences and explanations 85
Mind and body 91 The unity of the method 98
Appendix: the rainbow 100
PART II
Descartes’s Meditations on First Philosophy 109
4 Meditation One: doubts and suppositionsssss 111
New foundations: the task of the Meditations 112 Epistemological doubts 114
The hypothetical doubts 120 Conclusions 128
5 Meditation Two: the beginning of the ascent 129
A new foundation 129
The Cogito outside the Meditations 131
The first Cogito arguments in the Meditations 143
Res Cogitans and the second Cogito 146
The piece of wax 155 Conclusions and cautions 163
6 Meditation Three: reaching the peak, or variations
on the existence and idea of God 166
Clarity, distinctness, and a classification of thoughts 166 The first argument for the existence of God 175 The second argument for the existence of God 187 Odds and ends 191
Clarifying the idea of God 193 Conclusions 202
7 Meditation Four: truth and falsity: reflections
from the summit 203
God and error 204
8 Meditation Five: the beginning of the descent 214
True and immutable natures 215 An ontological interlude 221
Memory and divine non-deception 230
9 Meditation Six: the world restored 237
Material objects as probable, and the real distinction between mind and body 237
The argument for the nature and actual existence of the corporeal world 242
What “nature” can teach about minds and bodies 244 Human error and divine non-deception, revisited 249 Conclusions 251
10 Circles 252
Notes 258
Bibliography 293
Figures
1 Triangle 16
2 The rainbow 102
3 The prism 105
In working on this study, we have benefited greatly from discussions and comments from a large number of friends and colleagues. In particular, we would like to thank Jonathan Bennett, Willis Doney, Donald Cress, Phillip Cummins, Ronald Glass, Jeffrey Tlumak, the late William Williams, Gordon Fisher, Jeffrey Coombs, Madeleine Pepin, Véronique Foti, Michael Gass, Kenneth Winkler, Frederick O’Toole, Russell Wahl, Stephen Wagner, George Stengren, James Petrik, Patrick Murphy, Barbara Tovey, Charles Huenemann, Lisa Hall, Steven Voss, Eric Palmer, Kent Baldner, Joseph Campbell, Rocco Gennaro, Eric Sotnak, Susanna Goodin, Matthew Stuart, and Sam Levey for their helpful comments and encouragement in working on various parts of this work. We would also like to thank Susan Bonnen for helping us eliminate many of the misspellings, typos and other infelicities in the text.
Research for this book was supported in the summer of 1992 by a Summer Research Grant from James Madison University (Flage) and a research grant from Penn State Erie (Bonnen), which allowed us to collaborate actively for several weeks that summer. In 1994, Flage received the Edna T. Shaeffer Humanist Award, presented by the College of Letters and Sciences of James Madison University, which supported further research for the book. In addition, Bonnen participated in Willis Doney’s 1991 NEH Summer Seminar, “The Philosophy of Descartes”, and we both participated in Jonathan Bennett’s 1995 NEH Summer Seminar, “Descartes, Spinoza, and Leibniz: Central Themes”. We appreciate each of these organizations for their support and encouragement.
Some of the early research for Descartes and Method: a Search for Method
in Meditations was presented in articles. We acknowledge the editor of History of Philosophy Quarterly for granting us permission to reprint revised
versions of “Descartes’s Cogito” (Flage 1985) and “Descartes and the Epistemology of Innate Ideas” (Flage and Bonnen 1992a). We thank the editor of Modern Schoolman for permitting us to reprint revised versions of “Descartes’s Factitious Ideas of God” (Flage and Bonnen 1989) and “Descartes’s Three Hypothetical Doubts” (Flage 1993). The editor of The
Review of Metaphysics receives our thanks for allowing us to reprint an
expanded version of “Descartes on Causation” (Flage and Bonnen 1997). We thank John Cottingham and Cambridge University Press for permission to quote extensively from The Philosophical Writings of Descartes.
Finally, both of us are eternally grateful to wives and families for their encouragement, patience, and tolerance during the writing of this book. Clarence Bonnen would especially like to thank his parents, James and Sarah Bonnen, for all of those times that they expressed to him their sincere belief that he partakes in one of the most noble of human activities, philosophical contemplation and dialogue.
Daniel E. Flage Harrisonburg, Virginia Clarence A. Bonnen Austin, Texas
The following abbreviations will be used throughout the book. AT x: y Oeuvres de Descartes, volume x: page y CSM x: y The Philosophical Writings of Descartes,
volume x: page y
CB §x The Conversation with Burman, section x M x Le Monde, ou Traité de la Lumière, page x O x The Discourse on Method, Optics, Geometry,
and Meteorology, page x
P x: y Principles of Philosophy, part x: section y POS §x Passions of the Soul, section x
This is a book on René Descartes’s method in his most famous work,
Medi-tations on First Philosophy. Although we briefly discuss his celebrated
“method of doubt”, our attention centers on the method championed in the
Discourse on Method. Of specific concern is the method of analysis to
which Descartes alludes in the Second and Sixth Replies (AT 7: 155–7, 424– 5, 444–7; CSM 2: 110–12, 286–7, 299–301) and which he describes as the fifth way of reaching wisdom – the search for first causes – in the Preface to the French edition of the Principles (AT 9B: 5, CSM 1: 181). Once one understands that method, the argumentative structure of the Meditations should appear far clearer and much less eclectic than it would be otherwise.
Whither a Cartesian method
Some will greet our task with a healthy dose of skepticism, suggesting either that Descartes had no method (Schuster 1993) or that he abandoned his method in the late 1630s or early 1640s (Garber 1992: 46–8). If Descartes abandoned all commitments to method by the late 1630s, one has little reason to believe that considerations of method are germane to the interpretation of the Meditations of 1641. Others might suggest that even if he had a method, all knowledge of its nature followed him to his grave. Leibniz put it this way:
There have been many beautiful discoveries since Descartes, but, as far as I know, not one of them has come from a true Cartesian. I know these people a little, and I defy them to name one such discovery from their ranks. This is evidence that either Descartes did not know the true method, or else that he did not leave it to them.
If Descartes had a method but did not successfully communicate it to his successors, then he is guilty of the same intellectual sin with which he charged the ancient geometers, namely, “these writers themselves, with a kind of pernicious cunning, later suppressed this mathematics [method] as, notoriously, many inventors are known to have done where their own dis-coveries were concerned” (AT 10: 336, CSM 1: 19; cf. AT 7: 157, CSM 2: 111). Certainly he did not go out of his way to teach his method to others. His remark in the Discourse, that “My present aim, then, is not to teach the method which everyone must follow in order to direct his reason correctly, but only to reveal how I have tried to direct my own” (AT 6: 4, CSM 1: 112; cf. Letter to Mersenne, 27 February 1637: AT 1: 349, CSM 3: 53) suggests that the method is to be revealed like the form of a Wittgensteinian world: it can be shown, but not described. Such an approach bodes ill for the com-mentator on the Cartesian method. Finally, some would find Descartes’s talk of the method of analysis misleading. In the Second Replies, he does not vaunt analysis as a method of discovery or justification; rather, he says it is “the best and truest method of instruction” (AT 7: 156, CSM 2: 111, our emphasis); it is a method of demonstration (AT 7: 155, CSM 2: 110). So some might conclude that the textual evidence we would bring to bear in our account of the nature of the Cartesian method of discovery and justification is not germane to the task.
In reply, we stress that our approach will be conservative, perhaps even naive.1 The sole reason we contend that approaching the Meditations
through an examination of the Cartesian method might prove fruitful is that Descartes says he applied his method to metaphysical topics in the
Meditations. In the Dedicatory letter he writes:
I was strongly pressed to undertake this task by several people who knew that I had developed a method for resolving certain difficulties in the sciences – not a new method (for nothing is older than the truth), but one which they had seen me use with some success in other areas; and I therefore thought it my duty to make some attempt to apply it to the matter at hand.
(AT 7: 3, CSM 2: 4) Further, the suggestion that the “method of analysis” is merely a method of instruction or demonstration is misleading. As a method of demonstration, analysis mirrors the method of discovery. Descartes says:
Analysis shows the true way by means of which the thing in question was discovered methodically and as it were a priori, so that if the reader is willing to follow it and give sufficient attention to all points, he will make the thing his own and understand it just as perfectly as if he had discovered it for himself.
(AT 7: 155, CSM 7: 110) He also alludes to his “method of analysis” at several points in the Sixth Replies (AT 7: 424, 444–5, CSM 2: 286, 299–300). Furthermore, to suggest that he proposed a “method of analysis” places him within a definable historical tradition. Descartes himself suggests that his method has much in common with the method of the ancient geometers (AT 10: 376–7, 7: 4 and 156, CSM 1: 18–19, 2: 5 and 111). We also show that his remarks on method have strikingly close parallels in the methodological writings of the Italian school of Padua, which was a leader in the revival of classical studies and the development of a scientific method for over two centuries before the publication of Descartes’s Discourse (Randall 1968).
Nor did concerns with the “method of analysis” die with Descartes. In
The Art of Thinking, Arnauld draws the distinction between the method of
analysis and the method of synthesis along the following lines:
Generally speaking, method may be called the art of arranging well a sequence of thoughts either to discover a truth of which we are ignorant or to prove to others a truth we already know. We distinguish two kinds of method: The one for discovery of truth is called analysis or the
method of resolution or the method of invention; the second, used to
make others understand a truth, is called synthesis or the method of
composition or the method of instruction.
(Arnauld 1964: 302) Arnauld’s discussion of the method of analysis concludes with the four rules of method in Descartes’s Discourse (AT 6: 18–19, CSM 1: 120; Arnauld 1964: 308–9). Kant (1950: 11) tells us that his Prolegomena to any Future
Metaphysics follows the method of analysis, and he carefully distinguishes
between analysis as a method and analyticity as a property of propositions (ibid.: 23n.). Indeed, as we show in Chapter One, there are conceptual affinities between the method of analysis and what C. S. Peirce called “abduction” (Peirce 1955; see also Hanson 1958: 85–92). But it is one thing to claim that
the expression “method of analysis” can reasonably be taken to mark a method of discovery; it is something else to provide an elucidation of that method.
Descartes provided some account of his method of inquiry in at least three works: Rules for the Direction of the Mind (hereafter Regulae), the
Discourse on the Method, and Second Replies. In none of these works does
he provide a step-by-step account of his preferred procedures of inquiry. Further, since the Regulae were neither completed nor published in his lifetime, it is a matter of debate whether Descartes changed his method, whether there are substantial differences between methods before and after about 1629.2
We do not enter that debate; rather, we construct our account of the Cartesian method on the basis of the Discourse, the Essays, and other works published after 1637. While we do not ignore the Regulae, we use it only, first, to show that further evidence exists that Descartes was cognizant of a distinction or methodological move that his later works seem to support and second, in those cases where the Regulae provide a particularly clear statement of a doctrine that appears in the later works. To put it differently, we use the Regulae to find secondary evidence for our account of the method, but we draw primary evidence from Descartes’s later works.
An outline for a search for a method in the Meditations
In the first three chapters we examine the method as such. Even a cursory examination of Descartes’s works suggests that he employs an ostensible distinction between two objectives of methodological inquiry: first, to discover causes or principles or laws, and second, to discover essences. In the first chapter we focus on laws; in the second chapter we focus on essences. In both cases we attempt to show how the Cartesian method of analysis works: it is a search for principles that explain why a phenomenon, accepted as given, is as it is. In both chapters we show how Descartes’s abstract remarks on method suggest a procedure, and show how that procedure is employed in his nonmetaphysical works. In the third chapter we examine the Cartesian notion of a cause. We argue that the notion of a cause operative in Cartesian explanation is a formal cause. We show that this effectively collapses the distinction between a law and an essence and
that it makes intelligible both his remarks on the mind–body relation and some of his remarks on method.
The fourth through the ninth chapters examine the individual Meditations. In Chapter Four we argue, following Frankfurt (1970), that the Descartes of the First Meditation focused his attack on the presumed epistemic fundamentality of an empiricist principle. We also show that various assumptions give life to specifiable doubts. These assumptions become crucial at later points in the Meditations, and, in particular, the deceiver arguments raise the most specific doubts.
In Chapter Five we argue that there are four versions of the Cogito argument and that there is an intimate relationship between Descartes’s proof of his existence and his clarification of the idea of himself. In Chapter Six we show that there are two themes in the Third Meditation. His primary objective is to show that God exists, and that his arguments presented to prove that point are, perhaps, the clearest applications of the analytic method in the Meditations. A secondary objective is to clarify the idea of God, a clarification which remains implicit throughout the discussion.
In Chapter Seven we show that Descartes introduces his theory of judgment in the Fourth Meditation to explain the compatibility of a nondeceptive God with the fact of human error. In Chapter Eight we argue that his ontological argument is best construed as a means of confirming that his clear and distinct idea of God as a perfect being is true. We also argue that his concerns with memory in the closing paragraphs constitute an argument that the notion of a nondeceptive God is broader than the Fourth Meditation understanding: it must allow for certainty in mathematical proofs, even when one merely remembers that one had clearly and distinctly perceived a conclusion reached earlier in the proof. In Chapter Nine we argue that Descartes again widened the implications of the nondeceptive-God hypothesis to justify the belief in the material world. Throughout chapters Seven through Nine, we also show that there are claims introduced as working hypotheses in the earlier Meditations that are only later confirmed. In Chapter Ten we examine the Cartesian Circle. While most Descartes scholars – beginning with his contemporaries (AT 7: 124–5, 214, CSM 2: 89, 150) – contend that at some point he assumes what he sets out to prove, there is anything but agreement on where the circularity arises. We show that, if our account of the method is correct, the Descartes of the
Medita-tions avoids Arnauld’s charge (1964) of circularity. But this victory is
regard-ing the second proof of the existence of God in Meditation Three (AT 2: 243, CSM 2:170), he effectively steps into Arnauld’s circle.
Method and metaphor
Before turning to the method of analysis as such, we examine two of Descartes’s famous metaphors: the house/foundations and the tree of philosophy. In the course of discussing these metaphors we elucidate some of the interpretive assumptions with which we approach the Cartesian texts. Descartes’s most famous metaphor compares his previous system of beliefs to a house with weak foundations. Like the owner of such a home, he will tear it down and build anew (see AT 6: 13, CSM 1: 117). Anyone with even a modicum of exposure to Descartes knows that it is his doubts that raze his house to the ground. But what does he do with his demolished house? In the Discourse he suggests that some of the materials will be recycled into his new house:
And, just as in pulling down an old house we usually keep the remnants for use in building a new one, so in destroying all those opinions of mine that I judged ill-founded I made various observations and acquired many experiences which I have since used in establishing more certain opinions.
(AT 6: 29, CSM 1: 125) If one takes the analogy at face value, it suggests that he incorporates certain elements of the old house into the new one. If one examines Part Four of the Discourse and the Meditations, one notices, at the least,
prima facie resemblances between the old house and the new: both contain
a God; both contain a human being composed of a body and a soul; and both grant a significant place to the empiricist principle. The old house and the new also differ in each of those ways: the new house contains a carefully analyzed concept of a God whose existence is proven; the analysis of body and soul (mind) in the new house differs from that in the old; and although Descartes gives the empiricist principle a significant place in his new house, it no longer provides the foundation for the house, and it no longer functions as the naive principle found early in the
Nor should one find it surprising that sensory experience, which is the fundamental object of attack early in the Meditations, is ascribed a significant place by the end of that work. In the Preface to the French edition of the Principles, Descartes places it fairly high in the levels of wisdom. Notice the levels of wisdom to which he alludes:
The first level contains only notions which are so clear in themselves that they can be acquired without meditation. The second comprises everything we are acquainted with through sensory experience. The third comprises what we learn by conversing with other people. And one may add a fourth category, namely what is learned by reading books – not all books, but those which have been written by people who are capable of instructing us well; for in such cases we hold a kind of conversation with the authors. I think that all the wisdom which is generally possessed is acquired in these four ways. . . . Now in all ages there have been great men who have tried to find a fifth way of reaching wisdom – a way which is incomparably more elevated and more sure than the other four. This consists in the search for the first causes and the true principles which enable us to deduce the reasons for everything we are capable of knowing; and it is above all those who have laboured to this end who have been called philosophers. I am not sure, however, that there has been anyone up till now who has succeeded in this project.
(AT 9B: 5, CSM 1: 181) As ordinarily understood, knowledge based on sense experience is the second highest form of knowledge. Thus, it is not surprising that Descartes should grant a significant status to the empiricist principle. But he remarks that there is a fifth way – the Cartesian method – which is superior to the other four in so far as it provides a method for discovering first principles. These first principles provide the ground for all knowledge. Given these first principles, one will be able to explain why each of the principles at the lower levels obtains and what its limits are. It is in this way that he can champion a modified empiricist principle at the end of the Meditations: the higher principles specify the limits of the empiricist principle’s applicability. Returning to the house metaphor, if the foundation is discovered through the method, the lower elements on the scale of wisdom are built upon it in the same way that the studs, joists, and rafters are built upon the foundation of a house.
Houses come in many styles, and houses of many styles can be built on any given foundation. So if one pushes the house metaphor further, one might inquire into the architectural style of the house Descartes builds. We suggest that his house be understood on the model of the half-timbered buildings that were common during the middle ages, what the Germans called a Fachwerkhaus. Whatever else might be said about the house of knowledge built on a Cartesian foundation, the method requires that the various elements which are discovered should be systematically integrated, and that one should clearly perceive how the various elements of the epistemic structure support one another. In this regard, there is no better model than the open timbers of a Fachwerkhaus. A visual examination of the facade of a half-timbered house allows one to see which timbers provide the structural support for the others. We argue that throughout the early
Meditations, Descartes introduces assumptions that only later are given
support. For example, in Meditation Two, he claims that he is “only a thing that thinks” (AT 7: 27, CSM 2: 18). As he acknowledges in the Preface to the Reader, the “only” is unwarranted at the point it is introduced, adding, “I shall, however, show how it follows from the fact that I am aware of nothing else belonging to my essence, that nothing else does in fact belong to it” (AT 7: 8, CSM 2: 7). The latter point is proven in the Sixth Meditation (AT 7: 78, CSM 2: 54), and we argue that this connection between Meditations Two and Six is one of many lateral supports (visible timbers) in Descartes’s house. If the house metaphor suggests that Descartes’s philosophy is systematic, that later elements are logically and conceptually dependent upon earlier elements, this point is driven home even more forcefully by the tree metaphor in the Preface to the French edition of the Principles. There Descartes writes:
Thus the whole of philosophy is like a tree. The roots are metaphysics, the trunk is physics, and the branches emerging from the trunk are all the other sciences, which may be reduced to three principal ones, namely medicine, mechanics and morals. By “morals” I understand the highest and most perfect moral system, which presupposes a complete knowledge of the other sciences and is the ultimate level of wisdom.
(AT 9B: 14, CSM 1: 186) While Descartes suggests that a system of moral principles is the final and most important fruit of his inquiry, moral knowledge is grounded in a physics
– and ultimately a metaphysics – from which it is deduced. Like the foundation in the house metaphor, the health and strength of the tree is dependent upon the health and strength of its roots. The objective of the
Meditations is to build a sturdy house, or to establish that the roots of his
philosophical tree are strong and healthy.
Regardless of which metaphor one follows, one point is clear: Descartes’s philosophy is properly systematic. It is hierarchical. The principles of metaphysics are at the top of the hierarchy (or, to use the tree metaphor, are the roots), and everything in his system rests upon those principles. The principles of metaphysics themselves are hierarchically related to one another. In the next three chapters we examine his method as a procedure utilized to find the most general principles of a discipline. If one takes the tree and house metaphors seriously, wherever one might begin in the system, one must ultimately relate one’s conclusions (deductively) to the principles of metaphysics, and the principles of metaphysics must be hierarchically arranged. Descartes’s philosophy may be understood on the model of a complete and unified science, in which the principles of biology are reduced to those of chemistry and the principles of chemistry are reduced to the principles of physics.
The question remains, however, how did Descartes believe one should proceed in discovering the ultimate principles of the sciences and metaphysics? To answer that question we must turn to a consideration of his method.
The search for laws
At the end of the Second Objections to the Meditations, Mersenne invites Descartes to “set out the entire argument in geometrical fashion, starting from a number of definitions, postulates and axioms” (AT 7: 128, CSM 2: 92). While Descartes complies with Mersenne’s request (AT 7: 160–70, CSM 2: 113–20), he initially responds that the arguments of the Meditations are set forth in accordance with a geometrical method, namely, the method of analysis.
We begin with a sketch of what we believe Descartes meant by “analysis”. Next we examine the Cartesian texts to show the plausibility of our reconstruction of Cartesian analysis. In this chapter we focus on analysis as the search for general laws or principles. In the next we examine conceptual analysis: the search for clear and distinct ideas, or, more properly, the method by which ideas are clarified.1 While we demonstrate the textual consistency
of our reconstruction of Cartesian analysis, we shall deem it correct only to the extent that it clarifies the structure of the Meditations, since, as Descartes tells us, “it is analysis . . . alone which I employed in my Meditations” (AT 7: 156, CSM 2: 111).
Analysis
In the Second Replies, Descartes alludes to analysis as a method of demonstration. As a method of demonstration, analysis mirrors the method of discovery: “Analysis shows the true way by means of which the thing in question was discovered methodologically and as it were a priori” (AT 7: 155, CSM 2: 110). Given this mirroring, one should be able to delineate the steps operative in the method. Given its universality, the same method should be found in the physical sciences, mathematics, and metaphysics, although
one might discover additional constraints appropriate to each of those fields. For example, the “method of doubt” is appropriate in metaphysical inquiries, since the primary notions in metaphysics are:
as evident as, or even more evident than the primary notions which the geometers study; but they conflict with many preconceived opinions derived from the senses which we have got into the habit of holding from our earliest years, and so only those who really concentrate and meditate and withdraw their minds from corporeal things, so far as is possible, will achieve perfect knowledge of them.
(AT 7: 157, CSM 2: 111) While the “method of doubt” is a necessary supplement to the method of analysis in metaphysical inquiries, it is not identical to the Cartesian method.2
What, then, is the nature of that method?
We suggest that the method of analysis is a search for eternal truths (common notions, axioms), propositions which are recognized as true as soon as they are considered (P 1: 49). Eternal truths vary in degrees of generality. Descartes’s paradigms of eternal truths are: “It is impossible for
the same thing to be and not to be at the same time; What is done cannot be undone; He who thinks cannot but exist while he thinks” (P 1: 49: AT 8A:
24, CSM 1: 209, Descartes’s emphasis) and “Nothing comes from nothing” (P 1: 75: AT 8A: 38, CSM 1: 221). Eternal truths constitute the essences of things (AT 1: 152, CSM 3: 25). Consequently, the generality (simplicity) of eternal truths varies with the generality of the object(s) under consideration (see AT 1: 149, CSM 3: 24).
Insofar as analysis is the complement of synthesis and the latter is the deductive method found in works such as Euclid’s Elements and Spinoza’s
Ethics (see AT 7: 156, 160–70; CSM 2: 110–11, 113–20), the method of analysis
is the search for the most basic principles (axioms, eternal truths, common notions) in a certain domain. So geometrical analysis yields the most general principles in geometry; physical analysis yields the most general principles of physics; and metaphysical analysis yields the most general principle of metaphysics, namely, the existence of God (AT 1: 149, CSM 3: 24). Furthermore, as we show, the domains in which one seeks eternal truths stand in a hierarchical order: metaphysical truths are higher than mathematical truths which are higher than physical truths (see AT 9B: 14, CSM 1: 186). In general, the degree of fundamentality of a truth (or a domain of discourse) is inversely
proportional to the corporeality of the domain. This is exemplified in the
Geometry, where Descartes reduces the truths of geometry to those of
arithmetic.
But while this might tell us what Descartes sought, it does not specify a procedure for discovering those truths. Is there such a procedure? And if there is, can one elucidate it in terms of a commonly understood model? In what follows we suggest that his procedure was to propose a hypothesis which, if true, would explain the phenomenon in question. Confirmation of the hypothesis is a two-fold process. First, its truth must be recognized by the natural light (light of reason). Second, either it must be subsumed under a more general hypothesis known by the natural light, or it must unify the domain from which it is taken. As we argue below, the sense of “truth” operative in these two cases is not the same. We argue that the natural light recognizes material truth (cf. Wilson 1978: 107–9; Wolfson 1934 vol. 2: 98– 9); coherence is evidence of formal truth. Still, this fails to tell us how Descartes could claim to systematically construct hypotheses. To understand that, let us begin with his Geometry.
In the Geometry Descartes gives us a hint regarding the procedure for solving any problem. He writes:
Thus, if we wish to solve some problem, we should first of all consider it solved, and give names to all the lines – the unknown ones as well as the others – which seem necessary in order to construct it. Then, with-out considering any difference between the known and the unknown lines, we should go through the problem in the order which most natu-rally shows the mutual dependency between the lines, until we have found a means of expressing a single quantity in two ways. This will be called an equation, for the terms of the one of the two ways [of express-ing the quantity] are equal to those of the other. And we must find as many such equations as we assume there to be unknown lines. Or else, if we cannot find many of them, and if nonetheless we have omitted nothing that is to be desired in the question, this indicates that it is not entirely determined; and in that case, we can take at random lines of known length, for all the unknown lines to which no equation corre-sponds.
(AT 6: 372, O 179) Here the procedure is fairly straightforward. Assume you are given a triangle ABC (see Figure 1) and want to find the length of side BE of a similar triangle BDE (AT 6: 370; O 178). If the lines AC and DE are parallel, then:
Figure 1 Triangle
BE BD — = — BC AB One cross multiplies:
BE × AB = BC × BD
and, assuming AB = 1 unit, one concludes that: BE = BC × BD
This is a means of solving an equation for an unknown variable. Insofar as the lines of a geometric construct are treated in terms of numerical values, one reduces geometry to arithmetic, which was one of Descartes’s objectives in the Geometry (AT 6: 369–70, O 177).3 Insofar as the problem is arithmetic,
the method is strictly deductive. But not all the problems which Descartes attempted to solve were arithmetic or reducible to arithmetic problems. Does this provide us with any general clues regarding the nature of the method? We believe it does. Solving arithmetic equations for a given variable is analogous to finding the missing premise in an enthymematic argument. Given one premise and the conclusion, one can formally and unambiguously determine what premise, if any, will yield a valid categorical syllogism. If Descartes used a deductive nomological model of explanation, the search for an explanatory principle (natural law) may be construed as the search for the missing premise of a valid enthymematic argument.4 Of course, formal
validity provides no more than a necessary condition for the acceptability of the missing principle. One must also recognize the truth of the principle
by the natural light. So, did Descartes, like the logical positivists of our own time (see Hempel 1965), construe explanation in terms of a deductive nomological model?
Yes. Evidence for this can be drawn from his remarks on the methodology in the Optics and Meteorology. Descartes writes:
Should anyone be shocked at first by some of the statements I make at the beginning of the Optics and the Meteorology because I call them “suppositions” and do not seem to care about proving them, let him have the patience to read the whole book attentively, and I trust that he will be satisfied. For I take my reasonings to be so closely interconnected that just as the last are proved by the first, which are their causes, so the first are proved by the last, which are their effects. It must not be supposed that I am here committing the fallacy that the logicians call ‘arguing in a circle’. For as experience makes most of these effects quite certain, the causes from which I deduce them serve not so much to prove them as to explain them; indeed, quite to the contrary, it is the causes which are proved by the effects. And I have called them “suppositions” simply to make it known that I think I can deduce them from the primary truths I have expounded above; but I have deliberately avoided carrying out these deductions in order to prevent certain ingenious persons from taking the opportunity to construct, on what they believe to be my principles, some extravagant philosophy for which I shall be blamed.
(AT 6: 76–7, CSM 1: 150; see also AT 9B: 5, CSM 1: 181, P 4: 206) Notice the role of supposition or hypothesis formation.5 Descartes says
that in the Optics and Meteorology he introduces various assumptions that are later proven insofar as they provide adequate causal explanations of the phenomena in question. His remark that there is a mutual proof of causes and effects – the assumption qua cause is proven insofar as it explains the phenomenon in question and the phenomenon is proven insofar as it follows deductively from the assumption qua cause – shows the role of coherence in his system. To the extent that the supposition explains and deductively implies the claim that a certain effect must occur, one is justified in accepting the (formal) truth of the cause qua supposition. Notice that the coherence Descartes has in mind is theoretical. Even if one recognizes a supposition as
(materially) true by the natural light, it also must cohere with more general truths in a given system. As Descartes notes, “I have called them “suppositions” simply to make it known that I think I can deduce them from the primary truths I have expounded above.” Further, it is at least in part observable phenomena which are explained, since “experience makes most of these effects quite certain.”
Placing this discussion of suppositions in the context of the levels of wisdom enumerated in the Preface to the French edition of the Principles (AT 9B: 5, CSM 1: 181) suggests a deductive (explanatory) relationship between the levels of wisdom exemplified in Descartes’s method. He notes that the four standard levels of wisdom consist of, first, “notions which are so clear in themselves that they can be acquired without meditation,” second, “everything we are acquainted with through sensory experience,” third, “what we learn by conversing with people,” and fourth, “what is learned by reading books . . . written by people who are capable of instructing us well” (AT 9B: 5, CSM 1: 181). There is a fifth way which “consists in the search for the first causes and the true principles which enable us to deduce the
reasons for everything we are capable of knowing” (AT 9B: 5, CSM 1: 181,
our emphasis). Descartes’s call for deductive explanations ultimately suggests that one will develop a complete and coherent explanation of the world by following his method.
The double method of coherence to which Descartes alludes in the passage above was not original to him. At several points he suggests that his method was drawn from the Pappus and other ancient geometers (AT 10: 376, CSM 1: 18–19; AT 7: 4, CSM 2: 4). Pappus describes the method of analysis as follows:
Now analysis is the way from what is sought – as if it were admitted – through its concomitants [the usual translation reads: consequences] in order to something admitted in synthesis. For in analysis we suppose that which is sought to be already done, and we inquire from what it results, and again what is the antecedent of the latter, until we on our backward way light upon something already known and being first in order. And we call such a method analysis, as being a solution backwards. In synthesis, on the other hand, we suppose that which was reached last in analysis to be already done, and arranging in their natural order as consequences the former antecedents and linking them one with another, we arrive at the construction of the thing sought. . . .
In the theoretical kind we suppose the thing sought as being and as true, and then we pass through its concomitants [consequences] in order, as though they were true and existent by hypothesis, to something admitted; then, if that which is admitted be true, the thing sought is true, too, and the proof will be the reverse of the analysis.
(Hintikka and Remes 1974: 8–9) The methodological similarity between this passage and the description of his method that Descartes proposed in the Geometry is striking. Analysis consists of two phases. The first or upward phase is a search for principles. Here one assumes what one wants to prove and seeks principles that will deductively explain it. The second or downward phase – the proof of the analysis – is a synthetic argument based on the principles discovered.
Another analytic tradition can be traced back through the medievals to Aristotle.6 In 1334, Urban the Averroist wrote the following in his
commentary on Aristotle’s Physics:
[D]emonstrations which proceed from causes . . . though they are always prior and more known quoad naturam, are often posterior and less known to us. This occurs in natural science, in which those things prior for us, such as effects, we investigate their causes, which are posterior and less known to us. And this is the way of the method of resolution. But after we have investigated the causes, we demonstrate the effects through those causes; and this is the way of the method of composition. Thus physical demonstrations follow after mathematical demonstrations in certainty, because they are the most certain after those in mathematics. (Quoted in Randall 1968: 232) There are several points to notice here. First, Urban draws a distinction between two orders in which things are known. On the one hand, there is the order of reality, in which general principles (natural laws) are prior to the phenomena they explain; on the other hand, there is the temporal order in which things become known to us. Descartes draws a similar distinction. In both the Regulae (AT 10: 418, CSM 1: 44) and the Fifth Replies (AT 7: 384, CSM 2: 263–4), he indicates that insofar as one is concerned with epistemic issues, we must distinguish between the order of epistemic priority (which follows the metaphysical order, the order of reality) and the order of consideration, that is, the order in which one actually considers things.7 As
Urban notes, in the double process of proof, one considers various issues before one offers explanations of them. Thus, sensible knowledge might be prior in the order of consideration, but knowledge of the causes of those sensed phenomena are prior in the epistemic order. Just as the Descartes of
Discourse, Part Six, stressed that one can claim knowledge of sensible
appearance – which is prior in the order of consideration – only when subsuming it under (explaining it by) a causal principle which is epistemically prior to it (prior in reality), Urban stresses that one obtains knowledge only when what is epistemically prior supplies a coherent explanation of what is prior in the order of consideration.
Nor was the “double method” to which Descartes alludes in the Discourse anticipated only by Urban the Averroist.8 Paul of Venice (1429) makes much
the same point by quoting Averroes’ commentary on Aristotle’s Physics: Scientific knowledge of the cause depends on a knowledge of the effect, just as scientific knowledge of the effect depends on knowledge of the cause, since we know the cause through the effect before we know the effect through the cause. This is the principal rule of all investigation, that a scientific knowledge of natural effects demands a prior knowledge of their causes and principles. [This is not a circle, however.] In scientific procedure there are three kinds of knowledge. The first is of the effect without any reasoning, called quia, that it is. The second is of the cause through knowledge of the effect; it is likewise called quia. The third is of the effect through the cause; it is called propter quid. But the knowledge of why (propter quid) the effect is, is not the knowledge that (quia) it is an effect. Therefore the knowledge of the effect does not depend on itself, but upon something else.
(Quoted in Randall 1968: 233) Notice that again one finds a distinction between kinds of knowledge. The first kind to which Paul of Venice alludes seems to be sensible knowledge: it is knowledge (or, at least, the presumption) that something is a certain way. Such knowledge is prior in the order of consideration to causal knowledge. The second kind is knowledge of a cause through its effect, which is little more than knowledge that a given effect must have a certain cause. One will also have this second kind of knowledge prior to the search for the cause itself: in the parlance we introduced above, it is prior in the order of consideration to knowledge of an effect by way of its cause, even though the cause is prior in the epistemic order. Descartes seems to follow Paul of
Venice in acknowledging this distinction, since it presupposes the eternal truth that “Nothing comes from nothing” (AT 8A: 38, CSM 1: 221; P 1: 49), that is, it sets forth the need to inquire into the cause of a phenomenon.9 Of
course, it is not until the third and final stage that one can claim scientific knowledge of the phenomenon, for one only then conceives of the phenomenon as the effect of a particular kind of cause.
Both Paul of Venice and Descartes claim that the procedure avoids the charge of arguing in a circle. How can this be? Is one not simply assuming what one sets out to discover and arguing that, since what one has discovered will explain the phenomenon in question, one is justified in accepting it as true?
No. In Descartes’s works we are concerned with two different issues, discovery and confirmation, and confirmation itself consists of two phases. This is how Descartes proceeds. Having isolated a phenomenon, one inquires into its cause. The “cause” for which one is looking is a principle or natural law that will explain the phenomenon. The phenomenon is prior in the order of consideration to the question of its cause, and the question, “What is the cause of phenomenon x?” is prior in the order of consideration to any candidate for an explanatory principle. The question “What is the cause of
x?” identifies the cause only by description. In answering the question,
Descartes distinguishes between two phases. In positing a causal principle (statement of natural law), one’s initial question is one of its material truth: is the posited principle recognized as true by the natural light? An affirmative answer initially confirms the law; it shows that the posited law is internally consistent: it could be an explanatory principle.
In the second phase, one shows that positing the law explains the phenomenon in question. For example, if one questions why the water on the stove is boiling, one might make various observations: the water is heated to 212°F.; the atmospheric pressure is 29.92 inches of mercury. This might lead one to posit as an explanatory principle that all water at an atmospheric pressure of 29.92 inches of mercury that is heated to 212°F boils. This principle would be recognized as true by the natural light; that is, it would be recognized as materially true (internally consistent). If, in turn, it would explain why the water on the stove is boiling, there would be evidence of the formal truth of the causal principle. One is concerned with two issues in distinguishing between the two phases of the explanation. The natural light provides an initial and very limited confirmation of the causal principle: it shows the plausibility of the law by revealing the law as materially true. The deduction of the phenomenon to be explained from the law and the set
of initial conditions shows that the law in question explains the phenomenon. This is evidence for the formal truth of the law. Further evidence of its formal truth is derived from subsuming the law in question under more general laws, the material truth of each being recognized by the natural light.
But one could always construct alternative explanations, each of which is based on a principle that is recognized by the natural light. How does one choose among those explanations? Descartes accepted the principle of parsimony: given a choice between two explanations, he deemed the simpler explanation – the explanation appealing to fewer fundamentally different kinds of entities or a smaller number of laws – the most probably true. This is not a principle Descartes trumpets from the rooftops. Indeed, as he suggests in a letter to Regius of January 1642, it is at least politically prudent to leave existential questions open; all one need show is that the entities assumed by one’s opponents are not necessary to explain the phenomenon at hand (AT 3: 491–2, CSM 3: 205).10 In the same letter he points to his own strategy
in the Meteorology. He counsels Regius:
[W]hy did you need to reject openly substantial forms and real qualities? Do you not remember that on page 164 of my Meteorology, I found them unnecessary in setting out my explanations? If you had taken this course, everybody in your audience would have rejected them as soon as they saw they were useless, and in the mean time you would not have become so unpopular with your colleagues.
(AT 3: 491–2, CSM 3: 205) In the passage to which he alludes, Descartes explains observable changes in the material world on the hypothesis that observable objects are composed of minute parts, and that macroscopic changes are the result of changes in the configuration and movement of the particles of which they are composed. He does not deny the existence of the Scholastics’ “‘substantial forms’, their ‘real qualities’, and so on. It simply seems to me that my arguments will be all the more acceptable insofar as I can make them depend on fewer things” (AT 6: 239, CSM 2: 187n.2, O 268).
Nor is this the only place Descartes appeals to the principle of parsimony. In the First Discourse of the Optics, and to a lesser extent in the Fourth Discourse, he suggests that there is no reason to posit the intentional forms of the Scholastics insofar as his theory will explain vision without such a postulation. Indeed, he remarks, “By this means, your mind will be delivered from all those little images flitting through the air, called ‘intentional forms’,
which so exercise the imagination of the philosophers.” (AT 6: 85, CSM 1: 153–4; cf. AT 6: 112, CSM 1: 165). Thus, it seems clear that Descartes at least implicitly appeals to parsimony as a basis for deciding between two theories. To summarize, we believe that the Cartesian method is a type of argument to the best explanation.11 Descartes begins by seeking an explanation for a
certain phenomenon. He proposes a hypothesis, a general principle which, if true, would provide the lawful basis for explaining the phenomenon in question. This is subject to a two-phase process of confirmation. First, the natural light must recognize it as materially true. Second, it must provide the basis for a deductive–nomological explanation of the phenomenon in question. This provides evidence that the hypothesis is formally true, and the degree of evidence is increased if the hypothesis itself can be subsumed under a higher level law (hypothesis). In addition to this, he implicitly appeals to the principle of parsimony as the basis for choosing between two hypotheses which are equally plausible on the basis of the previous criteria. Simplicity is the ground for deciding which theory is “best”.
In our account of Cartesian analysis as a search for natural laws, we introduced a distinction between material and formal truth, and we assigned a central role to the light of nature. Before showing the consistency of our account of the method with the four methodological rules Descartes sets forth in the Discourse, we must digress and elucidate the distinction between material and formal truth, the role of the natural light (intuition) in his method, and the kinds of certainty found in his philosophy. These are our topics for the next three sections.
Material and formal truth
In the Third Meditation Descartes introduces the notion of an idea, distinguishes an idea simpliciter from other forms of thought, and draws a distinction between formal falsehood and material falsehood. Formal falsehood is a property of judgments, rather than of ideas simpliciter (AT 7: 37, 43; CSM 2: 26, 30; see also AT 7: 233, CSM 2: 163). Judgment is the proper domain of error, “[a]nd the chief and most common mistake which is to be found here consists in my judging that ideas which are in me resemble, or conform to, things located outside me” (AT 7: 37, CSM 2: 26). Judgments are complex mental acts insofar as they require an affirmation or denial by the will with respect to an idea (see AT 7: 56, CSM 2: 39). While ideas provide the subject matter for judgments, ideas as such are not formally true or false.
Descartes contends that if one is to avoid error – formal falsity – “the perception of the intellect should always precede the determination of the will” (AT 7: 60, CSM 2: 41).
If any sense of truth or falsehood applies to ideas as such, then it is material truth and falsity.12 When he introduces the notion of material falsity
in Meditation Three, Descartes indicates that the notion applies strictly to ideas having a low degree of clarity and distinctness, ideas that “represent non–things as things” (AT 7: 43, CSM 2: 30; see also AT 7: 233, CSM 1: 163). Ideas of heat or cold, for example, are so obscure and confused, that “they do not enable me to tell whether cold is merely the absence of heat or vice versa, or whether both of them are real qualities, or neither is” (AT 7: 44, CSM 2: 30). Because ideas present themselves as if they represent things, materially false ideas provide the subject matter for false judgments (AT 7: 231, CSM 2: 162).
His more extended discussion of material falsity in the Fourth Replies repeats the same theme: material falsity is a function of an idea’s obscurity. Focusing on the idea of cold, he says, “[M]y only reason for calling the idea [of cold] ‘materially false’ is that, owing to the fact that it is obscure and confused, I am unable to judge whether or not what it represents to me is something positive which exists outside my sensation” (AT 7: 234, CSM 2: 164; cf. AT 7: 233, CSM 2: 163). Material falsity is a function of the obscurity of an idea of sensation, the idea itself being “something positive as its underlying subject” (AT 7: 234, CSM 2: 164; see also AT 7: 234–5, CSM 2: 164). “The greatest scope for error is provided by the ideas which arise from the sensations of appetite,” which explains, for example, why a dropsical person may seek to satisfy a craving for water, but does so at serious risk of injury (AT 7: 234, CSM 2: 163–4).
A materially false idea is so obscure that one does not know of what it is an idea, that is, one does not know the essence of the thing putatively represented. Since “according to the laws of true logic, we must never ask about the existence of anything unless we first understand its essence” (AT 7: 107–8, CSM 2: 78), the fact that an idea is materially false (obscure and confused), increases the probability of error in any judgment based upon that idea. If an idea is materially false (obscure and confused), one cannot determine its degree of objective reality, and, consequently, one cannot apply Descartes’s maxim that an idea’s degree of objective reality must be the result of “some cause which contains at least as much formal reality as there is objective reality in the idea” (AT 7: 41, CSM 2: 28–9). Hence, a materially false idea can provide no solid ground for judging the nonideational nature of the cause of one’s idea.13
Given Descartes’s contention that obscure and confused ideas are materially false, we may extrapolate a notion of material truth. Clear and distinct ideas are materially true: they provide the basis for formally true judgments.14 While even Descartes’s most extensive discussion of clear
and distinct ideas (P 1: 45) tells one less than one would like regarding their nature, at least it shows that a clear and distinct idea includes a sufficient number of the constituent properties of a thing of a kind to allow one to distinguish it from all other kinds. Given this level of clarity, one can inquire into the cause of one’s idea. At this point one may move from the realm of ideas to that of formal reality, that is, to the reality of material objects and God (see AT 7: 37, CSM 2: 26).
But even if clear and distinct ideas are materially true, this does not guarantee that all clear and distinct ideas provide the basis for formally true judgments, that is, judgments regarding the actual existence of objects. In the Fifth Meditation, Descartes indicates that he finds within himself:
countless ideas of things which even though they may not exist anywhere outside me still cannot be called nothing; for although in a sense they can be thought of at will, they are not my invention but have their own true and immutable natures.
(AT 7: 64, CSM 2: 44) His example is an idea of a triangle, which:
even if perhaps no such figure exists, or has ever existed, anywhere outside my thought, there is still a determinate nature, or essence, or form of the triangle which is immutable and eternal, and not invented by me or dependent on my mind.
(AT 7: 64, CSM 2: 45) One’s idea of a triangle is innate (AT 7: 382, CSM 2: 262). One’s idea of a triangle cannot be called nothing, for one can demonstrate that a triangle has various properties (AT 7: 64–5, CSM 2: 45). To put this differently, an object possibly exists that corresponds to the idea (AT 7: 71, CSM 2: 50).
But possible correspondence is one thing; actual correspondence is something else. Descartes raises the possibility that no triangles are actual, even though the idea of a triangle is (materially) true.15 This implies that all
eternal truths about triangles have no existential import: no judgments of formal truth (existence) follow immediately from them.
The conclusions we have reached regarding one’s clear and distinct ideas of triangles seem applicable to all eternal truths except the claim that God exists. At Principles 1: 13, Descartes places eternal truths or common notions in the same class of ideas as those of numbers or triangles.16 After
noting that one avoids error so long as one makes no affirmations or denials regarding the ideas one finds within oneself, he writes:
Next, it [the mind] finds certain common notions from which it constructs various proofs; and, for as long as it attends to them, it is completely convinced of their truth. For example, the mind has within itself ideas of numbers and shapes, and it also has such common notions as: If you
add equals to equals the results will be equal; from these it is easy to
demonstrate that the three angles of a triangle equal two right angles, and so on.
(P 1: 13: AT 8A: 9, CSM 1: 197; see also P 1: 49, CB §52) Descartes indicates that mathematical truths and other eternal truths, such as, “He who thinks cannot but exist while he thinks,” are free from existential import (see P 1: 10, 49). Hence, they cannot be formally true. Consequently if, as the texts suggest, the distinction between formal and material truth is exhaustive, eternal truths can be only materially true, and, with the exception of the claim of divine existence, entail no formal truths. If we are correct in this, then among the eternal truths are some that assert the necessary and sufficient conditions for claims of real (formal) existence, but which, apart from any factual truths, will not warrant judgments of real (formal) existence.17
Thus, an eternal truth in conjunction with a factual claim, and only in conjunction with a factual claim, can provide the basis for justifying a claim of real existence. If our reconstruction of analysis in the first section of this chapter is correct, eternal truths are the general principles that are discovered in analysis. But one will generally claim that it is one thing to “discover” a principle that will allow one to deduce a factual claim; it is something else to know that the principle discovered is true. Further, we have already seen that Descartes holds that the deducibility of a claim from a general principle is a necessary, but not a sufficient, condition for asserting the truth of the claim deduced. But if independently-known, eternal truths serve as the deductive anchor in the justification of factual claims, then how does one know these eternal truths? He answers this question in terms of intuition and the natural light.
Intuition and the natural light
Throughout his works, Descartes alludes to principles known by the “natural light” or the “light of nature” or the “light of reason.” In the Principles of
Philosophy, he identifies the “light of nature” with the “faculty of knowledge
which God gave us” (AT 8A: 18, CSM 1: 203; P 1: 30). In the Synopsis of the
Meditations, he claims that “speculative truths . . . are known solely by
means of the natural light” (AT 7: 15, CSM 2: 11). In the Third Meditation he notes:
Whatever is revealed to me by the natural light . . . cannot in any way be open to doubt. This is because there cannot be another faculty both as trustworthy as the natural light and also capable of showing me that such things are not true.
(AT 7: 38–9, CSM 2: 27) In Meditation Four he identifies the natural light with the “power of understanding . . . which God gave me” (AT 7: 60, CSM 2: 42). Indeed, the explanatory subtitle of The Search for Truth by Means of the Natural Light asserts, “This light alone, without any help from religion or philosophy,
determines what opinions a good man should hold on any matter that may occupy his thoughts, and penetrates into the secrets of the most recondite sciences” (AT 10: 495, CSM 2: 400, Descartes’s emphasis). The light of
nature is the power or the faculty by which one discerns eternal truths. It is what the Descartes of the Regulae (AT 10: 366–70, CSM 1: 13–15) called “intuition,” a term he used almost exclusively in that work.18 In this section
we examine the Regulae to show that intuition provides knowledge of eternal maths, that is, knowledge of material truths; that deductively valid movements are recognized as such by intuition; and that knowledge of formal truths requires a combination of intuition and deduction.19
Descartes’s discussions of intuition and deduction begin in the Third Rule and continue intermittently through the Twelfth. Claiming that there are only two sources of “knowledge of things with no fear of being mistaken,” namely intuition and deduction (AT 10: 368, CSM 1: 14), he defines ‘intuition’ as follows:
By ‘intuition’ I do not mean the fluctuating testimony of the senses or the deceptive judgement of the imagination as it botches things
together, but the conception of a clear and attentive mind, which is so easy and distinct that there can be no room for doubt about what we are understanding. Alternatively, and this comes to the same thing, intuition is the indubitable conception of a clear and attentive mind which proceeds solely from the light of reason.
(AT 10: 368, CSM 1: 14) We have already noticed that Descartes identifies the “natural light” with the faculty that discerns truth. Intuition, then, initially seems nothing more than the ability to recognize truth by the light of reason. The passage tells us a bit more, however, for it requires that the mind be “clear and attentive.” The call for clarity implies that the mind be free of preanalytic biases, e.g. that one reject the assumption that all knowledge is derived from sense perception.20 Further, one must “attend” to what is discovered, e.g. to the
extent possible, one should ignore the bombardment of sensuous information.21
But intuition is not only the recognition of truth; it is also the recognition of deductive validity. As Descartes continues:
The self-evidence and certainty of intuition is required not only for apprehending single propositions, but also for any train of reasoning whatever. Take for example, the inference that 2 plus 2 equals 3 plus 1: not only must we intuitively perceive that 2 plus 2 make 4, and that 3 plus 1 make 4, but also that the original proposition follows necessarily from the other two.
(AT 10: 369, CSM 1: 14–15) In deducing “that 2 plus 2 equals 3 plus 1,” intuition plays two roles. By intuition one recognizes the serf-evidence of the premises from which the deduction proceeds, and one recognizes the necessary connections among a very limited number of premises and a conclusion. As Descartes goes on to indicate, deduction, “the inference of something necessarily following from some other propositions which are known with certainty” (AT 10: 369, CSM 1: 15), differs from intuition insofar as it involves a “continuous and uninterrupted movement of thought” (AT 10: 369, CSM 1: 15), while no such movement is found in intuition. Deductive arguments often proceed from several premises and require that one draw subconclusions before reaching one’s final conclusion. Such arguments lack the immediate self-evidence of intuition insofar as they require that one remember the premises and
subconclusions, that is, “deduction in a sense gets its certainty from memory” (AT 10: 370, CSM 1: 15). Nonetheless, each step of a deductive argument involves an intuitive move, and consequently Descartes claims that:
those propositions which are immediately inferred from first principles can be said to be known in one respect through intuition, and in another respect through deduction. But the first principles themselves are known only through intuition, and the remote conclusions only through deduction.
(AT 10: 370, CSM 1: 15). Notice that Descartes claims that first principles are known through intuition. As he indicated in the Introduction to the French edition of the
Principles, such first principles have two characteristics:
First, they must be so clear and so evident that the human mind cannot doubt their truth when it attentively concentrates on them; and, secondly, the knowledge of other things must depend on them, in the sense that the principles must be capable of being known without knowledge of these other matters, but not vice versa.
(AT 9B: 2, CSM 1: 179–80; see also AT 10: 401–2, CSM 1: 33–4) What counts as a “first principle” might vary with the subject matter of one’s inquiry. But it is clear that these “first principles” are what Descartes alternatively calls “simple propositions” (AT 10: 428–9, CSM 1: 50), “simple natures which the intellect recognizes by means of a sort of innate light” (AT 10: 419, CSM 1: 44; see also AT 7: 65, CSM 2: 44–5), “common notions” (AT 10: 419–20, CSM 1: 45; see also CB §1: AT 5: 146, CSM 3: 332–3), or “eternal truths” (P 1: 48–50, CB §52: AT 5: 167). These “first principles” are necessarily true and, when attentively considered, are recognized as such by the natural light. It is these first principles that provide the basis for deductions which establish the certainty of less primary claims.
Types of certainty
While Descartes claims that there is but one method for discovering truth, and while he claims that certainty rests on either immediate intuitions of
