Willis Doney. the Cartesian Circle

The Cartesian CircleAuthor(s): Willis DoneySource: Journal of the History of Ideas, Vol. 16, No. 3 (Jun., 1955), pp. 324-338Published by: University of Pennsylvania PressStable URL: http://www.jstor.org/stable/2707635 .

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THE CARTESIAN CIRCLE

BY WILLIS DONEY

Perhaps the most common criticism of Descartes' Meditations, voiced by his earliest critics 1 and repeated in more recent discussions,2 is that his reasoning is circular. The objection can be stated quite simply. In order to remove his doubt about even those beliefs which seemed to him most certain, Descartes demanded that the existence of a Creator who would not deceive him be proven. But in any proof of God's existence and veracity he would have to assume what he could not rightly assume, that at least some of the things which seemed most evident to him were true. That is, he would have to trust his clear and distinct perceptions of the grounds of God's existence; and this was forbidden before he knew that God, and not the Evil Genius, was the source of these perceptions.

This objection has been variously assessed. Descartes was himself quite unimpressed. In replying to his critics 3 he suggested that they re-read what he had written. The answer to the objection was apparent in his writings; it was simplicity itself. This is certainly an ex- aggeration. Although Descartes was prepared with an answer, it was not really obvious. It raised questions which he did not explicitly answer. And it seemed inconsistent with any number of statements in the Meditations and the Discourse and irreconcilable with the general plan of his metaphysics. This has led one recent writer to dis- miss Descartes' answer as sophistry; 4 another, after a painstaking investigation, to report " contradictory positions " rooted in a " con- cealed philosophical antagonism." 5

I shall argue in defense of Descartes' answer.6 It did meet the 1 In the second and fourth sets of objections printed with the Meditations (AT,

VII, 124-125, 214; HR, II, 26, 92). The objection was also raised by Gassendi in the Disquisitio Metaphysica, in reply to which Descartes referred to these passages (AT, IX, 211). AT stands for the Adam and Tannery edition of Descartes' works (Paris, 1904); HR for the Haldane and Ross translation (Cambridge, 1912).

2 Norman Kemp Smith, Studies in the Cartesian Philosophy (London, 1902), 54; A. Boyce Gibson, The Philosophy of Descartes (London, 1932), 293-328; H. A. Prichard, Knowledge and Perception (Oxford, 1950), 85-86; Stuart Hampshire, Spinoza (Penguin Books, 1951), 66, 104-5.

3 In his replies to the second and fourth sets of objections (AT, VII, 140, 146, 245-246; HR, II, 38, 42-43, 114).

4 Kemp Smith, op. cit., 54. In his New Studies in the Philosophy of Descartes (London, 1952), 186-7, 273ff., Professor Kemp Smith takes Descartes' answer more seriously. 5 Gibson, op. cit., 309.

6 In doing so I accept the conclusion reached by the following commentators: Louis Liard, Descartes (Paris, 1882), 149-174; 0. Hamelin, Le Systeme de Descartes (Paris, 1911), 136-151; S. V. Keeling, Descartes (London, 1934), 73-82, 108-112;

324



THE CARTESIAN CIRCLE 325

objection raised; it was consistent with the position taken in the Meditations; and, in short, Descartes was not guilty of circular reasoning. This side of the question is at least initially plausible. For how could Descartes have fallen into so obvious a logical trap as the so- called Cartesian circle? What's more, even if he had, how could he have failed to realize the force of the objection when it was so clearly presented to him on three occasions? I shall try to show that the evidence for Descartes' having committed this monumental gaffe is certainly inconclusive and in fact rests on a misinterpretation of passages which, admittedly, are misleading but which are made clear by Des- cartes' answer to the objection. First, however, I shall state the objection in its clearest form and present Descartes' answer.

Arnauld put the objection most succinctly in terms of clear and distinct perceptions.7 He was uncertain " as to how a circular reasoning is to be avoided in saying: the only secure reason we have for believing that what we clearly and distinctly perceive is true, is the fact that God exists. But we can be sure that God exists, only because we clearly and evidently perceive that; therefore prior to being certain that God exists, we should be certain that whatever we clearly and evidently perceive is true." At the risk of laboring an obvious point, I shall introduce symbols, letting p stand for the statement that what we clearly and distinctly perceive is true, and q for the statement that God exists (and is not a deceiver). The form of Arnauld's objection is, then, that Descartes asserted or assumed both that we can know p only if we first know q and that we can know q only if we first know p. If he held both of these beliefs, he could not consistently claim to know either p or q. And, since he did claim to know both p and q, he must have reasoned in a circle.

Descartes' reply was in effect to distinguish two senses of p. One, it might mean: what in fact he at present clearly and distinctly perceived was true. Or, two, it might mean: what he recalled having clearly and distinctly perceived was true. In the first sense he could know p without first knowing q. Present clear and distinct perceptions were never subject to doubt. Anything so perceived did not

A. Gewirtz, "The Cartesian Circle," Phil. Rev. 50 (1941), 368-395; Etienne Gilson, etudes sur le role de la pensee medievale dans la formation du systeme cartesien (Paris, 1951), 234-244, and his commentary on the Discourse (Paris, 1947), 360- 362. In the additions and corrections to his commentary on the Discourse Gilson expressed his dissatisfaction with the account which he had given and adopted the skeptical view that the question of circularity could not be definitively answered (483-484).

7 In the fourth set of objections (AT, VII, 214; HR, II, 92).



326 WILLIS DONEY

depend on God as guarantor of its truth. In the second sense of p, when memory was involved and his present state was not one of clear and distinct perception, he could not know p without first knowing q. Memory being fallible, God must vindicate its use. But he could know q (that God exists) without first knowing p (that what he re- membered having clearly and distinctly perceived was true). Knowl- edge of God's existence need not depend on memory: he could clearly and distinctly perceive in a single view, so to speak, the reasons com- pelling him to believe that God existed. So, taking p consistently in either of these senses, he did not have to know both p in order to know q and q in order to know p.

In answering the objection in this way, Descartes reaffirmed what he had stated in considerable detail in the Rules: reason, properly conducted, was infallible; errors in reasoning were to be charged to memory. In this early work no question was raised about the justification of reason. This might be because Descartes was writing on method and not on metaphysics, or because he had not at the time seen the necessity of a metaphysical justification of the use of reason. I am convinced, however, that he never saw the necessity of such a justification and that reason, meaning the actual perception of necessary truths and their consequences, was, as in the Rules, never doubted and so never stood in need of justification. To show this, I shall first ask, what beliefs could be known by reason without appeal to memory. The answer will be based largely on the Rules. Then, an explanation will be given of the passages in the Discourse and the Medita- tions which seem to show that even these beliefs could not be absolutely certain without knowledge of God's existence and veracity. Finally, a general objection will be answered: how, on my view, could Descartes conceive of metaphysics as the foundation of mathematics and physics? or, really the same question, what could he mean by his repeated assertion that knowledge of God's existence was pre-requisite to his certainty about all other things?

(1) Just which beliefs were known by reason without the use of memory? Certainly not his commonsense beliefs about material things: they derived from obscure and confused perceptions, and not from the clear and distinct ideas of reason. And not all of the beliefs which he had reached by reasoning: for some of these were not based on actual clear and distinct perceptions. Memory was in part re- sponsible for his holding these beliefs. And, when this was so, not even the simplest propositions of mathematics could be known with absolute certainty unless God guaranteed his use of memory. He might remember being certain of something which in fact he had never clearly and distinctly perceived. Or, when he was concerned,




not with an axiom or first principle or intuitive truth, but with a statement requiring proof, he might recall having proved it when actually he had not and, in fact, could not have proved it.

In this way the Evil Genius might tamper with his memory. But a demonstration based on clear and distinct ideas could not be mistaken: "deduction, the pure illation of one thing from another . . . cannot be erroneous when performed by an understanding that is in the least degree rational." 8 Intuition and deduction, untainted by memory, were infallible. In reasoning he ran the risk of error only when he relied on his memory to assure him that something had been proved. But not all reasoning involved memory. So not all beliefs requiring proof were suspect without God's guarantee; only those the proof of which he did not have clearly in mind.

In the Rules and, implicitly, in the fourth rule of the Discourse Descartes distinguished two sorts of proof: those which depended in part on memory and those which were the work of reason alone. In the Rules he had in mind linear proofs; such as the proof of a proposition t from a self-evident principle p by seeing that p entailed q, q entailed r, r entailed s, and finally s entailed t. An inference of this sort would consist of the intuition of a self-evident principle and a series of steps or, in Cartesian language, of movements of thought from one proposition to its successor in the series. There could be no doubt in Descartes' mind about the first principle when he clearly and distinctly perceived it; nor could he be in doubt about any one of the steps as it was taken. But, when he reached t, he had travelled such a distance that he might no longer clearly perceive either his first principle or the first steps in the proof. He might have to remember,

8 Rule II (AT, X, 365; HR, I, 4-5). In Rule III (AT, X, 368; HR, I, 7) Des- cartes claims that deduction, although it can not be erroneously conducted, is less certain than intuition. This may mean, as L. J. Beck has suggested in his recent commentary on the Rules [The Method of Descartes (Oxford, 1952), 65-66 and 87-99], that deduction, considered as movement or inference or illation from one point to the next in an argument, is not infallible; but, taken as the perception or intuition of the logical relation between two propositions, deduction is indis- tinguishable from intuition and equally certain. A good case can be made out, however, for Descartes' having held that immediate inference, or the " pure illation of one thing from another," is infallible even when there is movement of thought. On this view, deduction would be less certain than intuition only in the case of mediate inference or a chain argument when there are successive movements of thought and memory is needed.

9 See especially Rules IV and V. No doubt Descartes had in mind more complicated types of inference in the sections of the Rules devoted to enumeration, e.g., arguments by elimination. It is reasonable to believe, however, that he considered all of the more complicated proofs reducible to parts consisting of linear inferences.



328 WILLIS DONEY

for instance, that he had already proved s. Since his memory was fallible, he could not be absolutely certain of this. And, even though he clearly perceived that t followed from s, he could not be absolutely certain that t was true. The proof of t, since it depended on memory, could not be certain so long as Descartes entertained doubts about his memory. The Evil Genius could have influenced him to remember having proved s when in fact he had not or, for that matter, when s could not be proved.

The proof of t could be made certain by God's certification of the use of memory. But it could also be made certain without divine assistance. To do this, Descartes recommended that all of the steps in the proof should be present to the mind, thus obviating the need of memory.'0 In effect, he recommended eliminating movement of thought from the proof. Each of the steps could be viewed either as an intuition or a deduction." In the second case there would be a movement from r to s, for instance, which would take some time. Once this was completed, however, he would see that s followed from r. There would no longer be an inference or movement of thought; and his seeing that s followed from r would not take time. The same thing could happen in the case of the chain inference from p to t. At first there would be a series of movements of thought. Since s was required for the move from s to t, the movement from r to s would have to pre- cede the movement from s to t. But, if he ran through these steps a number of times, he would come to see how each proposition followed from the one before, and how the last in the series followed from the first. The steps would no longer be immediate inferences, one necessarily prior in time to the next. And the whole proof could be simul- taneously present to his mind in one encompassing intuition (provided, of course, that the inference did not consist of so many steps that he could not keep them all in mind at once).12 When at last he understood the proof and saw how the conclusion followed from the premises, he could not be mistaken.

10 In Rule VII (AT, X, 388; HR, I, 19) and Rule XI (AT, X, 409; HR, I, 34). In both places Descartes recommends the elimination of movement from the inference as a goal which, it is suggested, can not be attained in the case of lengthy proofs. In a shorter proof an enumeration or review would culminate in intuition.

1 "Simplicem vero deductionem unius rei ex altera ibidem diximus fieri per intuitum " (Rule XI, AT, X, 407; HR, I, 33). Also, in Rule III (AT, X, 370; HR, I, 8), although here Descartes considers only immediate inferences from first principles: "Dici posse illas quidem propositiones, quae ex primis principiis immediate concluduntur, sub diversa consideratione, modo per intuitum, modo per deductionem cognosci .... "

12 As in Rule XI, (AT, X, 408; HR, I, 33).




There were, then, two sorts of beliefs that could be absolutely certain without God's guarantee of memory: those based on present intuitions and some of those requiring proof; specifically, those the proof of which was neither so long nor so complex as to exceed the span of his attention. A belief of the second sort would in fact be absolutely certain when its derivation from self-evident principles was clearly and distinctly perceived. But, if he did not attend to every step in the proof, his belief was not certain. He could not trust his memory as having established the truth of a belief. Nor could he consider proof of a belief, no matter how evident it might seem, super- erogatory. For " the mind perceives these and other facts to be true (only) so long as the premises from which they are derived are attended to." 13 Given God's guarantee of memory, however, he could then, and only then, be absolutely certain of some beliefs without attending to their proofs.

(2) If this account is correct, Descartes' reasoning was not circular. But a number of his statements seem to jar. They have been used to show that he was committed to one of two views: that no belief could be absolutely certain without knowledge of God, or that no belief requiring proof could be certain without this knowledge.14 (The weaker view would involve Descartes in the circle if he believed that the existence of God could not be known intuitively but only by demonstration.) I shall consider at some length two passages which have been used to show that he was committed to one or the other of these views. And I shall try to show that neither passage is really inconsistent with the preceding account.

The first is the section of the first meditation in which Descartes expressed his doubt about the simplest matters: "as I sometimes imagine that others deceive themselves in the things which they think they know best, how do I know that I am not deceived every time that I add two and three, or count the sides of the square, or judge of things yet simpler, if anything simpler can be imagined? "15

13Principles, I, xiii (AT, VIII, 9; HR, I, 224). 14 A. Koyre is of this opinion: Essai sur l'idee de Dieu et les preuves de son exist-

ence chez Descartes (Paris, 1922), 59-61 and 119-123. On his view Descartes' metaphysics is not viciously circular, however, since God's existence could be known in a primordial intuition which is its own justification and at the same time the justification of all truths known by clear and distinct ideas.

15 AT, VII, 21; HR, I, 147. Beck's explanation of the apparent inconsistency of this passage and Descartes' views in the Rules is unsatisfactory: he says that "the metaphysical doubt of the Meditationes is not due to the nature of the object which is put before the mind nor does it correspond on our part to any real psychological experience of a cognitive nature. It is by a purposive act of will that we refuse our assent to the self-evident data of mathematics and this is possible because, strictly



330 WILLIS DONEY

It is tempting to think that in this passage Descartes was referring to beliefs based on intuitions. Otherwise, why speak of simpler things, if anything simpler can be imagined? But note the instance of possibly mistaken beliefs. Both stemmed from operations of the mind that took some time; e.g., adding two and three and counting the sides of a square. There was movement of thought, during which a mistake of memory might have occurred: he might have forgotten in the course of adding two and three how many units he had already counted and come up with the wrong answer, or, in the other case, he might have forgotten that he had counted one side of the square, counted it again, and thus fallen into error.

In neither case is it clear that he was questioning a belief based on intuition. It seems more likely that these beliefs were the result of reasoning of some sort. No doubt they could be known by intuition.1 But from the references to adding, counting, and judging it appears that he had in mind situations in which, as a matter of fact, these beliefs were not based on intuitions. As further evidence for this: the parallel passage in the Discourse deals specifically with the possibility of mistakes in reasoning: there were, he noted, "men who deceive themselves in their reasoning and fall into paralogisms, even concerning the simplest matters of geometry." 17 That there might be mistaken intuitions of seemingly self-evident truths was not suggested in this section of the Discourse.

Thus the passage from the Meditations does not prove that he held the stronger view, that nothing, not even his intuitions of first principles, could be trusted without knowledge of God. It may indicate, however, his acceptance of the weaker view, that nothing requiring proof could be known without knowledge of God. I think that in fact it does not, although there is some reason for thinking that it does. The discussion of mistakes in reasoning is juxtaposed with the skeptical arguments concerning perceptual beliefs. And it is natural to sup- pose that Descartes used the same sort of argument as he had used to establish his skeptical conclusion about sense-perception.l8 In both

speaking, ideas in themselves are neither true nor false" (op. cit., 42; my italics). This account is untenable; for in the fourth meditation, Descartes claims that it is psychologically impossible to withhold assent from what is clearly and distinctly present to the mind.

16 In Rule III Descartes offers as examples of intuitive truths that 2 and 2 make 4 and that the triangle is bounded by three lines (AT, X, 368-369; HR, I, 7-8).

17 Part IV (AT, VI, 32; HR, I, 101). 18 Thus it is natural to attribute to Descartes the sort of argument Hume used

in the Treatise, " Of Scepticism with Regard to Reason."




cases he noted mistaken beliefs: there were mistakes in reasoning as well as perceptual illusions. To prove that all of his beliefs based on sense-perception were doubtful, he made use of the following principle: if some beliefs resting on evidence of a certain sort turned out to be mistaken, then any belief resting on evidence of the same sort was doubtful. It seems as if this principle could very naturally be applied to beliefs based on reasoning. And it seems as if Descartes did just this to show that, since the conclusions of some proofs turned out to be mistaken, the conclusion of any proof was doubtful.

But this is not so. Descartes realized that an argument of this sort, sound enough when he was questioning sense-perception, could not be used to undermine reasoning as a source of knowledge. Sense- perception and reasoning differed in an all-important respect. A premise necessary for the validity of an argument of this sort was true when he was considering sense-perception, but admittedly false when he turned to reasoning. The premise was this: the mistaken beliefs which aroused his doubts about a particular source of certainty must be typical of all beliefs arising from this source. It would not do if the mistake had occurred in circumstances which he could have recognized to be abnormal had he been sufficiently attentive at the time. For instance, from the fact that he was sometimes mistaken about an object seen at a distance or in a dim light it did not follow that he could be mistaken about any object, including those viewed close at hand and in a good light. By attending to what he seemed to see, he could tell whether the object appeared to be distant or near, barely perceptible or well illuminated. If he could tell this, he could also tell when he was in danger of error, and when not.

To prove that all perceptual beliefs were doubtful, Descartes had to base his argument on the sort of mistakes that occurred in halluci- nations and dreams. There were dreams in which what he seemed to see was in no way distinguishable from what he seemed to see when he was, or thought that he was, awake. Given that there were " no certain indications by which he might clearly distinguish wakefulness from sleep," 19 he could reach his skeptical conclusion extending to all

19 In the first meditation (AT, VII, 19; HR, I, 146). It would seem that Des- cartes denies this in the sixth meditation: ' Praesertim summa illa de somno, quem a vigilia non distinguebam; nunc enim adverto permagnum inter utrumque esse discrimen, in eo quod nunquam insomnia cum reliquis omnibus actionibus vitae a memoria conjungantur, ut ea quae vigilanti occurrunt ..." (AT, VII, 89; HR, I, 198-199). The only plausible interpretation that would remove the inconsistency is that veridical and dream perceptions can not be distinguished in themselves although they can be distinguished extrinsically; that is, reason and memory can be used to discover whether a perception is related to other perceptions in a coherent pattern. But I am not sure that Descartes can be saved from inconsistency on this point.



332 WILLIS DONEY

beliefs based on sense-perception. And he could reach this conclusion only if he could show that some mistaken beliefs could not have been recognized as such, no matter how carefully he had examined the evidence on which he had accepted these beliefs.

Descartes realized in the case of beliefs based on reasoning that there were no mistakes of this sort. If at times he had erred, his error could have been prevented had he attended carefully enough to what was going on in his mind at the time. He could have seen that his conclusion was not based on a clear and distinct perception of the demonstration, but depended, at least in part, on memory. Knowing that conclusions of this sort were often mistaken, he could have with- held his assent. The mistakes which had evoked his doubts were of a detectable kind. There had been no mistakes when he had clearly and distinctly perceived the reasons for his conclusions. So he could not argue, as he had about perceptual beliefs: sometimes mistaken, therefore, always possibly mistaken.

This is roughly Descartes' answer to Bourdin, who had assumed that in the first meditation he meant to extend his skeptical arguments to all beliefs, even those based on clear and distinct perceptions.20 Descartes rebuked Bourdin severely. For it seemed clear to him that what he had written in the first meditation did not lend itself to this interpretation. I can sympathize with Bourdin. The discussion of mistakes about the simplest matters reads as if Descartes were trying to give reasons for doubting all beliefs, no matter how certain.

And, in a qualified sense, he was. He was delivering an ad homi- nem argument which he thought was of great therapeutic value, addressed to those who failed to distinguish, or were unable to distinguish, cases in which their conclusions were based on clear and distinct ideas and other cases in which they only seemed to perceive the necessity of their conclusions.21 If they could not distinguish the two, the fact that they were sometimes mistaken about matters that seemed most certain would be a reason for doubting anything that seemed certain. Indeed, the hypothesis of an Evil Genius would seem reasonable so long as they failed to detect this difference in the grounds of their convictions. Descartes thought it desirable for his readers to adopt this hypothesis provisionally: they would then realize the necessity of finding a secure ground for their certainty; when they

20 AT, VII, 460; HR, II, 266. 21 As in the following passage: "id quod dare percipitur, a quocunque demum

percipiatur, verum esse, non autem videri, aut apparere verum dumtaxat. Etsi pro- fecto pauci sint, qui recte distinguant inter id, quod revera percipitur, & id quod percipi putatur, quia pauci claris ac distinctis perceptionibus sunt assueti" (AT, VII, 511; HR, II, 307).




did find it, in the sort of evidence to be found in mathematics, they would demand certainty of this sort in all matters. The universal doubt personified in the Evil Genius was, to use the conventional term, methodic. To someone accustomed to the certainty of mathematical demonstrations it was groundless and hyperbolic. But, to someone satisfied with less, it was a reasonable hypothesis which, Des- cartes hoped, would incite a more discriminating attitude towards the grounds of his beliefs.

Thus the problem raised in the first meditation was not one of justifying reason, although Descartes sometimes suggested that it was in order to impress upon those who were precipitous and undiscrimi- nating in their judgments that their certainty was precarious. As indeed it was. It could be shaken by the facts of disagreement and mistake. What was really needed, as Gassendi suggested and Des- cartes agreed, was not a proof of God's existence. Instead, the problem was to find " a method for deciding whether we err or not when we think that we perceive something clearly." 22 Once this method was attained, all doubts concerning reason would be groundless. Mis- takes and disagreements could be easily explained. For

nothing whatsoever can be clearly and distinctly perceived, whoever be the person perceiving, that is not perceived to be such as it is. ... But because it is the wise alone who know how to distinguish rightly between what is so perceived, and what merely seems or appears to be clear and distinct, I am not surprised that our good friend mistakes the one for the other.23

The wise had no grounds for distrusting their reason; only the foolish need be misologists.

A second passage, from the Discourse, is more difficult to explain: If we did not know that everything which is true and real in us comes from a perfect and infinite Being, however clear and distinct our ideas might be, we should have no reason to assure us that they had the perfection of being true.24

This quotation seems to challenge, not just pre-critical certainty, but clear and distinct ideas themselves. The same challenge, ap- parently, was issued in Descartes' discussion of the relation of necessary truths to the will of God: God could have willed that the truths which seemed to him to be necessarily so should have been false, although how He could have willed this is beyond human com- prehension. None the less, He could have willed that equals added to

22 AT, VII, 361; HR, II, 214. 23AT, VII, 461-462; HR, II, 267. 24Part IV, AT, VI, 39; HR, I, 105.



334 WILLIS DONEY

equals should not yield equals or that the sum of the angles of a triangle should be greater than two right angles. It would seem that He could also have willed that there be clear and distinct ideas in the minds of His creatures which do not correspond to what in fact He willed to be the case. With this possibility in mind it would then seem necessary for Descartes to doubt and, impossible task, validate his clear and distinct ideas.

The difficulty about the possible perversity of God's will can be set aside for the time; and the question asked, does the passage from the Discourse by itself commit Descartes to this disastrous consequence? It does not if we distinguish, consistent with his intentions, (a) the general rule that all clear and distinct ideas are true, and (b) an assertion of the truth of a particular clear and distinct idea. In the passage quoted Descartes was referring to (a) and not to (b). This is clear from the context.25 He was denying that he could be certain of (a) prior to knowing God's existence, but he was not thereby denying that he could be certain of (b). From his writings on method it is quite clear that knowledge of a general rule or principle was not a necessary condition of knowledge of a particular statement derivable from the rule or principle.2 And in the Meditations it is clear that Descartes considered knowledge of this rule about all clear and distinct ideas posterior in the order of knowing to his assurance that a particular clear and distinct idea, the cogito, was true.

Even though knowledge that the rule was true was impossible before the proofs of God's existence, knowledge that a particular clear and distinct idea was true need not be. When he later came to know that all clear and distinct ideas were true, he then had reason (and the only possible reason) for claiming that any idea of this sort was true. The reason would be of a synthetic kind: 28 he could formally deduce

25 Several sentences before this: "Car, premierement, cela mesme que i'ai tantost pris pour une reigle, a scavoir que les choses que nous concevons trs clairement & tres distinctement, sont toutes vrayes, n'est assure qu'a cause que Dieu est ou existe, & qu'il est un estre parfait, & que tout ce qui est en nous vient de luy" (AT, VI, 38; HR, I, 105).

26 In reply to the second set of objections: " Ea enim est natura nostrae mentis, ut generales propositiones ex particularium cognitione efformet " (AT, VII, 140-141; HR, II, 38). 27The rule was introduced provisionally in the third meditation, prefaced by videor pro regula generali posse statuere (in the Discourse, by ie iugay que ie

pouvois prendre pour reigle generale) (AT, VII, 35, VI, 33; HR, I, 158, I, 102). It is proposed as an induction or generalization based on a genuine instance of certainty, derived from reflection on the knowledge of his own existence.

28 The distinction between analytic and synthetic reasoning is drawn in the reply to the second set of objections (AT, VII, 155-159; HIR, II, 48-51). This distinction




a statement about any or this clear and distinct perception from the universal statement expressing the rule. But, in reasoning of an analytic sort, such as he was recording in the Meditations, he could know the truth of the particular statement first, and he did not need to offer a further reason in support of this statement when the clear and distinct idea was present to his mind.

At least two objections can be raised against this account, however. First, why did Descartes consider the rule about all clear and distinct ideas necessarily provisional and uncertain before the proofs of God's existence? Since it was true, presumably it could be clearly and distinctly perceived to be so; and this clear and distinct perception, like any other, could be certain independently of knowledge of God. The answer cannot be, simply, that the rule was an induction universal in scope and that God's veracity was the justification of such an induction. For Descartes believed that other universal propositions could be known without this guarantee: e.g., the principle of causation used in the first two proofs of God's existence. The answer lies in another direction. On Descartes' view, although all clear and distinct ideas were true, not all true statements could be clearly and distinctly perceived to be so. Some of them could not be so perceived within the compass of a single intuition. The rule about all clear and distinct ideas was just such a statement. To know that any idea was true, this idea had to be present to his mind. To know that all were true, all of them would have had to be present at once. This was humanly impossible. Therefore, an assertion about the truth of all clear and distinct ideas was dependent on knowledge of God's veracity.

The second objection is the difficulty of explaining some of the statements made in the third meditation when the rule was proposed: "Certainly in this first knowledge there is nothing that assures me of its truth, excepting the clear and distinct perception of that which I state, which would not indeed suffice to assure me that what I say is true, if it could ever happen that a thing which I conceived so clearly and distinctly could be false .., "29 and, two paragraphs beyond, " ... if I find that there is a God, I must also inquire whether He may be a deceiver; for without a knowledge of these two truths I do not see that I can ever be certain of anything." 30 The second statement can be disposed of easily enough. In answer to the second set of objections Descartes explained one of the senses of certain used in the

forms the basis of Descartes' criticism of the Scholastic logic, which was synthetic or, to use a rough equivalent, formal.

29 AT, VII, 35; HR, I, 158. 30 AT, VII, 36; HR, I, 159.



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Meditations, a sense which seemed to have confused his critics. By certain he meant, roughly, incapable of being doubted at any time. Indeed nothing could be certain in this sense without knowledge of God. Any truth could be doubted while it was not being perceived. In another sense of certain, however, Descartes admitted that even an atheist could be certain of some things.

The first statement is less easily disposed of. In a simplified ver- sion it reads: if it could turn out that his present clear and distinct perception was false, then he did not know that it was true. The objection is that, at this stage of his argument, Descartes did not know that his perception could not turn out to be false and, therefore, he could not know that it was true. But this objection vanishes if we distinguish (a) the statement that his idea could not turn out to be false and (b) the statement that his idea could not be false. Although Descartes could not know (b) at the moment of the cogito, he could know (a). His conviction was " so strong that nothing could remove it ": so strong that he could imagine nothing which would show him that he was mistaken.31 In order to know that a present idea was true, he need only know (a) and did not have to know (b). There- fore, he could know that his idea was true even though he did not know that it could not be false. Actually, it could not be false. Even though eternal truths were in some way dependent on God's will, it would have been impossible for Him not to effect a correspondence between His creatures' clear and distinct ideas and what He had willed. Yet Descartes did not have to know this in order to know that his present idea was true.

(3) A last question: why did Descartes think of the Meditations as an argument proceeding from knowledge of his own existence to knowledge of God's existence and finally to absolute certainty in mathematics and natural philosophy? The first philosophy of the Meditations was presented as the foundations of these sciences. But how could this be if even an atheist could be absolutely certain of some mathematical truths so long as he clearly and distinctly perceived them and did not rely on his memory of having proved them? And in what way was metaphysics necessary for physics if an atheist, consulting his clear idea of extension, could know the nature of the

31 AT, VII, 145; HR, II, 41. Descartes gave a vivid description of this state of mind in the third meditation: " When I direct my attention to things which I believe myself to perceive very clearly, I am so persuaded of their truth that I let myself break out into words such as these: Let who will deceive me, He can never cause me to be nothing while I think that I am, or some day cause it to be true to say that I have never been, it being true now to say that I am ..." (HR, I, 158-159; AT, VII, 36).




material world as easily as Descartes. Finally, why was the cogito pre-requisite to his knowledge of God's existence when the latter was obvious on inspection of his idea of an infinitely perfect Being?

(a) The predicament of the atheist mathematician was such, according to Descartes, that he could not have absolute and immuta- ble knowledge of his science.32 He could know that the three angles of a triangle were equal to two right angles, however.33 But his knowledge of this truth would be fleeting, his knowledge of mathematics fragmentary and severely limited. In every demonstration he would have to start fresh from the axioms. Since this would be impossible in a long proof, he could know only those theorems of geometry near the beginning of Euclid's Elements; the rest would lie beyond his field of clear vision. Consequently, anything more than a meager and fugitive grasp of the subject depended on knowledge of God's existence. Lacking this, a mathematician would have no real certainty about mathematics considered as a body of true propositions.

Moreover, if an atheist were to reflect upon the grounds of his certainty, he would find reason in his atheism to doubt even his clear and distinct ideas; for " in proportion to the impotence assigned to the author of his being, the greater will be his reason for doubting whether he may not be of such an imperfect nature as to be deceived in matters which appear most evident to him ...." 34 Actually, the reason for his doubt would not be a good one. Yet, if he was inclined to accept reasons of this sort and failed to see the evidence for God's existence, he was in the same unfortunate state as those who could not distinguish a good reason from a bad one, or, in Cartesian terms, what was really clear and distinct from what only seemed so. The doubting atheist needed, not so much to be enlightened by a proof of God's existence, as to learn to tell what was really evident. Until he could do so, the foundation of his certainty about mathematical truths could be shaken by the skeptical arguments in the first meditation.

(b) The physicist needed a divine guarantee for his science as well, since, without it, he could not know that a material world existed. It might seem that he could be certain of this so long as he attended to Descartes' proof in the sixth meditation, just as he could be certain of the Pythagorean theorem while attending to its proof. The two cases were obviously different, however. God's existence was a necessary premise in the proof of a material world; whereas the proof of Pythagoras' theorem did not contain this premise. Not a single statement presupposing the existence of a material world could

32AT, VII, 428; HR, II, 245. 33AT, VII, 141; HR, II, 39. 34 AT, VII, 428; HR, II, 245.



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be known with certainty prior to knowledge of God. Necessary existence was not contained in the clear and distinct idea of extension. And, from the obscure and confused ideas of sense-perception, the existence of a material world could be proved only with the premise that God, who gave his creatures strong inclinations to believe that there were material things and provided them with no means for dis- covering that these inclinations were mistaken, existed and did not deceive.

There has been some confusion about this point. One explanation of the order of the Meditations is that knowledge of God's existence could be had by intuition, knowledge of the existence of a material world only by demonstration, and that demonstrations, but not intuitions, must be certified by God.35 Another suggestion is that the proof of a material world was longer and more involved than proof of God's existence and, presumably, would depend in part on memory, whereas the latter could be present to the mind all at once.36 Neither of these explanations will do, however. Even if the ontological proof derived from intuition and was not a demonstration, Descartes offered two demonstrations prior to this one. These would have to be considered logical blunders if the first explanation were accepted. Against both suggestions: there is no reason to believe that all demonstrations were questioned. Since the proof of the material world was not so much more difficult than the a posteriori proofs in the third meditation, it might have been mastered had it not contained the existence of God as a premise.

(c) The priority of the cogito can be easily explained. The first proof of God's existence was a posteriori from the existence of the idea of an infinite and perfect Being. Descartes would have to know that the effect existed in order to infer the cause. The second was an inference from the existence of res cogitans to God as the cause. And the ontological argument, although it was not a causal inference, presup- posed the existence of the idea of an infinitely perfect Being. Having resolved to take nothing for granted, Descartes would first have to know that this idea existed.

Ohio State University. 35 Koyre, op. cit., 59-61, 119-123. 36 Keeling, op. cit., 112.



Documents

Willis Doney. the Cartesian Circle