Gaukroger, Stephen (1992). Descartes's Early Doctrine of Clear and Distinct Ideas. Journal of the History of Ideas 53 (4):585-602.
Intuitus and the Doctrine of Clear and Distinct Ideas in the Early Regulae
Our first concern will be with the early Rules, dating from around 1620. Having established the unity of knowledge in Rule 1, Descartes sets out in Rule 2 the reasons we need a method if we are to succeed in our inquiries; and he holds up the mathematical sciences as models in virtue of the certainty of their results. Rules 3 and 4 then set out the two operations on which that method relies, namely, intuition and deduction. Rules 5, 6, and 7 provide details of how we are actually to proceed on this basis, and Rules 8 to 11 elaborate on specific points. The central topics here are the doctrines of intuition (intuitus) and deduction, and it is in these that the novelty of Descartes's account resides.
"Deduction" is a notoriously slippery term in Descartes. Desmond Clarke has drawn attention to contexts in which it is used to mean explana tion, proof, induction, or justification; and on occasion it seems to do little more than describe the narration of an argument.3 In Rule 2 Descartes makes a claim about deduction which at first makes one wonder just how he is using the term. He writes:
There are two ways of arriving at a knowledge of things, through experience and through deduction. Moreover, we must note that while our experiences of things are often deceptive, the deduction or pure inference of one thing from another can never be performed wrongly by an intellect which is in the least degree rational though we may fail to make the inference if we do not see it. Those chains by which dialecticians hope to regulate human reason seem to me to be of little use here, though I do not deny that they are useful for other purposes. In fact, none of the errors to which men-men, I say, not brutes-are liable is ever due to faulty inference. They are due only to the fact that men take for granted certain poorly understood experiences, or lay down rash or groundless judgements.4
But to maintain that we can never make a mistake in deductive inference is nonetheless a remarkable claim. In order to find out precisely what he means, it is worth asking what precisely he is rejecting. What are the "chains" by which the "dialecticians" hope to regulate inference? These are presumably the rules governing syllogistic, those rules that specify which inference patterns are (formally) valid. The problem is to determine what it is that Descartes finds objectionable in such rules.
The claim is certainly not that these rules are wrong and that others must be substituted for them, that new "chains" must replace the old ones. Rather, the question hinges on the role that one sees these rules as having, since Descartes admits that they may "be useful for other purposes." What he is rejecting is their use as rules of reasoning, as something one needs to be familiar with in order to reason properly. If one looks at the logical texts with which we know him to have been familiar, above all those of Toletus and Fonseca, then we can identify the culprit with some degree of certainty: the Jesuit account of "directions for thinking" (directio inge nii).
The Jesuit account of logic which Descartes learned at La Flech was one in which logic or dialectic was construed above all as a psychologi cal process which required regulation if it was to function properly.5 In the light of this, one thing that we can take Descartes to be denying is that mental processes require external regulation, that rules to guide our thought are needed.
This is an important point, for it is often implicitly assumed that the provision of such rules is just what Descartes is trying to achieve in the Regulae. But this cannot be their aim. Descartes's view is that inference is something which we, as rational creatures, perform naturally and cor rectly. What then do the "rules for the direction of our native intelligence" do that is different from what the old rules of dialectic did? Well, the difference seems to lie not so much in what the rules do as in what they rely upon to do it. In Descartes's view syllogistics relies on rules imposed from outside, whereas his rules are designed to capture an internal process which operates with a criterion of truth and falsity that is beyond question. This is that we accept as true all and only that of which we have a "clear and distinct" perception. But the elaboration of this principle is largely confined to the discussion of "intuition," and with good reason, for it soon becomes clear that deduction reduces, in the limiting case, to intuition
Towards the end of Rule 3 Descartes tells us that "the self-evidence and certainty of intuition is required not only for apprehending single propositions but also for deduction, since in the inference 2 + 2 = 3 + 1, we must not only "intuitively perceive that 2 plus 2 make 4 and that 3 plus 1 make 4 but also that the original proposition follows from the other two." Here the first two perceptions are intuitions, whereas seeing the connection between them is a deduction. But the deduction seems in all important respects to be simply an intuition, albeit an intuition whose content is a relation between other intuitions. This clearly raises the question of the difference between an intuition and a deduction, and so Descartes sets out why he believes it necessary to distinguish deduction from intuition at all.
Hence we are distinguishing mental intuition from certain deductions on the grounds that we are aware of a movement or a sort of sequence in the latter bu
There may be some doubt here about our reason for suggesting another mode of knowing in addition to intuition, viz. deduction, by which we mean the inference of something as following necessarily from some other propositions which are known with certainty. But this distinction had to be made, since very many facts which are not self-evident are known with certainty, provided they are inferred from true and known principles through a continuous and uninterrupted movement of thought in which each individual proposition is clearly intuited. This is similar to the way in which we know that the last link in a long chain is connected to the first: even if we cannot take in at one 3 70 glance all the intermediate links on which the connection depends, we can. have knowledge of the connection provided we survey the links one after the other, and keep in mind that each link from first to last is attached to its neighbour. Hence we are distinguishing mental intuition from certain deduction on the grounds that we are aware of a movement or a sort of sequence in the latter but not in the former, and also because immediate self-evidence is not required for deduction, as it is for intuition; deduction in a sense gets its certainty from memory. It follows 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.
This is rather puzzling, given Descartes's example. Memory in any genu ine sense would seem to play no real role in the deduction from 2 + 2 = 4 and 3 + 1 = 4 that 2 + 2 = 3 + 1. Why does he specify that remote consequences are known only through deduction? Could it be that the consequence in the example, which is far from being remote, is known not by deduction but by intuition? No: it is the example that Descartes himself gives of a deduction, and the only example at that. He seems concerned above all to restrict intuition to an absolutely instantaneous act, so that if there is any temporal interval of any kind, no matter how brief, we are dealing with deduction rather than intuition. But this is the only difference; and even this difference is undermined in Rule 7, where Descartes elaborates on the question of how to make sure that deductions are reliable.
It is necessary to observe the points proposed in this Rule if we are to admit as certain those truths which, we said above, are not deduced immediately from first and self-evident principles. For this deduction sometimes requires such a long chain of inferences that when we arrive at such a truth it is not easy to recall the entire route which led us to it. That is why we say that a continuous movement of thought is needed to make good any weakness of memory. If, for example, by way of separate operations, I have come to know first what the relation between the magnitudes A and B is, and then between B and C, and between C and D, and finally between D and E, that does not entail my seeing what the relation is between A and E; and I cannot grasp what the relation is just 388 from those I already know, unless I recall all of them. So I shall run through them several times in a continuous movement of the imagina tion, 'simultaneously intuiting one relation and passing on to the next, until I have learnt to pass from the first to the last so swiftly that memory is left with practically no role to play, and I seem to intuit the whole thing at once. In this way our memory is relieved, the sluggishness of our intelligence redressed, and its capacity in some way enlarged.
In short, the more it approaches intuition, the more reliable deduction is. It is hard to avoid the conclusion that deduction is ultimately modelled on intuition and that in the limiting case becomes intuition.