Descartes - Rules For The Direction of The Mind
Philosophy from Descartes

RULE VII

In order to complete our knowledge we must scrutinize all the several points pertinent to our aim, in a continuous and uninterrupted movement of thought, And comprise them all in an adequate and orderly enumeration.

The observance of these precepts is necessary in order that we may admit to the class of certitudes those truths which, I previously said, are not immediate deductions from the first self-evident principles. For sometimes the succession of inferences is so long that when we arrive at our results we do not readily remember the whole road that has led us so far; and therefore I say that we must aid the weakness of our memory by a continuous movement of thought.

For instance, suppose that by excessive mental acts I have learnt first the relation between the magnitudes A and B, then that between B and C then that between C and D, and finally that between D and E; I do not on this account see the relation between A and E; and I cannot form a precise conception of it from the relations I know already, unless I remember them all. So I will run through these several times over in a continuous movement of the imagination, in which intuition of each relation is simultaneous with transition to the next, until I have learnt to pass from the first to the last so quickly that I leave hardly any parts to the care of memory and seem to have a simultaneous intuition of the whole. In this way memory is aided, and a remedy found for the slowness of the understanding, whose scope is in a way enlarged.

I add that the movement must be uninterrupted because it often happens that people who try to make some deduction in too great haste and from remote principles do not run over the whole chain of intermediate conclusions with sufficient care to avoid making many unconsidered jumps. But assuredly the least oversight immediately breaks the chain and destroys all the certainty of the conclusion. Further, I say that enumeration is required in order to complete our knowledge. For other precepts are helpful in resolving very many questions, but it is only enumeration that enables us to form a true and certain judgment about anything whatever that we apply our mind to, and, by preventing anything from simply escaping our notice, seems to give us some knowledge of everything.

This enumeration, or induction, ranging over everything relevant to some question we have set before us, consists in an inquiry so careful and accurate that it is a certain and evident conclusion that no mistaken omission has been made. When, therefore, we perform this, if the thing we are looking for still eludes us, we are at any rate so much the wiser, that we can see with certainty the impossibility of our finding it by any way known to us; and if we have managed to run over all the ways of attaining it that are humanly practicable (as will often be the case) then we may boldly affirm that knowledge of it has been put quite out of reach of the human mind.

It must further be observed that by adequate enumeration or induction I mean exclusively the sort that makes the truth of conclusions more certain than any other type of proof, apart from simple intuition, makes it. Whenever a piece of knowledge cannot be reduced to simple intuition (if we throw off the fetters of syllogism), this method is the only one left to us that we must entirely rely on. For whenever we have deduced one thing from others, if the inference was an evident one, the case is already reduced to genuine intuition. If on the other hand, we make a single inference from many separate data, our understanding is often not capacious enough to grasp them all in one act of intuition, and in that case we must content ourselves with the certitude of this further operation. Inthe same way, we cannot visually distinguish all the links of a longish chain in one glance (intuitu); but nevertheless, if we have seen the connexion of each with the next, this will justify us in saying that we have actually seen how the first is connected to the last.

I said this operation must be adequate, because it may often be defective, and consequently liable to error. For sometimes our enumeration includes a number of very obvious points; nevertheless, the least omission breaks the chain and destroys all the certainty of the conclusion. Again, sometimes our enumeration covers everything but the items are not all distinguished, so that we have only a confused knowledge of the whole.
Sometimes, then, this enumeration must be complete, and sometimes it must be distinct; but sometimes neither condition is necessary., This is why I say merely that the enumeration must be adequate. For example, if I want to establish by enumeration how many kinds of things are corporeal, or are in some way the objects of sensation, I shall not assert that there are just so many without first assuring myself that my enumeration comprises all the kinds and distinguishes each from the others. But if I want to show in the same way that the rational soul is not corporeal, a complete enumeration will not be needed; it will be enough to comprise all bodies in a certain number of classes and show that the rational soul cannot be referred to any of these. Again, if I want to show by enumeration that the area of a circle is greater than the areas of all other figures of equal periphery, I need not give a list of all figures; it is enough to prove this in some particular cases, and then we may inductively extend the conclusion to all other figures.

I added further that the enumeration must be orderly for the defects already enumerated cannot be remedied more directly than they are by an orderly scrutiny of all items. Again, it is often the case that nobody could live long enough to go through each several item that concerns the matter in hand; either because there are too many such items, or because we should keep going back to the same items. But if we arrange these items in the ideal order, then as a rule they will be reduced to certain classes; and it may be enough to have an exact view of one class, or of some member of each class, or of some classes rather than others; at any rate, we shall not ever go futilely over and over the same point. This is a great help; a proper arrangement often enables us to deal rapidly and easily with an apparently unmanageable multitude of details.

This order of enumeration is variable, and depends on the free choice of the individual; skill in devising it requires that we bear in mind the terms of Rule V. There are, indeed, a good many ingenious, trivialities where the device wholly consists in effecting this sort of arrangement. For example, suppose you want to make the best anagram you can by transposing the letters of a certain name. Here there is no need to advance from easy to difficult cases, or to distinguish between what is underived and what is dependent; for these problems do not arise here. It will be enough to determine an order for examining transpositions of letters, so that you never go over the same arrangement twice over, and to divide the possible arrangements into certain classes in a way that makes the most likely source of a solution immediately apparent. The task will then often be no long one-child's play, in fact.

Really, though, these last three Rules are inseparable; in most cases they have all to be taken into account at once, and they all go together towards the completeness of the method. The order of setting them forth did not much matter; I have explained them here briefly because almost all the rest of this treatise will be a detailed exposition of what is here summed up in a general way.