René Descartes

“ It is an indubitable conception formed by an unclouded mental mind; one that originates solely from the light of reason, and is more certain even than deduction, because it is simpler (though, as we have previously noted, deduction, too, cannot go wrong if it is a human being that performs it) . Thus, anybody can see by mental intuition that he himself exists, that he thinks, that a triangle is bounded by just three lines, and a globe by a single surface, and so on; there are far more of such truths than most people observe, because they disdain to turn their mind to such easy topics. ”

“ And yet we should not be surprised to find that plenty of people of their own accord prefer to apply their intelligence to other studies, or to Philosophy. The reason for this is that every person permits himself the liberty of making guesses in the matter of an obscure subject with more confidence than in one which is clear, and that it is much easier to have some vague notion about any subject, no matter what, than to arrive at the real truth about a single question however simple that may be. ”

“ Rule IX dealt only with intuition, and Rule X only with enumeration; then comes this Rule, explaining how these two activities cooperate-operate and supplement one another-seem, in fact, to merge into a single activity, in which there is a movement of thought such that attentive intuition of each point is simultaneous with transition to the next. I mention two advantages of this: the greater certainty in our knowledge of the conclusion we have in view, and the greater aptitude of our mind for making further discoveries. ”

“ From this we may gather that when propositions are direct conclusions from first principles, they may be said to be known by intuition or by deduction, according to different ways of looking at them; but first principles themselves may be said to be known only by intuition; and remote conclusions, on the other hand, only by deduction. These are the two most certain ways to knowledge; and on the side of the mind no more must be admitted; all others must be rejected as suspect and liable to mislead. ”

“ 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. ”

“ But whenever two men come to opposite decisions about the same matter one of them at least must certainly be in the wrong, and apparently there is not even one of them who knows; for if the reasoning of the second were sound and clear he would be able so to lay it before the other to succeed in convincing his understanding also. Hence apparently we cannot attain to a perfect knowledge in any such case of probable opinion, for it would be rashness to hope for more than others have attained to. ”

“ In ourselves there are just four faculties that can be used for knowledge: understanding, imagination, sense, and memory. Only the understanding is capable of perceiving truth, but it must be aided by imagination, sense, and memory, so that we may not leave anything undone that lies within our endeavor. ”

“ If we perfectly understand a problem we must abstract it from every superfluous conception, reduce it to its simplest terms and, by means of an enumeration, divide it up into the smallest possible parts. Rule XIV
The problem should be re-expressed in terms of the real extension of bodies and should be pictured in our imagination entirely by means of bare figures. Thus it will be perceived much more distinctly by our intellect. ”

“ This furnishes us with an evident explanation of the great superiority in certitude of arithmetic and Geometry to other sciences. The former alone deal with an object so pure and uncomplicated, that they need make no assumptions at all which experience renders uncertain, but wholly consist in the rational deduction of consequences. They are on that account much the easiest and clearest of all, and possess an object such as we require, for in them it is scarce humanly possible for anyone to err except by inadvertence. ”

“ For example: things that are the same as a single third thing are the same as one another; things that cannot be related in the same way to a third thing are in some respect diverse, etc. The understanding may know these common properties either by its own bare act, or by an intuition of images of material things. Further, among these simple natures I wish to count also privations or negations of them, in so far as we conceive of such; for my intuition of nothingness, an instant, or rest is not less genuine knowledge than my concept of existence, duration, or motion. ”

“ Thus they erroneously compare the sciences, which entirely consists in the cognitive exercise of the mind, with the arts, which depend upon an exercise and disposition of the body. They see that not all the arts can be acquired by the same man, but that he who restricts himself to one, most readily becomes the best executant, since it is not so easy for the same hand to adapt itself both to agricultural operations and to harp-playing, or to the performance of several such tasks as to one alone. ”

“ In order to make our knowledge complete, every single thing relating to our undertaking must be surveyed in a continuous and wholly uninterrupted sweep of thought, and be included in a sufficient and well-ordered enumeration. ”

“ Concerning objects proposed for study, we ought to investigate what we can clearly and evidently intuit or deduce with certainty, and not what other people have thought or what we ourselves conjecture. For knowledge can be attained in no other way. ”

“ The inference of one fact from several, which often has to be carried out, requires that we should discard any element in our ideas that does not need our attention at the moment, in order to make it easier to keep the remainder in our memory ”

“ As I said, when conclusions are too complex to be held in a single act of intuition, their certainty depends on memory; and since memory is perishable and weak, it must be revived and strengthened by this continuous and repeated movement of thought. For example, suppose I have learnt, in a number of successive mental acts, the relations between magnitudes 1 and 2, magnitudes 2 and 3, magnitudes 3 and 4, and, finally, magnitudes 4 and 5; this does not make me see the relation between magnitudes 1 and 5, nor can I deduce it from the ones I already know, unless I remember them all ”

“ My fifth and last supposition is that the power of cognition properly so called is purely spiritual, and is just as distinct from the body as a whole as blood is from bone or a hand from an eye; and that it is a single power. Sometimes it receives images from the common sensibility at the same time as the phantasy does ”

“ For we shall never be mathematicians, say, even if we retain in memory all the proofs others have given, unless we ourselves have the mental aptitude of solving any given problem; we shall never be philosophers, if we have read all the arguments of Plato and Aristotle but cannot form a solid judgment on matters set before us ”

“ It is of no small importance to observe this; for the chief reason why in the common philosophy there is nothing to be found whose certitude is so apparent as to be beyond controversy is that those who practice it have not begun by contenting themselves with the recognition of what is clear and certain, but have ventured on the further assertion of what was obscure and unknown and was arrived at only through probable conjectures. ”

“ In the first place, we must think differently when we regard things from the point of view of our knowledge and when we are talking about them as they are in reality. For example, take a body that has shape and extension. We shall admit that objectively there is one simple fact; we cannot call it, in this sense, ' a compound of the natures body, extension, and figure ', for these ' parts ' have never existed separate from one another. But in respect of our understanding we do call it a compound of these three natures ”

“ This, however, does not prevent our believing that divine revelation is more certain than any knowledge; for our faith in it, so far as it concerns obscure matters, is an act not of the mind but of the will ”

“ Further, memory (considered, that is, as a corporeal faculty like the recollections of brutes) is nothing distinct from imagination. From this it is a certain inference that if the understanding is occupied with objects that have no corporeal or quasi-corporeal aspect, it cannot be aided by these faculties; on the contrary, we must prevent it from being hindered by them; sense must be banished, and imagination stripped (so far as possible) of every distinct impression. ”

“ In order to acquire discernment we should exercise our intelligence by investigating what others have already discovered, and methodically survey even the most insignificant products of human skill, especially those which display or presuppose order. ”

“ The aim of our studies should be to direct the mind with a view to forming true and sound judgements about whatever comes before it. Whenever men notice some similarity between two things, they are wont to ascribe to each, even in those respects in which the two differ, what they have found to be true of the other. ”

“ 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. ”

“ Seventhly, this 'compounding' may take place in three ways; on impulse, or from conjecture, or by deduction. People compound their judgments about things 'on impulse' when their own mind' leads them to believe something without their being convinced by any reasoning; they are determined to do so either by a higher power, or by their own spontaneity, or by the disposition of the phantasy; the first never misleads, the second rarely, the third almost always. But the first does not concern us here, since it is not something attainable by our technique. ”

“ 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. ”