The rules to be observed in the search for truth

Making the mind more attentive and more extensive are the only ways that can make it more perfect, more enlightened and more penetrating.

the rules that it is absolutely necessary to observe in the resolution of all questions.

I shall dwell on this at length, and I shall try to explain it well through several examples, in order to make its necessity better known, and to accustom the mind to put them into practice, because the most necessary and most difficult thing is not to know them well, but to practice them well.

One must not expect here to have something very extraordinary, which surprises and greatly engages the mind; on the contrary, in order for these rules to be good, they must be simple and natural, few in number, very intelligible and dependent on one another; in a word, they must only guide our mind and regulate our attention without dividing it, for experience makes it sufficiently known that Aristotle’s logic is not of great use, because it occupies the mind too much, and diverts it from the attention it should bring to the subjects it examines.

Let those therefore who love only mysteries and extraordinary inventions put aside for a while this bizarre humor, and let them bring all the attention of which they are capable, in order to examine whether the rules that are about to be given suffice to always preserve evidence in the perceptions of the mind and to discover the most hidden truths. If they do not unjustly preoccupy themselves against the simplicity and ease of these rules, I hope they will recognize through the use that we will show in the following that one can make of them, that the clearest and simplest principles are the most fruitful, and that extraordinary and difficult things are not always as useful as our vain curiosity leads us to believe.

The principle of all these rules is that one must always preserve evidence in one’s reasoning in order to discover truth without fear of being mistaken. From this principle depends this general rule concerning the subject of our studies, namely: that we should reason only about things of which we have clear ideas; and, as a necessary consequence, that we must always begin with the simplest and easiest things, and dwell on them for a long time before undertaking the investigation of the more composite and more difficult ones.

The rules concerning the manner in which one must proceed to resolve questions also depend on this same principle, and the first of these rules is: that one must conceive very distinctly the state of the question that one proposes to resolve, and have ideas of its terms sufficiently distinct to be able to compare them, and thus to recognize the relations that one seeks.

But when one cannot recognize the relations that things have between them by comparing them immediately, the second rule is: that one must discover, by some effort of mind, one or several intermediary ideas that can serve as a common measure to recognize by their means the relations that exist between them. It must be inviolably observed that these ideas be clear and distinct in proportion as one tries to discover more exact relations and in greater number.

But when the questions are difficult and of long discussion, the third rule is: that one must carefully remove from the subject that one must consider all the things that are not necessary to examine in order to discover the truth that one seeks. For one must not uselessly divide the capacity of the mind, and all its force must be employed solely on the things that can enlighten it. The things that can thus be removed are all those that do not touch the question, and which being removed, the question subsists in its entirety.

When the question is thus reduced to the least terms, the fourth rule is: that one must divide the subject of one’s meditation into parts, and consider them all one after another according to natural order, beginning with the simplest, that is to say, with those that contain fewer relations, and never pass to the more composite before having distinctly recognized the simpler ones, and having made them familiar.

When these things have become familiar through meditation, the fifth rule is: that one must abridge their ideas and then arrange them in one’s imagination, or write them on paper, so that they no longer fill the capacity of the mind. Although this rule is always useful, it is absolutely necessary only in very difficult questions that require a great extent of mind, because one extends the mind only by abridging one’s ideas. The use of this rule and of those that follow is well recognized only in algebra.

The ideas of all the things that it is absolutely necessary to consider being clear, familiar, abridged and arranged in order in the imagination or expressed on paper, the sixth rule is: that one must compare them all according to the rules of combinations, alternately with one another, either by the sole view of the mind, or by the movement of the imagination accompanied by the view of the mind, or by the calculation of the pen joined to the attention of the mind and the imagination.

If, among all the relations that result from all these comparisons, there is none that is the one that one seeks, one must again remove from all these relations those that are useless to the resolution of the question; make the others familiar, abridge them and arrange them in order in one’s imagination, or express them on paper; compare them together according to the rules of combinations, and see whether the composite relation that one seeks is one of all the composite relations that result from these new comparisons.

If there is not one of these relations that one has discovered which contains the resolution of the question, one must from all these relations remove the useless ones, make the others familiar, etc… And by continuing in this manner, one will discover the truth or the relation that one seeks, however composite it may be, provided that one can sufficiently extend the capacity of the mind by abridging its ideas, and that in all these operations one always has in view the term towards which one must tend. For it is the continual view of the question that must regulate all the steps of the mind, since one must always know where one is going.

One must especially take care not to be satisfied with some glimmer or some verisimilitude, and to recommence as often as necessary the comparisons that serve to discover the truth that one seeks, until one cannot help but believe it, without feeling the secret reproaches of the master who responds to our demand—I mean to our work, to the application of our mind and to the desires of our heart. And then this truth can serve us as an infallible principle for advancing in the sciences.

All these rules that we have just given are not generally necessary in all kinds of questions; for when the questions are very easy, the first rule suffices; one needs only the first and the second in some other questions. In a word, since one must make use of these rules until one has discovered the truth that one seeks, it is necessary to practice them all the more as the questions are more difficult.

These rules are not numerous. They all depend on one another. They are natural, and one can make them so familiar that it will not be necessary to think much about them at the time one wishes to use them. In a word, they can regulate the attention of the mind without dividing it—that is to say, they possess part of what one desires. But they appear so little considerable in themselves that it is necessary, in order to make them recommendable, that I show that philosophers have fallen into a very great number of errors and extravagances, because they have not even observed the first two, which are the easiest and the principal ones, and that it is also by the use that M. Descartes made of them that he discovered all those great and fruitful truths that one can learn in his works.