Descartes’ Method: A Philosophical and Mathematical Approach
1. Statement of Method
1.1 Precautions Before
But as a man who has to walk alone in the dark, I resolved to move as slowly and use as much restraint in all, which, in exchange for moving forward a bit, I would keep at least from a very bad trip and fall. And even I did not start completely rid of any of the opinions that may slip once in my beliefs, without having been introduced by reason, even after spending some time devoted to project work that was undertaken, looking for the real method to the knowledge of all things that my spirit was capable.
1.2. Origins of the Method
He had studied a bit, when I was younger, parts of philosophy, logic, and mathematics, the analysis of geometry and algebra, three arts or sciences which were, apparently, to contribute something to my purpose. But when I looked, I had to note that, in terms of logic, its syllogisms and most of the other rules that give more help to explain other things already known or even, as the art of Lully, for speaking without trial of the unknown, which to learn. And while it contains, indeed, many very good and true precepts, are, however, mingled with them, many other harmful or unnecessary, that separating them is almost as difficult as taking a Diana or a Minerva from a block of marble without grinding. Then, as regards the analysis of ancient and modern algebra, except that it does not relate to very abstract matters, which do not appear to be of any use, the first is always so constrained to consider the figures, which do not can exercise the understanding without greatly tiring the imagination, and second, whether its practitioners have been subjected to certain rules and certain figures, which have made it a confused and obscure art, good to mess with wit, rather than a science it cultivates.
1.3 Rules of the Method
Wherefore, I thought we had to find some other method to gather together the advantages of those three, excluding its flaws. And as the multitude of laws often serve very sorry to vices, being a State ruled much better when there are few, but very strictly observed, so, instead of the large number of provisions contained within the logic, I thought I would be sufficient the next four course to take a firm and constant resolution not stop watching them for once:
- It was the first to admit not as true anything, as obviously did not know as that is, carefully to avoid precipitation and prevention, and not understand anything in my judgments than what is presented so clearly and distinctly to my mind, not had any opportunity to put in doubt.
- Second, divide each of the difficulties, I will examine, in many parts wherever possible and in as many required his best solution.
- The third, to conduct my thoughts, starting with the simplest objects and easier to learn, to go slowly rising gradually to knowledge of the most compounds, even if an order among those who do not naturally precede.
- And finally, do all tallies so integral and some reviews so general, which were to be sure not to miss anything.
2. Application of the Method
2.1 Application to Mathematics
Those long chains of reasons are very simple and easy, which geometers usually use to get their most difficult demonstrations had given me occasion to imagine that all things that man can acquire knowledge, they follow each other in the same way and that, with only refrain from admitting the truth of one that is not always save and order necessary to deduct from each other, there can be none, for which it is located far away or hidden it is, it will not come to reach and discover.
And I became very tired in searching for what was necessary to start because I knew that for the most simple and easy to learn, and considering that, among all those who until now have investigated the truth in the sciences, mathematicians have only been able to find some shows, that is, some certain and evident reasons, no doubt that had to start the same as they have examined, even if they expect to get from here if no other purpose except my genius who get used to carefully consider the truth and not content with false reasons.
But not therefore conceived in order to attempt to learn all the particular sciences commonly denominated mathematics, and seeing that, though their objects are different, all, however, agree that it does not consider the various relations or proportions as found in such objects, I thought it was better to confine itself to examining these ratios generally give only those issues that serve to make me more easy to your knowledge and not subject to them in any way, then apply to the more freely to all others to may agree.
Then I realized that to know them, would sometimes need to consider each particular, and sometimes, just to retain or understand various boards, and I thought that to consider best in particular, should assume in line because there was nothing simpler and more distinctly that I could represent my imagination and senses, but to retain or understand various boards, it was necessary to explain that in some figures, the shorter it was possible, and that, by this means taking the best that is in geometric analysis and algebra, and corrected all defects and one for the other.
And indeed, I dare say that the exact observation of the chosen few precepts for me, I got it so easy to disentangle all the issues dealt with these two sciences, that in two or three months I spent in examining them, having begun the most simple and general, and since every truth that was a rule that I used then to find others not only managed to resolve several issues, which had previously considered too difficult, but even I thought also, towards the end, that even those that know, would determine by what means and how far it was possible to resolve them. In which, perhaps not excessive vanity accuse me if you consider that, provided that there is but one truth in everything, which is knows everything there is to know of it, and that, for example, a child who knows arithmetic and makes a sum according to the rules, you can be sure of having found, on examining the sum, everything that human ingenuity can find, because after all the method that teaches to follow the true order and retell exactly all the circumstances of what is sought, contains everything which gives certainty to the rules of arithmetic.
2.2 Application to Philosophy
But what made me happier in this method was that with him, was sure to use my reason at all, if not an entirely perfect, at least it better be in my possession. Moreover, I realized that the practice of my wits gradually accustomed himself to conceive a more clear and distinct objects and since he had not confined to any particular matter, I applied with equal utility promised to difficulties of other sciences as well as he had done with the algebra. Why not bring myself to start then examine all who presented, for that same is contrary to the prescribed method, but having noted that the principles of science had to be all taken from philosophy, in which even not find any that were true, I thought that it was first necessary to try to establish some of this kind and, this being the most important thing in the world and where they are more afraid of precipitation and prevention, I thought the company should not undertake before reaching a more mature age of twenty-three, who was then, and have spent a good amount of time to prepare, uprooting of my mind all the bad reviews that had input before that time, also making collection several experiences that were later the subject of my arguments and, finally, working out constantly in the method I had prescribed, to anchor better in my mind.