The 4 Precepts of Descartes

Among the branches of philosophy, I had earlier given some attention to:

• logic and mathematics
• geometry
• algebra

Logic has very excellent precepts. But it also has many injurious or superfluous ones mixed in. It is as difficult to seperate the true from the false.

The ancients had analysis. The moderns have algebra. Both embrace only matters highly abstract, and, to appearance, of no use.

• The ancient analysis is restricted to the consideration of shapes. It can exercise the understanding by greatly fatiguing the imagination.
• Modern algebra has so many certain rules and formulas that it is full of confusion and obscurity that embarrasses instead of cultivating the mind.

I had to find some other method which would:

• have the advantages of the 3 and
• be exempt from their defects.

A multitude of laws often only hampers justice. Likewise, a state is best governed when, with few laws, these are rigidly administered.

Similarly, instead of having many precepts of logic, I use 4 precepts:

1. Never accept anything for true which I did not clearly know to be such

Carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.

2. Divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.

3. Conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little to the knowledge of the more complex;

assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.

4. Make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.

Geometericians use long chains of simple and easy reasonings in order to reach the conclusions of their most difficult demonstrations.

This had led me to believe that:

• all things, which humans know, are mutually connected in the same way
• there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, as long as we:
  • abstain from accepting the false for the true, and
  • always preserve in our thoughts the order necessary for the deduction of one truth from another.

I had little difficulty in determining the objects with which it was necessary to commence, for I was already persuaded that it must be with the simplest and easiest to know.

Of all those who have previously sought truth in the sciences, only the mathematicians have been able to find any demonstrations, that is, any certain and evident reasons.

Such must have been the rule of their investigations.

But I had no intention to master mathematics.

All of math agrees in considering only the various relations or proportions in mathematical objects.

And so I thought of these proportions in the most general form.

This would let me better apply them to every other class of objects to which they are legitimately applicable.

In order to understand these relations, I would consider them:

• one by one or
• embrace them in the aggregate.

In order the better to consider them individually, I should view them as subsisting between straight lines.

Straight lines are the most simple objects, most capable of being more distinctly represented to my imagination and senses.

In order to retain them in the memory or embrace an aggregate of many, I should express them by certain characters the briefest possible.

In this way, I could:

• borrow all that was best both in geometrical analysis and in algebra
• correct all the defects of the one by help of the other.

The accurate observance of these few precepts gave me such ease in unravelling all the questions embraced in these 2 sciences, that in the 2-3 months I examined them, I reached solutions to:

• questions I had formerly deemed exceedingly difficult
• questions of which I continued ignorant

This allowed me to determine how a solution was possible. This is the result of me using the simplest and most general truths. Each truth discovered was a rule available in the discovery of subsequent ones Nor in this perhaps shall I appear too vain, if it be considered that, as the truth on any particular point is one whoever apprehends the truth, knows all that on that point can be known.

The child who has been instructed in arithmetic, and added something, arrives at a sum that is the same sum that a genius would arrive at.

Now, in conclusion, the method which teaches adherence to the true order, and an exact enumeration of all the conditions of the thing sought includes all that gives certitude to the rules of arithmetic.

But the chief ground of my satisfaction with thus method, was the assurance I had of thereby exercising my reason in all matters, if not with absolute perfection, at least with the greatest attainable by me= besides, I was conscious that by its use my mind was becoming gradually habituated to clearer and more distinct conceptions of its objects;

I hoped also, from not having restricted this method to any particular matter, to apply it to the difficulties of the other sciences, with not less success than to those of algebra.

I should not, however, on this account have ventured at once on the examination of all the difficulties of the sciences which presented themselves to me, for this would have been contrary to the order prescribed in the method, but observing that the knowledge of such is dependent on principles borrowed from philosophy, in which I found nothing certain, I thought it necessary first of all to endeavour to establish its principles.

This inquiry was of the greatest importance and the most dreaded when I was 23 years old. I thought that I should be older before I pursued it.