Chapter 2b

The 4 Precepts Icon

January 31, 2022

Among the branches of philosophy, I had, at an earlier period, given some attention to

I was intersted in:

  • logic and mathematics
  • geometry
  • algebra

logic, its syllogisms and the majority of its other precepts are of avail – rather in the communication of what we already know, or even as the art of Lully, in speaking without judgment of things of which we are ignorant, than in the investigation of the unknown;

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.

By these considerations I was induced to seek some other method which would comprise the advantages of the three 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.

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

  2. 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.

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

The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only 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, and, considering that of all those who have hitherto sought truth in the sciences, the mathematicians alone have been able to find any demonstrations, that is, any certain and evident reasons, I did not doubt but that such must have been the rule of their investigations.

But I had no intention to master mathematics.

But I saw that 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.

Perceiving further, that in order to understand these relations I should sometimes have to consider them one by one and sometimes only to bear them in mind, or embrace them in the aggregate, I thought that, in order the better to consider them individually, I should view them as subsisting between straight lines, than which I could find no objects more simple, or capable of being more distinctly represented to my imagination and senses; and on the other hand, that 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 believed that I could borrow all that was best both in geometrical analysis and in algebra, and correct all the defects of the one by help of the other.

The accurate observance of these few precepts gave me, I take the liberty of saying, such ease in unravelling all the questions embraced in these two sciences, that in the two or three months I devoted to their examination, not only did I reach solutions of questions I had formerly deemed exceedingly difficult but even as regards questions of the solution of which I continued ignorant, I was enabled, as it appeared to me, to determine the means whereby, and the extent to which a solution was possible; results attributable to the circumstance that I commenced with the simplest and most general truths, and that thus 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, for example, who has been instructed in the elements of arithmetic, and has made a particular addition, according to rule, may be assured that he has found, with respect to the sum of the numbers before him, and that in this instance is within the reach of human genius. 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; and 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.

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