Logic has borrowed, perhaps, the rules of geometry, without comprehending their force... it does not thence follow that they have entered into the spirit of geometry, and I should be greatly averse... to placing them on a level with that science that teaches the true method of directing reason.
One man will say a thing of himself without comprehending its excellence, in which another will discern a marvelous series of conclusions, which makes us affirm that it is no longer the same expression, and that he is no more indebted for it to the one from whom he has learned it, than a beautiful tree belongs to the one who cast the seed, without thinking of it, or knowing it, into the fruitful soil which caused its growth by its own fertility.
All who say the same things do not possess them in the same manner; and hence the incomparable author of the Art of Conversation pauses with so much care to make it understood that we must not judge of the capacity of a man by the excellence of a happy remark that we heard him make. ...let us penetrate, says he, the mind from which it proceeds... it will oftenest be seen that he will be made to disavow it on the spot, and will be drawn very far from this better thought in which he does not believe, to plunge himself into another, quite base and ridiculous.
If they have entered into the spirit if these rules, and if the rules have made sufficient impression on them to become rooted and established in their minds, they will feel how much difference there is between what is said here and what a few logicians may perhaps have written by chance approximating to it in a few passages of their works.
As to the objection that these rules are common in the world, that it is necessary to define every thing and to prove every thing, and that logicians themselves have placed them among their art, I would that the thing were true and that it were so well known... But so little is this the case, that, geometricians alone excepted, who are so few in number that they are a single in a whole nation and long periods of time, we see no others that know it.
It is necessary to show that there is nothing so little known [as the above rules], nothing more difficult to practice, or nothing more useful and universal.
These five rules [above] form all that is necessary to render proofs convincing, immutable, and to say all, geometrical; and the eight rules together render them even more perfect.
Rules necessary for demonstrations. To prove all propositions, and to employ nothing for their proof but axioms fully evident of themselves, or propositions already demonstrated or admitted; Never to take advantage of the ambiguity of terms by failing mentally to substitute definitions that restrict or explain them.
Rules necessary for definitions. Not to leave any terms at all obscure or ambiguous without definition; Not to employ in definitions any but terms perfectly known or already explained.
