
One of the principal reasons that diverts those who are entering upon this knowledge so much from the true path which they should follow, is the fancy that they take at the outset that good things are inaccessible, giving them the name great, lofty, elevated, sublime. This destroys everything. I would call them low, common, familiar: these names suit it better; I hate such inflated expressions.
The mind must not be forced; artificial and constrained manners fill it with foolish presumption, through unnatural elevation and vain and ridiculous inflation, instead of solid and vigorous nutriment.
I make no doubt... that these rules are simple, artless, and natural.
The best books are those, which those who read them believe they themselves could have written.
It is not among extraordinary and fantastic things that excellence is to be found, of whatever kind it may be. We rise to attain it and become removed from it: it is oftenest necessary to stoop for it.
Nature, which alone is good, is wholly familiar and common.
The method of not erring is sought by all the world. The logicians profess to guide it, the geometricians alone attain it, and apart from science, and the imitations of it, there are no true demonstrations.
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.
Nothing is more common than good things: the point in question is only to discriminate them; and it is certain that they are all natural and within our reach and even known to all mankind.
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.
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.
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.
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.
Rules necessary for axioms. Not to demand in axioms any but things perfectly evident.
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.
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.
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.
The principles of pleasure are not firm and stable. They are different in all mankind, and variable in every particular with such a diversity that there is no man more different from another than from himself at different times.
There are hardly any truths upon which we always remain agreed, and still fewer objects of pleasure which we do not change every hour, I do not know whether there is a means of giving fixed rules for adapting discourse to the inconstancy of our caprices.
This art, which I call the art of persuading, and which, properly speaking, is simply the process of perfect methodical proofs, consists of three essential parts: of defining the terms of which we should avail ourselves by clear definitions, of proposing principles of evident axioms to prove the thing in question; and of always mentally substituting in the demonstrations the definition in the place of the thing defined.
If we do not secure the foundation, we cannot secure the edifice.
A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the art of persuading.
Rules for Definitions. I. Not to undertake to define any of the things so well known of themselves that the clearer terms cannot be had to explain them. II. Not to leave any terms that are at all obscure or ambiguous without definition. III. Not to employ in the definition of terms any words but such as are perfectly known or already explained.
Rules for Axioms. I. Not to omit any necessary principle without asking whether it is admittied, however clear and evident it may be. II. Not to demand, in axioms, any but things that are perfectly evident in themselves.
Rules for Demonstrations. I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it. II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated. III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions.
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