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These eight rules [above] contain all the precepts for solid and immutable proofs.
Blaise Pascal
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Those who make antitheses by forcing the sense are like men who make false windows for the sake of symmetry. Their rule is not to speak justly, but to make accurate figures.
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That queen, of error, whom we call fancy and opinion, is the more deceitful because she does not always deceive. She would be the infallible rule of truth if she were the infallible rule of falsehood; but being only most frequently in error, she gives no evidence of her real quality, for she marks with the same character both that which is true and that which is false.
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When we see an effect happen always in the same manner, we infer that it takes place by a natural necessity; as, for instance, that the sun will rise to morrow; but nature often deceives us, and will not submit to its own rules.
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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.
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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.
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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.
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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.
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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.
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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.
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Five [of the above] rules are of absolute necessity, and cannot be dispensed with without essential defect and often without error.
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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.
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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.
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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.
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One must know oneself. If this does not serve to discover truth, it at least serves as a rule of life, and there is nothing better.
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I make no doubt... that these rules are simple, artless, and natural.
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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.
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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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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.
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It is not your strength and your natural power that subjects all these people to you. Do not pretend then to rule them by force or to treat them with harshness. Satisfy their reasonable desires; alleviate their necessities; let your pleasure consist in being beneficent; advance them as much as you can, and you will act like the true king of desire.
Blaise Pascal
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No written law has ever been more binding than unwritten custom supported by popular opinion.
Carrie Chapman Catt
Blaise Pascal
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Born:
June 19, 1623
Died:
August 19, 1662
(aged 39)
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