“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.”

— Blaise Pascal

The Art of Persuasion

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Blaise Pascal 144

French mathematician, physicist, inventor, writer, and Chri… 1623–1662

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“Dilettantes have not achieved anything lasting even in the applied arts. But they have rendered some service to the highest of all disciplines: philosophy. Montaigne, La Rochefoucauld, Vauvenargues are proof of this.”

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Dilettanten haben nicht einmal in einer sekundären Kunst etwas Bleibendes geleistet, sich aber verdient gemacht um die höchste aller Wissenschaften, die Philosophie. Den Beweis dafür liefern: Montaigne, La Rochefoucauld, Vauvenargues.
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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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“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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“The rule is perfect: in all matters of opinion our adversaries are insane.”

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Christian Science (1907)
Context: When I, a thoughtful and unblessed Presbyterian, examine the Koran, I know that beyond any question every Mohammedan is insane; not in all things, but in religious matters. When a thoughtful and unblessed Mohammedan examines the Westminster Catechism, he knows that beyond any question I am spiritually insane. I cannot prove to him that he is insane, because you never can prove anything to a lunatic — for that is a part of his insanity and the evidence of it. He cannot prove to me that I am insane, for my mind has the same defect that afflicts his. All Democrats are insane, but not one of them knows it; none but the Republicans and Mugwumps know it. All the Republicans are insane, but only the Democrats and Mugwumps can perceive it. The rule is perfect: in all matters of opinion our adversaries are insane.

“The subject matter of mathematics is the expressions themselves together with the rules for manipulating them—nothing more.”

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[Nelson, E., Predicative Arithmetic, 1986, Princeton University Press, Princeton, 0-691-08455-6, https://books.google.co.uk/books?id=pvr_AwAAQBAJ&printsec=frontcover#v=onepage&q&f=false, 86018730, 14001745, 173, harv]

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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.”

Blaise Pascal (1623–1662) French mathematician, physicist, inventor, writer, and Christian philosopher

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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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Blaise Pascal 144

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