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.
Blaise Pascal
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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.
Blaise Pascal
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.
Blaise Pascal
We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
Hans Reichenbach
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
If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. ...Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.
Hans Reichenbach
Pascal, Blaise
Passeroni, Giancarlo
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