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A demonstration really based upon the principles of Analytical Logic will be composed of a succession of propositions ; some, which will serve as pre… - Henri Poincaré
" "A demonstration really based upon the principles of Analytical Logic will be composed of a succession of propositions ; some, which will serve as premises, will be identities or definitions ; others will be deduced from the former step by step ; but although the connexion between each proposition and the succeeding proposition can be grasped immediately, it is not obvious at a glance how it has been possible to pass from the first to the last, which we may be tempted to look upon as a new truth. But if we replace successively the various expressions that are used by their definitions, and if we pursue this operation to the furthest possible limit, there will be nothing left at the end but identities, so that all will be reduced to one immense tautology. Logic therefore remains barren, unless it is fertilized by intuition.
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About Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912), generally known as Henri Poincaré, was one of France's greatest mathematicians and theoretical physicists, and a philosopher of science.
Biography information from Wikiquote
Also Known As
Alternative Names:
Jules Henri Poincare
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Henri Poincare
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Poincare
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Jules Henri Poincaré
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Poincaré
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Additional quotes by Henri Poincaré
Le savant doit ordonner ; on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison.
The Scientist must set in order. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
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The continuum so conceived is only a collection of individuals ranged in a certain order, infinite to one another, it is true, but exterior to one another. This is not the ordinary conception, wherein is supposed between the elements of the continuum a sort of intimate bond which makes of them a whole, where the point does not exist before the line, but the line before the point. Of the celebrated formula “the continuum is unity in multiplicity”, only the multiplicity remains, the unity has disappeared. The analysts are none the less right in defining the continuum as they do, for they always reason on just this as soon as they pique themselves on their rigor. But this is enough to apprise us that the veritable mathematical continuum is a very different thing from that of the physicists and the metaphysicians.
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