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The axioms of geometry, therefore, are neither synthetic a priori judgments nor experimental facts. They are conventions; our choice among all possib… - Henri Poincaré
" "The axioms of geometry, therefore, are neither synthetic a priori judgments nor experimental facts.
They are conventions; our choice among all possible conventions is guided by experimental facts; but it remains free and is limited only by the necessity of avoiding all contradiction. . . .
In other words, the axioms of geometry (I do not speak of those of arithmetic) are merely disguised definitions.
Then what are we to think of that question: Is the Euclidean geometry true?
It has no meaning.
As well ask whether the metric system is true and the old measures false.
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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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If... it be supposed that another way of measuring time is adopted... enunciation of the law would be... translated into another language... much less simple. So that the definition implicitly adopted by the astronomers may be summed up..: Time should be so defined that the equations of mechanics may be as simple as possible... [i.e.,] there is not one way of measuring time more true... only more convenient.
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(1) The rules applied are exceedingly various. (2) It is difficult to separate the qualitative problem of simultaneity from the quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether account must be taken of a velocity of transmission, as... of light, because such a velocity could not be measured without measuring a time.
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