A Ther Und Relativitts Theorie Geometrie Und Erfahrung L Englisch
A Ther Und Relativitts Theorie Geometrie Und Erfahrung L Englisch
Einstein Albert
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These entitiesdo not take for granted any knowledge or intuition whatever, butthey presuppose only the validity of the axioms, such as the onestated above, which are to be taken in a purely formal sense, i. E. As void of all content of intuition or experience. These axioms arefree creations of the human mind. All other propositions of geometryare logical inferences from the axioms (which are to be taken inthe nominalistic sense only). The matter of which geometry treatsis first defined by the a...xioms. Schlick in his book on epistemology hastherefore characterised axioms very aptly as "implicit definitions. " This view of axioms, advocated by modern axiomatics, purges mathematicsof all extraneous elements, and thus dispels the mystic obscuritywhich formerly surrounded the principles of mathematics. But a presentation of its principles thus clarified makes it alsoevident that mathematics as such cannot predicate anything aboutperceptual objects or real objects. In axiomatic geometry the words"point, " "straight line, " etc.
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