A science can be in a highly advanced state, even though its logical foundations are far from being clarified. Mechanics, for example, reached a stage of astounding perfection by the end of the 18th century, mainly through the genius of Galileo and Newton, although much room was left for controversy about the meanings of its fundamental concepts: length, simultaneity, mass, and force. Even the meaning of the simple law of inertia remained controversial right up to Einstein’s “unification” of inertia and gravitation. Similarly, mathematics was not prevented from reaching breathtaking heights of perfection by the Grundlagenstreit (dispute about foundations) which began in the 19th century and still continues.
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KEUPINK, A., SHIEH, S. (2006). MATHEMATICS, ABSTRACT ENTITIES, AND MODERN SEMANTICS (1957). In: KEUPINK, A., SHIEH, S. (eds) THE LIMITS OF LOGICAL EMPIRICISM. SYNTHESE LIBRARY, vol 334. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4299-X_13
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