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Logic depends upon mathematics. ...[I]ntuitive logical reasoning ...remains if ...one restricts oneself to relations of whole and part; the mathematical structures ...do not justify any priority of logical reasoning over ordinary mathematical reasoning.

— L. E. J. Brouwer On the Foundations of Mathematics (1907)

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Riemann was the first to show the right way for research on the foundations of geometry by starting from the idea that space is a Zahlenmannigfaltigkeit, thus a system built... by ourselves.

On the Foundations of Mathematics (1907)

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