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Nineteenth Century Philosophy

Philosophy of Mathematics and Logic

Who was Gottlob Frege?

Gottlob Frege (1848–1925) was a professor of mathematics at the University of Jena, who thought that Immanuel Kant (1724–1804) was mistaken in claiming that mathematical truth is synthetic—that is, about reality. (Kant had claimed that mathematical truths were synthetic a priori, which is to say both true of the world and known independently of experience of the world.) His task was to show how the concepts of mathematics could be defined in terms of logic alone, so that the theorems of mathematics would then appear as logical truths. If mathematics could be reduced to logic in this way, it would be shown that mathematics was merely true by definition, meaning that it had no empirical content, so that it could not be about the world. Mathematics would thereby be a priori, but not also synthetic, as Kant had insisted.



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