Displaying similar documents to “Scientific intuition of Genii against mytho-‘logic’ of Cantor’s transfinite ‘paradise’”

Dogmas and the changing images of foundations

José Ferreirós (2005)

Philosophia Scientiae

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We offer a critical review of several different conceptions of the activity of foundational research, from the time of Gauss to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical excavation of structures, (2) the program to find sound formal systems for so-called classical mathematics that can be proved consistent, usually associated with the name of Hilbert, and (3) the historicist...