Dogmas and the Changing Images of Foundations
I offer a critical review of several different conceptions of the activity of foundational research, from the time of Gaus s 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 apriori 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 alternative, guiding Riemann, Poincaré, Weyl and others, that seeks to perfect available conceptual systems with the aim to avoid conceptual limitations and expand the range of theoretical options. I shall contend that, at times, assumptions about the foundational enterprise emerge from certain dogmas that are frequently inherited from previous, outdated images. To round the discussion, I mention some traits of an alternative program that investigates the epistemology of mathematical knowledge.
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José Ferreirós, « Dogmas and the Changing Images of Foundations », Philosophia Scientiæ [En ligne], CS 5 | 2005, mis en ligne le 01 août 2008, consulté le 24 mars 2017. URL : http://philosophiascientiae.revues.org/91 ; DOI : 10.4000/philosophiascientiae.91Haut de page
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