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Dogmas and the changing images of foundations

José Ferreirós

Philosophia Scientiae (2005)

  • Volume: 9, Issue: S2, page 27-42
  • ISSN: 1281-2463

Abstract

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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 a priori 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assumptions about the foundational enterprise emerge from certain dogmas that are frequently inherited from previous, outdated images.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.

How to cite

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Ferreirós, José. "Dogmas and the changing images of foundations." Philosophia Scientiae 9.S2 (2005): 27-42. <http://eudml.org/doc/103772>.

@article{Ferreirós2005,
abstract = {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 a priori 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assumptions about the foundational enterprise emerge from certain dogmas that are frequently inherited from previous, outdated images.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.},
author = {Ferreirós, José},
journal = {Philosophia Scientiae},
language = {eng},
number = {S2},
pages = {27-42},
publisher = {Éditions Kimé},
title = {Dogmas and the changing images of foundations},
url = {http://eudml.org/doc/103772},
volume = {9},
year = {2005},
}

TY - JOUR
AU - Ferreirós, José
TI - Dogmas and the changing images of foundations
JO - Philosophia Scientiae
PY - 2005
PB - Éditions Kimé
VL - 9
IS - S2
SP - 27
EP - 42
AB - 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 a priori 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.
LA - eng
UR - http://eudml.org/doc/103772
ER -

References

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