[Ce n'est pas qu'ils n'auraient pas pu]
Cet article offre une critique de la notion de “concepts” en histoire des mathématiques. Certains historiens s'appuient parfois sur un argument mettant en avant une impossibilité conceptuelle, du style : certains auteurs ne pouvaient pas faire X, parce qu'ils n'avaient pas le concept Y. Nous discutons en détail ce que cela signifie dans le cas de la différence entre mathématiques grecques et mathématiques modernes. Nous montrons que l'argument de l'impossibilité conceptuelle est empiriquement et théoriquement peu solide. Pour rendre compte de la diversité historique, l'article offre une alternative fondée sur des pratiques qui s'auto-entretiennent et sur la notion de divergence interprétée non en termes des valeurs intellectuelles elles-mêmes (qui pourraient bien être universelles), mais des rangs que ces valeurs occupent dans différentes cultures et époques.
The article offers a critique of the notion of ‘concepts' in the history of mathematics. Authors in the field sometimes assume an argument from conceptual impossibility: that certain authors could not do X because they did not have concept Y. The case of the divide between Greek and modern mathematics is discussed in detail, showing that the argument from conceptual impossibility is empirically as well as theoretically flawed. An alternative account of historical diversity is offered, based on self-sustaining practices, as well as on divergence being understood not in terms of intellectual values themselves (which may well be universal) but in terms of their rankings within different cultures and epochs.
@article{RHM_2002__8_2_263_0,
author = {Netz, Reviel},
title = {It's not that they couldn't},
journal = {Revue d'histoire des math\'ematiques},
pages = {263--289},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {8},
number = {2},
year = {2002},
zbl = {1091.01004},
language = {en},
url = {http://archive.numdam.org/item/RHM_2002__8_2_263_0/}
}
Netz, Reviel. It's not that they couldn't. Revue d'histoire des mathématiques, Tome 8 (2002) no. 2, pp. 263-289. http://archive.numdam.org/item/RHM_2002__8_2_263_0/
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