POINCARÉ, KANT, AND THE SCOPE OF MATHEMATICAL INTUITION

摘要

In a series of important monographs and articles, Michael Friedman has helped us to appreciate this disjunction as philosophically deep and as historically momentous. [...] in Dynamics of Reason (2001), Reconsidering Logical Positivism (1999), and elsewhere, Friedman argues that, as a matter of intellectual history, Poincaré's refusal to extend Kant's account of mathematical synthesis from arithmetic to geometry contributed to the collapse of Kant's distinction between forms of intuition and concepts of the understanding - a collapse crucial to the formation of both the continental and analytical traditions in philosophy and to the development of his own version of neoKantianism.4 While we can now better appreciate its historical importance, I do not think we have yet a clear picture of the philosophical issues at stake in Poincaré's "yes and no" stance toward Kant's picture of mathematical synthesis.