Philosophy of mathematics : Bolzano's responses to Kant and Lagrange
Paul Rusnock (*)
In a late essay, Bolzano describes the philosophy of mathematics as an activity aimed at discovering the objective grounds of propositions which we already know with the greatest certainty and evidence (1). For him, philosophy of mathematics was simply what we would now call foundational research in the broadest sense - that is, it was not just a matter of « ultimate » foundations (for instance set theory, logic, or the like), but also of the foundations of particular mathematical theories (for instance geometry, the calculus, combinatorics...). Bolzano was certainly committed to dealing with questions of ultimate foundations, with developing a unified system of mathematics from first principles - his detailed
(*) Paul Rusnock, Department of Philosophy, Univ. of Alberta, 4-115 Humanities Centre, Edmonton, Alberta, Canada T6G2E5 ; all translations, unless otherwise noted, are by the author. (1) Bernard Bolzano, Was ist Philosophie ? (Wien, 1849), 23. Rev. Hist. ScL, 1999, 52/3-4, 399-427
