The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof. as a Case Study

Philosophia Scientiae 18 (1):113-129 (2014)
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In the 18th and 19th centuries two transitions took place in the development of mathematical analysis: a shift from the geometric approach to the formula-centered approach, followed by a shift from the formula-centered approach to the concept-centered approach. We identify, on the basis of Bolzano's Purely Analytic Proof [Bolzano 1817], the ways in which Bolzano's approach can be said to be concept-centered. Moreover, we conclude that Bolzano's attitude towards the geometric approach on the one hand and the formula-centered approach on the other were of a different nature; the for­mer being one of rejection, the latter of non-participation. Bolzano supports his concept-centered methodology by philosophical views, which were partially shared by mathematicians with a formula-centered approach to analysis.



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Author Profiles

Iris Loeb
VU University Amsterdam
Stefan Roski
Universität Hamburg

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Bolzano's Theory of Ground and Consequence.Armin Tatzel - 2002 - Notre Dame Journal of Formal Logic 43 (1):1-25.

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