The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof
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...
Main Authors: | , |
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Format: | Article |
Language: | deu |
Published: |
Éditions Kimé
2014-03-01
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Series: | Philosophia Scientiæ |
Online Access: | http://journals.openedition.org/philosophiascientiae/916 |
Summary: | 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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ISSN: | 1281-2463 1775-4283 |