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 |
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Éditions Kimé
2014-03-01
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| Series: | Philosophia Scientiæ |
| Online Access: | http://journals.openedition.org/philosophiascientiae/916 |
| _version_ | 1797402547081707520 |
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| author | Iris Loeb Stefan Roski |
| author_facet | Iris Loeb Stefan Roski |
| author_sort | Iris Loeb |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T02:26:50Z |
| format | Article |
| id | doaj.art-8f32ec22d05c4200a747ccbe5ad8ff33 |
| institution | Directory Open Access Journal |
| issn | 1281-2463 1775-4283 |
| language | deu |
| last_indexed | 2024-03-09T02:26:50Z |
| publishDate | 2014-03-01 |
| publisher | Éditions Kimé |
| record_format | Article |
| series | Philosophia Scientiæ |
| spelling | doaj.art-8f32ec22d05c4200a747ccbe5ad8ff332023-12-06T15:53:52ZdeuÉditions KiméPhilosophia Scientiæ1281-24631775-42832014-03-0118111312910.4000/philosophiascientiae.916The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic ProofIris LoebStefan RoskiIn 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.http://journals.openedition.org/philosophiascientiae/916 |
| spellingShingle | Iris Loeb Stefan Roski The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof Philosophia Scientiæ |
| title | The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof |
| title_full | The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof |
| title_fullStr | The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof |
| title_full_unstemmed | The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof |
| title_short | The Transition from Formula-Centered to Concept-Centered Analysis Bolzano's Purely Analytic Proof |
| title_sort | transition from formula centered to concept centered analysis bolzano s purely analytic proof |
| url | http://journals.openedition.org/philosophiascientiae/916 |
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