The 1910 *Principia*'s Theory of Functions and Classes and the Theory of Descriptions
It is generally acknowledged that the 1910 Principia does not deny the existence of classes, but claims only that the theory it advances can be developed so that any apparent commitment to them is eliminable by the method of contextual analysis. The application of contextual analysis to ontologica...
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| Format: | Article |
| Language: | English |
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University of Rijeka. Faculty of Humanities and Social Sciences
2007-01-01
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| Series: | European Journal of Analytic Philosophy |
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| Online Access: | https://hrcak.srce.hr/file/137204 |
| _version_ | 1818523658675552256 |
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| author | William Demopoulos |
| author_facet | William Demopoulos |
| author_sort | William Demopoulos |
| collection | DOAJ |
| description | It is generally acknowledged that the 1910 Principia does not deny the existence of classes, but claims only that the theory it advances can be
developed so that any apparent commitment to them is eliminable by the method of contextual analysis. The application of contextual analysis
to ontological questions is widely viewed as the central philosophical innovation of Russell’s theory of descriptions. Principia’s “no-classes theory of classes” is a striking example of such an application. The present paper develops a reconstruction of Principia’s theory of functions and classes that is based on Russell’s epistemological applications of the method of contextual analysis. Such a reconstruction is not eliminativist—indeed, it explicitly assumes the existence of classes—and possesses certain advantages over the no–classes theory advocated by Whitehead
and Russell. |
| first_indexed | 2024-12-11T05:47:34Z |
| format | Article |
| id | doaj.art-6087390beafc452994290b56f9e49957 |
| institution | Directory Open Access Journal |
| issn | 1845-8475 1849-0514 |
| language | English |
| last_indexed | 2024-12-11T05:47:34Z |
| publishDate | 2007-01-01 |
| publisher | University of Rijeka. Faculty of Humanities and Social Sciences |
| record_format | Article |
| series | European Journal of Analytic Philosophy |
| spelling | doaj.art-6087390beafc452994290b56f9e499572022-12-22T01:18:55ZengUniversity of Rijeka. Faculty of Humanities and Social SciencesEuropean Journal of Analytic Philosophy1845-84751849-05142007-01-0132159178The 1910 *Principia*'s Theory of Functions and Classes and the Theory of DescriptionsWilliam DemopoulosIt is generally acknowledged that the 1910 Principia does not deny the existence of classes, but claims only that the theory it advances can be developed so that any apparent commitment to them is eliminable by the method of contextual analysis. The application of contextual analysis to ontological questions is widely viewed as the central philosophical innovation of Russell’s theory of descriptions. Principia’s “no-classes theory of classes” is a striking example of such an application. The present paper develops a reconstruction of Principia’s theory of functions and classes that is based on Russell’s epistemological applications of the method of contextual analysis. Such a reconstruction is not eliminativist—indeed, it explicitly assumes the existence of classes—and possesses certain advantages over the no–classes theory advocated by Whitehead and Russell.https://hrcak.srce.hr/file/137204Principia Mathematicacontextual definitionramified type theoryaxiom of reducibilityimpredicative definitionpropositional function |
| spellingShingle | William Demopoulos The 1910 *Principia*'s Theory of Functions and Classes and the Theory of Descriptions European Journal of Analytic Philosophy Principia Mathematica contextual definition ramified type theory axiom of reducibility impredicative definition propositional function |
| title | The 1910 *Principia*'s Theory of Functions and Classes and the Theory of Descriptions |
| title_full | The 1910 *Principia*'s Theory of Functions and Classes and the Theory of Descriptions |
| title_fullStr | The 1910 *Principia*'s Theory of Functions and Classes and the Theory of Descriptions |
| title_full_unstemmed | The 1910 *Principia*'s Theory of Functions and Classes and the Theory of Descriptions |
| title_short | The 1910 *Principia*'s Theory of Functions and Classes and the Theory of Descriptions |
| title_sort | 1910 principia s theory of functions and classes and the theory of descriptions |
| topic | Principia Mathematica contextual definition ramified type theory axiom of reducibility impredicative definition propositional function |
| url | https://hrcak.srce.hr/file/137204 |
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