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Frontiers of Philosophy in China

Front Phil Chin    2012, Vol. 7 Issue (3) : 351-366     https://doi.org/10.3868/s030-001-012-0021-2
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Frege’s Result: Frege’s Theorem and Related Matters
Hirotoshi Tabata()
University Education Center, Tottori University, Tottori 680-8551, Japan
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Abstract

One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.

Keywords Frege's Theorem      Neo-Fregeans      abstraction principles      extensionalism      object theory     
Corresponding Authors: Hirotoshi Tabata,Email:tabata@uec.tottori-u.ac.jp   
Issue Date: 05 September 2012
 Cite this article:   
Hirotoshi Tabata. Frege’s Result: Frege’s Theorem and Related Matters[J]. Front Phil Chin, 2012, 7(3): 351-366.
 URL:  
http://journal.hep.com.cn/fpc/EN/10.3868/s030-001-012-0021-2
http://journal.hep.com.cn/fpc/EN/Y2012/V7/I3/351
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