Frege, Boolos, and Logical Objects
| 详细信息 | 推荐本文 | |
- 作者：David J. Anderson and Edward N. Zalta
- 关键词：abstract objects ; extensions ; George Boolos ; Gottlob Frege ; Hume''s Principle ; logical objects ; numbers ; object theory ; second ; order logic ; truth values
- 刊名：Journal of Philosophical Logic
- 出版时间：February, 2004
- 出版年：2004
- 期刊代码：23_00223611
- 类别：law
- 卷：33
- 期：1
- 页码：1-26
- 数据来源：sp
摘要
In this paper, the authors discuss Frege''s theory of logical objects (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the eta relation George Boolos deployed on Frege''s behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the eta relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values.