Frege, Boolos, and Logical Objects

被引：0
作者：
David J. Anderson
Edward N. Zalta
机构：
[1] Stanford University,
来源：
Journal of Philosophical Logic | 2004年 / 33卷
关键词：
abstract objects; extensions; George Boolos; Gottlob Frege; Hume's Principle; logical objects; numbers; object theory; second-order logic; truth values;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：1 / 26
页数：25
相关论文
共 17 条
  • [1] Bell J.(1994)Fregean extensions of first-order theories Math. Logic Quarterly 40 27-30
  • [2] Boolos G.(1986)Saving Frege from contradiction Proc. Aristotelian Society 87 137-151
  • [3] Boolos G.(1989)Iteration again Philosophical Topics 42 5-21
  • [4] Boolos G.(1993)Whence the contradiction? The Aristotelian Society Supplement LXVII 213-234
  • [5] Burgess J.(1998)On a consistent subsystem of Frege's Grundgesetze Notre Dame J. Formal Logic 39 274-278
  • [6] Ferreira F.(2002)On the consistency of the Δ J. Philos. Logic 31 301-312
  • [7] Wehmeier K.(2001)-CA fragment of Frege's J. Philos. Logic 30 613-616
  • [8] Goldfarb W.(1993)First-order Frege theory is undecidable J. Symbolic Logic 58 579-601
  • [9] Heck R.(1996)The development of arithmetic in Frege's History and Philosophy of Logic 17 209-220
  • [10] Heck R.(1987)The consistency of predicative fragments of Frege's Notre Dame J. Formal Logic 28 161-68
12