Journal of Philosophical Logic

, Volume 33, Issue 1, pp 1-26

First online:

Frege, Boolos, and Logical Objects

  • David J. AndersonAffiliated withStanford University
  • , Edward N. ZaltaAffiliated withStanford University

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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.

abstract objects extensions George Boolos Gottlob Frege Hume's Principle logical objects numbers object theory second-order logic truth values