In this talk, we discuss Frege's theory of "logical
objects" (extensions, numbers, truth-values) and the recent attempts to rehabilitate
Frege's theory of them. We focus on George Boolos's work and show that the
`eta' relation he 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.