Can Frege pose Frege's puzzle?

In Joseph Almog & Paolo Leonardi (eds.), The Philosophy of David Kaplan. Oxford University Press. pp. 202 (2009)
Abstract
Gottlob Frege maintained that two name-containing identity sentences, represented schematically as a=a and a=b,can both be true in virtue of the same object’s self-identity but nonetheless, puzzlingly, differ in their epistemic profiles. Frege eventually resolved his puzzlement by locating the source of the purported epistemic difference between the identity sentences in a difference in the Sinne, or senses, expressed by the names that the sentences contain.  Thus, Frege portrayed himself as describing a puzzle that can be posed prior to and independently of any particular theoretical position regarding names, and then resolving that puzzle with his theory of Sinn and Bedeutung. In this paper, I suggest that Frege’s presentation is problematic. If attempt is made to characterize the epistemic status of true identity sentences without appeal to Frege’s theoretical commitments, then what initially seemed puzzling largely dissolves. It turns out that, in order to generate puzzlement, Frege must invoke the theoretical account that he uses the puzzle to establish the purported necessity of. 
Keywords Frege's Puzzle  Logical Form  Descriptive Theories of Names
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