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Frege allows a functional letter to occur in a quantifier. . . . The result is that the difference between function and argument is blurred . . . in the derivation of formula (77) he substitutes 5 [a quantificationally bound function letter] for α [a quantificationally bound individual variable] i n / ( α ) , at least as an intermediate step. If we also observe that in the derivation of formula (91) he substitutes S for / [a " f ree" function letter], we see that he is on the brink of a paradox. He will fall into the abyss when (1891) he introduces the course-of-values of a function as something "complete in itself," which may be taken as an argument.

On an alleged contradiction lurking in Frege's Begriffsschrift.