[mafribe]

Thanks, that's a nice quote. I had read that text as a student, but overlooked this morsel.

I wonder if Frege's older Begriffsschrift (1879) doesn't already discuss, or at least mention, higher-order functions. After all, in this text Frege explains his new conception of function.

I also wonder if Cantor would have been aware that this is possible.

[voxfrege]

I haven't read the "Begriffsschrift", but you are right. It is probable that he had developed his formal apparatus already then.