 Though the present section is not required for understanding the proof of Frege’s Theorem, we include it so that the reader can get some sense of how second-order logic (with comprehension) gives rise to Russell’s paradox when one adds Frege’s theory of courses-of-values and extensions. Though we shall briefly discuss Frege’s notation for courses-of-values, we’ll subsequently switch to simpler notation for naming the extensions of concepts. For the purposes of this section, let us suppose that we have primitive function terms \(f\), \(g\), \(h\), … in our language and that functional applications such as \(f(x)\), \(g(y)\), etc., are allowed.