The hope of the Critique of the Diagonal Method was that math teachers would realize the many flaws of the method and do a better job of presenting it. After reading Everything and More, I decided that maybe I should move away from subtle hints that teachers improve their method to a stronger refutation.
In the article on the diagonal method on finite binary strings, I decided to emphasize that the diagonal method is simply a new variety of the liar's paradox. The liar's paradox is any statement that includes a self negation, like "This sentence is false."
The goal of the article dialectics is to show that the method was one of several foundational theories based on oppositional logic that were popular during the German Idealist movement. Freud, Hegel and Marx have been widely refuted. The dichotomy created by the diagonal method is really one of the last of these massive theories of everything left standing.
The next article will explore the Galileo paradox. That piece is really necessary to show the true origins of Cantor's dichotomy.