What the Tortoise Said to Achilles

A very short dialogue-story, where the Tortoise teaches Achilles that in the strictest sense of Logic, the process of inference from even 2 propositions to an almost automatically-implied third proposition involves an infinity of intermediate propositions, making it an infinite schema. The logic of that Logic is infuriating and an objection hard to nail down. To illustrate this, the Tortoise uses the statements of the First Proposition of Euclid and befuddles Achilles over the next couple of pages. In the end, Achilles proposes that the Tortoise be renmed, “Taught-Us”, and in response, the Tortoise proposes the other be called, “A Kill-ease”…

While this “story” is a piece of pedagogic catechism in the tradition of a seeker and the teacher, I suspect most people would categorize it as mathfiction since axioms & axiom-schemas, deductions, etc are all at the base of mathematics. And this story starts off with Euclid…