Sure. I'm actually reading through (a translation of) The Logic of Scientific Discovery right now, but I am already familiar with the ideas, conclusions, etc of

Sure. I'm actually reading through (a translation of) The Logic of Scientific Discovery right now, but I am already familiar with the ideas, conclusions, etc of Popper, Godel, and others whom have done related work. However, mathematical induction is different from "inductive reasoing" (as opposed to deductive, or "the deductive theory of testing", as Popper's translators call it). In fact, I don't believe it is a contrast to Popper's work; mathematical induction is actually a form of deductive reasoning (of course, this makes it rather confusing to talk about). Popper's method requires first formulating a system (axioms) in pure mathematics (logic). Then deriving the logical conclusions from the system and determining tests that could be performed that could contradict those conclusions. Popper also provides a schema for comparing systems, deriving contradictory conclusions, and designing experiments to distinguish between the various theories under consideration. >The way this works is: I don't mean to be obtuse, but it's not immediately clear to me at the moment what "this" refers to (although, from the context of the prior post, I would assume it refers to Inter-universal Teichmuller Theory). Is there another way you could clarify what we are talking about? Edit: Ok, I read my last post again and I think maybe you are giving a physical theory that is not based on integers or number theory? My concern with that interpretation is that I'm not sure how meaningful of a distinction can be made between Integers, ZFC, or Logic within the context of physical theories. Doesn't Shannon's work allow us to collapse all writable (a necessary precondition to execute Popper's method) theories to integers?