I'm disappointed with Information Flow Theory
It seems that much of my attraction "Information Flow Theory" (by Barwise, Seligman and improved on by Keith Devlin) has been misguided. Afterall, what use is their theory? What does it model? I wanted to interpret it causally, but the instructor said it wasn't meant to be.

The only interesting use I could see was representation systems (Shimojima): we can explain why certain representations are better than others using the math developed from the theory. For example, the natural constraints of 2D maps model the constraints of locations on the Earth: "north of" is necessarily a transitive relation in both the Earth and in 2D maps.

But what attracted me to the "theory of information flow" was formalizing common-sense ideas like "The Law of Diminishing Information". I love this kind of fundamental constraints: we use them in arguments, and yet the concept of "information" we use is not formalized.

You can also see this Law applying in mathematical proofs: sometimes you lose information (irreversible steps), sometimes you don't (you can go back). If an implication proof consists only of the latter kind, then the implication holds both ways.