Axiom talk:Condensation ↔ Protraction

I think I can see where you're coming from on this &mdash; it seems like metalogic of a kind. Is it an order of abstraction further back than the concept of semantics and models in propositional logic?

JA: Exactly. From what I can tell, one of the routes by which Peirce arrived at this point of view was through his consideration of "operator variables". For example, you write an operator equation like: $$a\ O_1\ (b\ O_2\ c) = (a\ O_1\ b)\ O_2\ (a\ O_1\ c)$$ Then you ask for what pairs of operators $$O_1\!$$ and $$O_2\!$$ is the equation an identity, that is, true for all the relevant values of $$a, b, c.\!$$ Jon Awbrey 23:56, 10 October 2008 (UTC)