Epistemic status: wild speculation

There's an interesting line in the old MIRI paper on Definability of Truth: "Tarski’s result on the undefinability of truth is in some sense an artifact of the infinite precision demanded by reasoning about complete certainty." This feels vaguely analogous here to the uncertainty principle in quantum mechanics, which also prevents infinite-precision knowledge. (Has anyone discussed this before?)

The connection jumped to my attention because I've also been thinking lately about the concept of causation in physical and logical universes. Intuitively speaking, the concept of Pearl's do-operator feels pretty sensible in our physical universe because there's a bounded lightcone which an event can affect—so that when we hypothesize taking an action, we can mostly ignore the implications for things in the past, or for simultaneous actions by other agents. (See this old post by Yudkowsky for more.)

FDT generalizes the do-operator to the realm of logic, which doesn't have either timelike or spacelike separation by default. There's no privileged direction such that some logical facts affect others but aren't affected by them. And there's no notion of "distance" between different logical facts—e.g. any two facts A and B can be combined to give a proof of A AND B.

It's possible that we could ground some version of logical timelike and spacelike separation using concepts like "what order does some proof system generate these facts in?", "how hard is it to prove one from the other?" or "how much computation do you save by calculating them together vs separately?" But I don't currently see much promise in this, since it all seems so representation-dependent.

An alternative idea (inspired by some of davidad's thinking) is that intelligent minds might create logical timelike and spacelike separation as a consequence of their decisions. Demski's conception of logical time (which was anticipated by Lacan!) is mostly motivated by the idea of agents recursively reasoning about each other. It seems like such agents could create a kind of directionality by simply refusing to reason in certain ways, as part of a correlated game-theoretic strategy. (As an aside, the idea of refusing to do certain kinds of reasoning about other agents seems like an important building block for defining concepts like respect, trust, and faith.) This could lead to a logical analogue of the lightspeed limit which is less of a hard constraint, and more like a highway speed limit: breakable, but in a way which might incur larger consequences (specifically, exclusion from the coalition that coordinates itself by imposing spacelike and timelike structure in the logic of rational minds).

More generally, I want to coin a term for the idea that there are strong parallels between the natural sciences and the mathematical/cognitive sciences at many different levels of abstraction, such that they could eventually be unified into a single theory of physico-logical phenomena. This is related to Deutsch's concept of a non-reductionist theory of everything, but he doesn't (to my knowledge) point specifically at the idea of parallelism between these two domains of inquiry. Meanwhile Friston's work on the free energy principle attempts to draw a link between cognition and thermodynamics, but (again, to my knowledge) he doesn't hypothesize that such links arise at many other levels (quantum physics, chemistry, biology, etc). For now I'll call this the physico-logical unification hypothesis, but I'm open to better suggestions.