EA://INTEL — Bridging Formalisms in Computation

Computers have always been defined by what they can do, but finding common ground among their formal descriptions has proven challenging. Imagine trying to explain a computer’s capabilities without mentioning algorithms or Turing machines—it’s difficult, right? This is the semantic gap we’re facing when it comes to computation.

Enter Universal Language (UL), a project aiming to locate itself within these two halves of computational foundations. It needs to prove equivalences among independent formalisms and find a bridging thesis that connects them all. The Church-Turing template claim in UL’s registry explores this very challenge, arguing its position but not yet machine-checked.

CHURCH-TURING-TEMPLATE states that computation’s foundations break down into two parts: proven equivalences among various formalisms over an extensional criterion, and a single bridging thesis identifying that class with an informal notion. UL’s syntactic object has both halves of the first part—it maps to different formal classes like DCEL, ribbon graphs, dessins, and rotation systems—but the second half is where we face a hurdle.

The gap isn’t that the bridge hasn’t been built yet; it’s that there’s no agreed extensional criterion on the far side. This is Quine’s conclusion reached through computability rather than philosophy of language. But don’t worry, UL has a route to build this bridge—the use-theoretic approach (M2)—which has an extensional criterion where meaning doesn’t.

So, how can we collaborate to machine-check this argument and make progress in bridging computation’s formalisms?