> That suggests a way forward will come from formalising natural language arguments.

Hot take (and continue with the derailment), but I'd argue that analytic philosophy from the last 100 years suggests this is a dead end. The idea that belief systems could be formalized was huge in the early 20th century (movements like Logical Positivism, or Russell's principia mathematica being good examples of this).

Those approaches haven't really yielded many results, and by far the more fruitful form of analysis has been to conceptually "reframe" different problems (folks like Hillary Putnam, Wittgenstein, Quine being good examples).

We've stacked up a lot of evidence that human language is much too loose and mushy to be formalised in a meaningful way.