Is 'the world' driven by a 'hidden' axiomatic system?

It is possible to imagine that the 'real' world is a system which only looks unpredictable to us because we don't know enough about it. Quantum theory seems to contradict this, as it assumes that certain kinds of event are fundamentally unpredictable (e.g. the time at which an unstable nucleus will emit an alpha particle).

There are other issues, though:

Would a 'complete' system also have to predict its own predictions? This is 'algorithmic information theory' territory. The system, and especially its mechanical substrate (if these can be formally distinguished), is part of the world it is trying to predict.

Would it also have to include us? Would our language (and it's mechanical substrate ...) be part of what it could explain? If it did, would it have to include an isomorph for a theory of truth for our language? (Since it would comprise, in some sense, an ultimate 'meta-language').

This has a funny consequence, which is that we could not translate the language of this theory into our own language - because we cannot state a theory of truth for our language in our language. This means that the language of the 'ultimate theory' would be incomprehensible to us, and so, therefore, would the theory.

And if we take a clear Davidson/Quine line on this, we not only can't translate this language, we have no grounds for treating it as a language.