Hi John,
Very good question! Thanks for asking it. By definition every quantity has do be defined and must be measurable within the theory. I would say as a first instance this can be decided formally within the theory. In the reconstruction in the essay you have a symmetry defining the basic quantities. Also the free evolution is defined. Then one needs an interaction, that correlates these quantities to another system or objects, which then serves transporting the information about the quantities of the first object to the other one. The interaction doing this is mostly defined by some gauge principles.
I would say, that quantum field theory, the standard model, are semantically closed theories, depending maybe on the Interpretation (relating to the measurment Problem). Except maybe for the time measurement, since time is entering the theory as external parameter and not as observable.
But also Newton classical mechanics might be a closed theory. Maxwell's theory also. Here I am not sure, if the length scales can be defined within the theory.
General relativity, I'm not sure if it is closable, because it needs rulers defined in another theory. It is questionable if a general covariant gheory can be a closed Theory, because no seaprable objects can be defined in it.
Now the question is: how do we know, this theory is realized? There are several problems here. One of them is connected to the Duhem-Quine thesis. In here to falsify theory trough observation needs always an auxiliary theory describing the measurement. Usually this theory is well established and no reason to doubt it. But for closed theories the observational theory is the same as the theory to be falsified. This looks really circular.
The objects and systems to be well defined must be separable from the rest. But this separability is only approximative. The rest can be modelled as external forces, that change the 'normal behaviour' of the system. But whether the theory has to be modified or the not normal behaviour explained by external forces might not be decidable from observation alone. See for instance dark matter vs. MOND.
Finally such a closed theory generated from symmetry and some principles is a big tautological construct. We might not expect to create some empirical theory from principles. So in order to give meaning to the concepts in the theory, the theory must contain Newtonian classical mechanics as limit, which is the language of our intuition.
Sorry. Long answer for a short question.
Luca