Dear Prof. Durham,
you've provided an intriguing exploration of the notion of comprehensibility that makes many subtle and interconnected points. I'm not sure I've grasped everything correctly, but in outline, you seem to start out by something not too far from Wittgenstein's anti-private language argument---there's no meaning to the arbitrary terms an individual observer, or experimenter, may assign to data. Meaning is intersubjective, as much of an objectification of the correlations between subjective experiences as is possible.
An interesting point one might explore, perhaps, is whether one could try to find some 'minimal' amount of intersubjective agreement to cement some meaning. For instance, you note the example of agreeing on a reference frame to establish a Bell inequality violation; but in fact, it's possible to violate a Bell inequality without agreeing on local directions. Hence, the removal of this condition entails that it wasn't instrumental in pinning down the meaning of 'Bell inequality violation' after all. Indeed, in a sense, it's the process of science to 'peel away' to these minimal conditions. But this is a side issue.
I have to say that I was initially somewhat confused by your 'principle of comprehensibility'. In some sense, it seems to me, that the fact that the answer to the question 'What is the color of your hair?' turns out to be something within the set {red, yellow, blue,...} is analytic, in the same sense that the answer to 'What is the marital status of any bachelor?' turns out to be one (i. e. the only) element of the set {unmarried}. The set of possible answers---{unmarried}, {red, yellow, blue,...}---is implicit in the terms themselves.
For the proper name 'my hair' under the functional expression 'the color of () is', the set of possible answers is {red, yellow, blue,...} in the same way as for the proper name 'any bachelor' under the functional expression 'the marital status of () is' it is {unmarried}. So, I wondered, in what way could the answer possible be something else? How could the 'principle of comprehensibility' be wrong? It seems like it's an analytic statement itself.
But I think maybe that's your point---this analyticity is precisely what hampers our inquiry into 'the things themselves', so to speak. To see at all, we have to don some pair of glasses, but which one we wear will color what we see. By asking for the color of hair, we implicitly specify the set of possible answers, but asking some other question, in some other way, might have provided a different set of possible answers, that map only imperfectly to colors. We could ask, perhaps, not for color, but for specularity and reflectance given certain wavelengths of light, and under most circumstances, the set of answers obtained that way will map well to that of color judgments. But given a different context than that which was implicitly specified in the way we asked our question, these answers may come apart---consider, for instance, the controversy regarding what color 'the dress' might have: asking one way, perhaps for RGB values of certain pixels, will yield a unique answer that, under ordinary circumstances, would map well on what a given person would answer if asked for color, while in this case, the color values diverge wildly between different observers.
Is this somewhat close to what you're saying?
Cheers
Jochen
