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Response The question of whether one mathematical (or observational) structure stands in a certain relationship to another, or whether, given a structure and a set of relational constraints formulated with respect thereto, another structure satisfying those constraints can be generated or identified in polynomial time (in a number of steps expressible as as a polynomial function of the total number of structural elements), is not the question I'm asking here...although this question can easily be related to the questions that I am asking. 

For present purposes, we might as well define an ""intractable (scientific) paradox"" as an apparent inconsistency which is agreed to exist by experts in the relevant field(s) of science, but which those experts have failed to conclusively and consensually resolve despite their protracted efforts to do so. (Such an inconsistency can be any of several kinds.) The question of whether such paradoxes owe to a ""lack of imagination"" on the parts of the experts ""in almost all cases"" is thus really about the creative competence of those experts. But although it would be possible to justify some fairly negative judgments along those lines, that's still not the question I'm asking here. 

The questions I'm asking here are (1) given such an inconsistency, can you resolve it without a metalanguage of the theory or theories (and data sets) which generate it, and (2) if you own that such a metalanguage is required, is this metalanguage - i.e., a language sufficient for the full expression of the interpretative mapping M:T<>U, where T stands for a (scientific) theory and U stands for the observable universe of that theory - necessarily scientific in nature? That is, in and of itself, does such a metalanguage necessarily involve observational applications of the scientific method (as opposed to the axiomatic method)?

You go on to discuss the UV catastrophe. As we all know, the UV catastrophe was ""resolved"" by the quantization of light, ultimately leading to the development of quantum mechanics. Unfortunately, there remains a problem with quantum mechanics: the formalism observably corresponds to reality only at limited junctures. The questions of if and how the rest of it corresponds to observable reality remain matters of widespread confusion, and have led to several conflicting interpretations of QM which are necessarily expressed in a ""philosophical"" metalanguage of QM (which can itself be cast as a metalanguage of classical mechanics). If one of these interpretations is ever refined to the extent that it can generate new falsifiable predictions, it will become ""scientific"". But until then, we're stuck with philosophical (observationally unfalsifiable) interpretations.

You have already identified ""imagination"" as important in the resolution of scientifc paradoxes. This alone casts doubt on the notion that there exists any algorithm generating a valid resolution in every case. However, you still seem to believe that there is a set of principles which can be used to conclusively identify such resolutions once they are given, and more generally, to quickly and superficially distinguish between valid and invalid resolutions. Prior to encountering you, the Hillman agent, and certain others here at Wikipedia, I hadn't known of any such principles. I am therefore asking you to share these principles - as opposed to the biases, hunches, rules of thumb, and other voodoo on which others have relied - with the rest of world. 

Can you do this? Thanks,  "