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 Im asking herealthough 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 fields 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 thats still not the question Im asking here   The questions Im asking here are  given such an inconsistency can you resolve it without a metalanguage of the theory or theories and data sets which generate it and  if you own that such a metalanguage is required is this metalanguage  ie a language sufficient for the full expression of the interpretative mapping MTU 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 were 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 hadnt 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