[Lovers of Shakespeare] do not need, of course, to imagine whereabouts the persons are to stand, or what gestures they ought to use; but they want to realise fully and exactly the inner movements which produced these words and no other, these deeds and no other, at each particular moment. This, carried through a drama, is the right way to read the dramatist Shakespeare; and the prime requisite here is therefore a vivid and intent imagination. But this alone will hardly suffice. It is necessary also, especially to a true conception of the whole, to compare, to analyse, to dissect. And such readers often shrink from this task, which seems to them prosaic or even a desecration. They misunderstand, I believe. They would not shrink if they remembered two things. In the first place, in this process of comparison and analysis, it is not requisite, it is on the contrary ruinous, to set imagination aside and to substitute some supposed 'cold reason'; and it is only want of practice that makes the concurrent use of analysis and of poetic perception difficult or irksome. And, in the second place, these dissecting processes, though they are also imaginative, are still, and are meant to be, nothing but means to an end. When they have finished their work (it can only be finished for the time) they give place to the end, which is that same imaginative reading or re-creation of the drama from which they set out, but a reading now enriched by the products of analysis, and therefore far more adequate and enjoyable.
What I'm mostly interested in is the domain or domains from which the term leached into literary critical usage, becoming central to it from the 1920s on. There's psycho-analysis, of course (though note that Bradley at least is a pre-Freudian); but there are also mathematical, philosophical and scientific varieties, and perhaps others besides. My sense - perhaps biased by the fact that it fits the argument I want to make - is that literary critics took up the term so enthusiastically because of its quasi-scientific cachet, wishing to be seen as doing to texts much what biologists did to living material (note Bradley's 'dissect') and chemists to things in test tubes.
Does that seem wildly off-kilter?