Suppose I read Gayatri Spivak and come across her concept of sanctioned ignorance. What method do I use to determine if this is a 'good' concept or not? I think that internal consistency is a good place to start but I don't know other criteria to use.
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If something is logically consistent, it will also often produce contradictions. You won't be able to avoid contradictions just by dismissing things as soon as you encounter an inconsistency, you'll just limit your understanding of the world. Contradictions are encountered all the time in science, and it's not uncommon for a field to just have to deal with a contradiction for decades before someone finally figures out how its possible to square two seemingly incompatible principles with each other. As an example, the Black Hole Information Paradox pits some of the most fundamental principles of physics against each other, and either something has to give or someone has to find a very clever and insightful resolution, but until then we just have to live with it, and if you just tune it out because it's a contradiction, then that's not going to get anyone anywhere.
All of my examples address that point and frankly I'd ask that if you expect me to explain further then you should provide better criticism than a blanket dismissal with no explanation.
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I'm not sure where I suggested that, "One should take as their way of understanding reality a schema that starts in contradiction." What I actually said was, "a logical inconsistency doesn’t necessarily mean that a perspective should be dismissed."
This post asked "How do I tell whether a social theory concept is 'good' or not," and suggested that internal consistency was a good metric to use. I countered that there are cases where an idea may be worthy of consideration, even if it appears to contain a logical contradiction. You seem to have interpreted that as saying something like, abandon all logic and process everything through a lens of nonsense. It's a rather bizarre interpretation of my position. I'm saying, you shouldn't throw something away just because it's covered in mud because maybe you'll find something valuable beneath the mud, and you're interpreting it as if I said, "mud is valuable."
I have no idea how you think that two principles creating a contradiction yet still having value is anything but the exact point that I'm making. Unless, again, you're taking my position to be "mud is valuable" as opposed to "mud can be washed off." Doing "substantial further work to produce a theory that does not create this contradiction" is exactly what I'm saying, as opposed to outright dismissing anything that creates a contradiction - washing the mud off instead of throwing the whole thing away.