Frank Kogan

because the nature of the change in cultural matters is always cumulative, and there are no systems of understanding (through language) that are "violated" in order to include some new idea

I don't understand this, and I can't make sense of your use of "cumulative." I'd say that what Kuhn means by science not being cumulative is that something of significance is lost: old meanings of words, old ways of behaving and connecting ideas, old ideas of what is like what, etc. This is every bit as true in matters of culture. E.g., when you go out dancing, you don't become the vehicle for supernatural spirits called "moas," do you? So something is lost in the "translation" from the dance's African antecedents* to your own dance. Wiki: "Alternatively, a language is said to be extinct if, although it is known to have been spoken by people in the past, modern scholarship cannot reconstruct it to the point that it is possible to write in it or translate into it with confidence (say, a simple dialogue or a short tale written in a modern language)." That certainly seems to be a case of cultural loss. And Kuhn's got a section of one of his essays where he talks about concepts in French that have no equivalent in English, so something is lost in translation. And Native American culture wasn't absorbed fundamentally unchanged into modern North American culture, was it? Whole social forms were obliterated, belief systems, etc. And where the beliefs have survived, they're not necessarily compatible with Christianity and atheism and so forth. Just because ideas exist at the same time as others and that some - a few - people are willing to understand the ones they don't subscribe to doesn't make the ideas compatible. And though astrology still exists, its ideas have been "lost" by modern astronomy. And if you want to say, "Oh, but astronomy is a science, but astrology hasn't been lost to the culture," this doesn't make a point. Astronomy is part of culture too, but astrology isn't part or astronomy. I'm an atheist, and atheism isn't a science (or an ism, actually), but astrology isn't part of my beliefs. Unless your criterion for "cumulative" is "exists on the same planet at the same time," I don't see how culture gets to be any more cumulative than science (and even there, lots of culture is no longer part of the planet).

I think you're confusing (1) conflicting ideas may nonetheless coexist within a field or enterprise (which I think is probably always true in all fields and enterprises that aren't sciences), and (2) those conflicting ideas therefore aren't incompatible, since they co-exist (this is false), (3) nothing is lost as such fields and enterprises change over time, since conflicting ideas can coexist within those fields (this is false too, since the fact that some ideas coexist doesn't mean either that those particular ideas will continue to coexist or that there aren't other ideas that haven't coexisted or can no longer coexist, etc.).

*I'm not saying that all the antecedents are African, just that the dance has some African ancestry.