I have to admit, at first I thought you were being nit-picky, and that "Part of the ridiculous divide in American politics stems from this misuse of the terms" was a significant overstatement, but as I read stePH's and Darwinist's posts, I see that you are not being nit-picky, and, furthermore, I think you're right about that being one of the reasons of the divisiveness... well, maybe not actually "misuse" of the terms, but having only (or primarily) those two terms with which we all get associated with (maybe that stems from having two primary political parties). But you're all right: we all most of us fit into a grayer area in which it would be incorrect to associate us with either one of those "philosophies."
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After further thought… So is having only two "climates" more divisive or less divisive than having more than two climates? It may be worse if we had more with which we tried to label ourselves... What do you think?
I'm tired, but I hope that made sense....