Hmm, my usage seems more like: “I think that…” means the reader/listener might disagree with me, because maybe I’m wrong and the reader is right. (Or maybe it’s subjective.) Meanwhile, “I claim that…” also means the reader might disagree with me, but if they do, it’s only because I haven’t explained myself (yet), and the reader will sooner or later come to see that I’m totally right. So “I think” really is pretty centrally about confidence levels. I think :)
Hmm, my usage seems more like: “I think that…” means the reader/listener might disagree with me, because maybe I’m wrong and the reader is right. (Or maybe it’s subjective.) Meanwhile, “I claim that…” also means the reader might disagree with me, but if they do, it’s only because I haven’t explained myself (yet), and the reader will sooner or later come to see that I’m totally right. So “I think” really is pretty centrally about confidence levels. I think :)