I think that we have to give up the idea that we can understand anything about thought and more generally cognitive processes by looking at how it "feels" think

I think that we have to give up the idea that we can understand anything about thought and more generally cognitive processes by looking at how it "feels" thinking (or doing math, vision, etc). The more we observe how we work, the more we learn that we really have no idea how we work. The ancient idea that we can understand reason by reasoning have to be abandoned: it is, after all, an idealistic belief; if we accept that our cognitive processes are physical phenomena, we also have to accept that reasoning without observation is powerless.