Half-baked Philosophy (Part 1)

Background: I am pursuing a graduate degree in philosophy.

Right, so I'm struggling to formulate essay ideas. I have two to write in the next three weeks, and my idea-generating faculty is going slowly. So this is an exercise to at least have something put down which could serve as the basis for further refinement. I don't know why I needed to spell out, but it helps.

Today, after class, there was an interesting exchange regarding instantaneous velocity. Our prof thought it was too simple to think instantaneous velocity is just out there in the world, since to properly define the idea you need the concept of limit, and thereby calculus. Before calculus, you had to impale yourself on one of the horns of Zeno's paradox: either at each time there is some finite velocity, which, given that there are infinite positions between position x and y means that you've gone infinite distance, or there is no velocity at a particular time, in which case motion is impossible. There was some back-and-forth about neo-Kantianism and whether this is really any different from realism, and what the sense of world was, and what Kant can help himself to. Is there an essay in this? Doesn't look like it. But so it goes.

Consider: "I have no knowledge of myself as I am, but merely as I appear to myself."