Magnus Anderson wrote:How can you test (i.e. verify or falsify) that any point (that you can pick) that is at a certain distance D away from some fixed point C is on the boundary of the shape?

Why do you need to test it? I'm talking about the

definition of a circle, not its verfication. I'm say:

assume the point is at a distance D from the center. Then it belongs in the set of points defined as those that are a distance D from the center. All such points in that set can be said to be on the circumference of the circle whose radius is D. What I mean by "all points on the circumference of the circle" is: the members of that set.

Magnus Anderson wrote:But in order to determine whether any shape is a circle or not you must focus on a finite number of points. No, you can't focus on a point (something with no dimensions), you can focus on segments. Otherwise, you cannot determine whether any given shape is a circle or not because you would be testing an infinite number of points Or a finite number of segments. which means you would be running your test infinitely i.e. forever. You will never be able to complete it.

You are talking about how to identify a circle through perception. We do so by identifying segments, not points (and now that I think about it, I think the brain just identifies circles

as is). We only

theorize that the circle is made of points simply because we can ask ourselves "what do these segments which I perceive break down into?" and we imagine the segments being broken down as far as possible, and that brings us to the idea of points. But at this point, we have left actual perception and (paradoxically) skipped an infinity of divisions such as to arrive at the concept of a points.

Magnus Anderson wrote:That's what we do in practice but not exactly in the manner that you describe here. We focus on a larger number of points. Five isn't enough. This is why a pentagon is not perceived as a circle but a hectogon is. Roughly speaking, we are checking at least 50 points on the boundary of the shape before deciding whether it is a circle or not.

Again, you are talking about how we

perceive circles, not the definition of a circle. And even with respect to perception, I don't think we perceive

points pe se, but segments (curves in particular).

Magnus Anderson wrote:Yes. In other words, you are dishonest.

Dishonesty requires

knowing that you are dishonest. I can guarantee you I believe in every word I say. You could say I am

mistaken, but there I will challenge you to show me how.

Magnus Anderson wrote:You can pick any problem you want. If one does not work then you can pick another.

True, but I still question why deviate from the main topic in the first place. Ur's point was that he had a reason for digressing the topic of cause and responsibility onto that of circles (whether they are made of lines or not)--namely, to exercise our skills at rational thinking (either that, or the question of whether circles are made of sides or not

really is pertinent to the question of cause vs. responsibility). I'm just skeptical of Ur's excuse. I think he just got caught by the debate--he had to prove himself simply because he had already dug his heels in and the discussion veered onto the topic of circles, and one doesn't just pick up one's heels when the topic changes. <-- This is my theory of the "migration of value" as I call it.