Spencer-Brown: Cataphatist

George Spencer-Brown (GSB) did some wonderful work for a system of logic that has us consistently painting ourselves into a corner. That's the problem. His work contributes to a system of reasoning that is consistent but incomplete. What he doesn't see (and few who I've encountered who understand his work) is that he is stuck…

The Law of Existence – Part 2

Law of Existence - continued In my previous post, I promised to illustrate how the Laws of Thought, as they are used today, emerge naturally from the Law of Existence. Time to make good on my promise. In a comment left by reader SelfAwarePatterns he mentioned that he didn't see how the Law of the…

The Circle in the Plane: How bizarre is this?

The circle is a strange creature, and most definitely not as simple as it seems. In fact, you will see that a circle in the plane doesn't enclose anything - that 'inside' and 'outside' are completely arbitrary and in the end, meaningless. Hold on to your seats! Imagine a sphere upon which you've written the…

Mathematics and the Real

To my previous post, Louis Kauffman, himself, generously took the time to reply. I have included his reply in the comments section of that post. In that comment, I'd promised to continue the discussion in a new post. Here it is, with the brief continuation of the dialogue I had begun with Mr. Kauffman. I…

More on Numbers

I'm still troubled by the notion of a number with relation to discrete vs. continuous, Rational vs. Real, etc. Why? Because you can't even talk about a number on a continuity which is infinite. There is simply no such thing, because there is no 'thing' upon which to attribute a number. The mere fact of…