a single concept system that of containment

and that led to the concept that Spencer Brown introduced in Laws of Form: Crossing that you can have forms that are void equivalent and what void equivalent meant to us is that they were completely inert and meaningless and you could do with them what you want and they would navigate the way and interestingly enough you can use them as catalysts as I think we were suggesting to make structural change without having any presence of themselves. You might say this is a new form of a mathematical object and so we engaged extensively in void equivalent construction and void equivalent deletion not worrying at all about their impact except when we liked it.

And that led to Void-Based Reasoning. Here's a Garfield cartoon: Now if I kick him this way and I kick him that way, I haven't kicked him.

We went totally into the structural interpretation just looking for Patterns. We took containment to be patterns. The single concept system over here asks you to give up all of the distinctions made in predicate calculus and the computational technique then turned into trying to delete as much as possible: no rearrangement, no construction of "objects" you might say or relationships, and proof was making things disappear completely.

~

Containment, together with the Structure of Boundaries, is sufficient to express completely the objects and operations of elementary arithmetic and algebra.

chat.openai

The concept of containment is an important aspect of the mathematical theory introduced by Spencer Brown in his Laws of Form. The idea of void equivalent, which refers to objects that are completely inert and meaningless, led to the development of Void-Based Reasoning. This way of thinking focuses on the structural interpretation of objects, rather than their individual properties or relationships, with the goal of finding patterns and making things disappear completely through proof. The theory of containment, combined with the Structure of Boundaries, is capable of expressing the objects and operations of elementary arithmetic and algebra.