Set of all sets
In the CTMU, the set of all sets is interpreted as reality, the set of all real objects. It is the largest set. All sets are contained by sets that are bigger than them and so we would demand that the largest set too is contained within another set. This is obviously a contradiction in terms. A way around this paradox is to see "containment" as having two aspects; topological and descriptive. Topological containment means containing something like a cupboard contains clothes. Descriptive containment means containing something the way that clothes define what the cupboard IS in the first place. Were not every aspect of the cupboard made specifically for the clothes that it was to contain, there would be no cupboard as a concept. In the same way the universe "holds" all the things inside it, but the things inside the universe define what it actually is. (The "dual" relationship between these two kinds of containment is covered at TD duality.)
Reality then evolves through a two stage process where one stage is descriptive and the other topological. In stage 1 all of the items in the universe reconsider their previous state, communicate and describe the rules and definitions for a future universe(the descriptive phase, where time operates). Stage 2 involves the physical reality coming into being where objects have boundaries that distinguish them from other objects and all of these objects are "contained" within space (the topological phase, time has become space). The name of the process given to the universe constantly topologically containing itself descriptively containing itself topologically and so on, is conspansion.
In view of this process of alternating topological and descriptive containment, reality is clearly more than just a set. Accordingly, the CTMU defines an extension of set theory incorporating these two kinds of containment, allowing them to work together to characterize reality. The name of this extension of set theory is SCSPL. Thus, in the CTMU, reality is not just a set, but an SCSPL (Self-Configuring Self-Processing Language), and elements of reality are not just set-theoretic objects, but syntactic operators. So in a nutshell:
- Reality is obviously a set (in fact the largest set), because "set" is defined as "a collection of distinct objects", and reality is a collection of distinct objects (and more).
- But reality is not just a set, because to fully characterize it requires a new extension of set theory called SCSPL incorporating topological and descriptive containment with objects as syntactic operators.