- “Being a set” is in fact a property of the universe. That’s because “set” is defined as “a collection of distinct objects”, and the universe is in fact a collection of distinct objects (and more). The definition of “set” correctly, if only partially, describes the structure of the universe, and nothing can be separated from its structure. Remove it from its structure, and it becomes indistinguishable as an object and inaccessible to coherent reference.
- The universe fulfills the general definition of "set" in numerous ways, and this indeed makes it a set (among other things with additional structure). Otherwise, its objects could not be discerned, or distinguished from other objects, or counted, or ordered, or acquired and acted on by any function of any kind, including the functions that give them properties through which they can be identified, discussed, and scientifically investigated. If something is “not a set”, then it can’t even be represented by a theoretical variable or constant (which is itself a set), in which case Mark has no business theorizing about it or even waving his arms and mindlessly perseverating about it.
- Because the universe fulfills the definitive criteria of the “set” concept (and more), it is at least in part a (structured) set. One may object that a “set”, being a concept or formal entity, cannot possibly describe the universe; after all, the universe is not a mere concept, but something objective to which concepts are attached as descriptive “tools”. But to the extent that concepts truly describe their arguments, they are properties thereof. The entire function of the formal entities used in science and mathematics is to describe, i.e. serve as descriptive properties of, the universe.
- Everything discernable (directly perceptible) within the physical universe, including the universe itself (as a coherent singleton), can be directly mapped into the set concept; only thusly are secondary concepts endowed with physical content. One ends up with sets, and elements of sets, to which various otherwise-empty concepts are attached.
- In search of counterexamples, one may be tempted to point to such things as time and process, “empty space”, various kinds of potential, forces, fields, waves, energy, causality, the spacetime manifold, quantum wave functions, “laws of nature”, “the mathematical structure of physical reality,” and so on as “non-material components of the universe”, but these are predicates whose physical relevance utterly depends on observation of the material content of the universe. To cut them loose from the elements of observational sets would be to deprive them of observational content and empty them of all physical meaning.
- Can a containment principle for the real universe be formulated by analogy with that just given for the physical universe? Let's try it: "The real universe contains all and only that which is real." Again, we have a tautology, or more accurately an autology, which defines the real on inclusion in the real universe, which is itself defined on the predicate real. This reflects semantic duality, a logical equation of predication and inclusion whereby perceiving or semantically predicating an attribute of an object amounts to perceiving or predicating the object's topological inclusion in the set or space dualistically corresponding to the predicate. According to semantic duality, the predication of the attribute real on the real universe from within the real universe makes reality a self-defining predicate, which is analogous to a self-including set. An all-inclusive set, which is by definition self-inclusive as well, is called "the set of all sets". Because it is all-descriptive as well as self-descriptive, the reality predicate corresponds to the set of all sets. And because the self-definition of reality involves both descriptive and topological containment, it is a two-stage hybrid of universal autology and the set of all sets.