/sci/ - Science & Math

>>9099253
Mathematicians view set theory as fundamental. Anything can be considered an object, even a space or a process, and wherever there are objects, there is a set to contain them. This something may be a relation, a space, an algebraic system, but it is also a set; its relational, spatial, or algebraic structure simply makes it a structured set. So mathematicians view sets, broadly including null, singleton, finite, and infinite sets, as fundamental objects basic to meaningful descriptions of reality. It follows that reality itself should be a set. In fact, the largest set of all. But every set, even the largest one, has a powerset which contains it, and that which contains it muct be larger, a contradiction. The obvious solution: define an extension of set theory incorporating two senses of containment which work together in such a way that the largest set can be defined as containing its powerset in the other. Thus it topologically includes itself in the act of descriptively including itself in the act of topologically including itself and so on, in the course of which it obviously becomes more than just a set.