Rob created a video explanation of his mathematical concept-sharing theory, which introduces a new type of point called “E” that differs from regular points “P” by not collapsing into a single entity when combined. He demonstrated how E’s can exist at different levels (upper and lower) and can move relative to each other while maintaining their distinct identity. Rob also explained how numbers can concept-share using notation like “1,2” to represent partially shared numbers, and showed how this concept relates to a new number plane and Goldberg’s conjecture, which he has written extensively about on his website.
In UCT I place an e with a point p. E is not p so it does not combine with p. Then e cannot combine with e either. This does not break the law of Identity though as e is different from p, it exists on two conceptual levels. Then one e is the place of places, a higher level to place and the other e is another form of place. Then this understanding makes UCT parallel to ZFC.
It seems the axiomatic foundation of Mathematics is made of concepts and thus subject to concept sharing. Then the axioms must have other levels. Then there is no irreducible axiomatic system.
A better foundation of Mathematics is seen when we look at the truths that concept sharing allows. Since we must have concept sharing we need to look at the Mathematics that comes from this.