The question: "Why is there anything at all, why not nothing?" must seemingly have 2 parts:
- Why does the foundational mathematical structure exist (of real-world mathematical categories, real-world relationships between the categories, and real-world numbers that apply to the categories)?
- Why is the foundational mathematical structure moving, i.e. why are the real-world numbers moving?
An already existing mathematical structure can’t explain its own existence, or why it is moving.
However, if a moving mathematical structure is taken to be a first-principles aspect of the world, then certain conclusions will be drawn about the true nature of the world.
But if THE SOURCE OF a moving mathematical structure is taken to be a first-principles aspect of the world, then quite different conclusions will be drawn about the true nature of the world.
So, for a start, instead of just assuming that the world moves, no questions asked, the “mechanism” of movement, i.e. the possible “mechanisms” of number movement in the foundational mathematical structure, need to be clarified.
Any “mechanisms” of real-world number movement can’t be explained in terms of the categories, relationships and numbers alone.
Any “mechanisms” of real-world number movement will also require logical connective symbols to represent aspects of the world, aspects of a real-world mathematical system, that can’t be represented in terms of the categories, relationships and numbers alone.
Logical connective symbols need to be used, e.g. in computer programs, to symbolically represent the analysis of symbolic situations, but also, to symbolically represent the creation of new numeric facts, new numeric outcomes.
And the “mechanism” of real-world number movement must seemingly involve the creation of new real-world numbers for some of the categories, whereby other numbers also jump, due to the relationships between the categories.
Number movement can seemingly only be explained as the creation of new facts about the world.