Final answer:
The inquiry into whether nonexistent entities can be quantified and how existing things emerge relates to philosophical debates on the nature of existence, the reality of mathematics, and free will versus determinism.
Step-by-step explanation:
The question of whether a set of nonexistent things can be determined and whether the existence of other things follows "mechanically" delves into the realms of metaphysics and ontology, which are branches of philosophy. The debate on the nature of existence often explores whether entities are discovered by humans or if they are creations of human minds. This philosophical pondering closely aligns with the inquiry into the nature of mathematics and whether it exists independently of humans or is a human invention.
Similarly, the concept of free will and determinism explores whether humans have the capacity to make choices that are not strictly determined by prior events and conditions, reflecting on our understanding of existence and reality. The essence of what makes something real and whether there can be multiple realities are fundamental questions that compel us to consider what exists and what does not, suggesting that the existence of certain phenomena may depend on our human conceptions.