Variability of Mathematical Foundations under the Ontology of View: An Extremely Rigorous Integrated Philosophical and Mathematical Argument

This study proposes a radical ontology where mathematical objects (e.g., the number "1") and computational symbols (e.g., the plus sign "+") are not merely abstract concepts or formal notations, but possess inherent "Views"—an ontological mode of being that dynamically constitutes mathematical truth. These intrinsic "Views" interact with cognitive observer "Views" and external ontological perturbations to dynamically shape mathematical truth. Traditional mathematics regards propositions like 1+1=2 as universally invariant truths, forming its cornerstone. However, we argue that this universality is merely an idealization. Through a rigorously formalized framework, we prove that even fundamental arithmetic, such as "1+1=2", is not universally true but rather context-dependent and variable under the influence of these hyper-multi-Views. This work fundamentally challenges the absolute objectivity of mathematics, offering a dynamic, relational, and symbolagentic perspective for the philosophy of mathematics. It further suggests that well-known meta-mathematical limitations (e.g., Gödel’s incompleteness, Tarski’s undefinability, Turing’s undecidability) may have deeper ontological roots within this View-dependent framework.