Infinity and Renormalization——A Self-Enclosed Language Game After Abandoning the Inquiry into Reality

In standard quantum field theory, infinities are "eliminated" through renormalization—by introducing cutoffs, subtractions, and redefining parameters, finite results are obtained and compared with experiments. This method is "effective" at the practical level, but at the epistemological level it conceals a fundamental problem: it replaces physical inquiry with mathematical manipulation, substituting "computability" for "what this means." Based on the Frequency World Theory (FWT) and the projection-layer framework, this paper argues that infinities are not "mathematical anomalies that need to be eliminated," but rather "readout overflow signals produced when the observer fails to declare which projection layer they are reading from." Renormalization does not "solve" infinities—it "uses a language game to conceal the cessation of inquiry." Once we ask "in which projection layer does this infinity appear," renormalization loses its necessity and is replaced by "switching projection layers" or "changing the ruler." This paper demonstrates that renormalization is a "self-enclosed language game" —it allows physicists to solve problems within mathematics without asking "why infinities arise in the first place." Keywords: Infinity; Renormalization; Projection Layer; Language Game; Frequency World Theory; Cessation of Inquiry