The Vast Scope and Blind Spots of Mathematics: The Reach and Limits of an Unbound Descriptive System

Building on the projection framework established by "How Does Intelligence Carve the World?" (projection theory), this paper describes the reach and limits of mathematics as a descriptive system within the framework of Civilization Boundary Theory. After surveying five major positions in the philosophy of mathematics (Platonism, formalism, intuitionism, logicism, structuralism), the structural characteristic of mathematics is summarized as "excluding the nature of elements and preserving only relations and conditions." This characteristic is redescribed as the "absence of binding" — the non-assignment of specific values to variables. It is shown that the absence of binding simultaneously generates the vast scope of mathematics (shareability across subjects with different MANES, and a connection space across different domains) and a threefold blind spot (inability to ask about binding itself, inability to define MANES-dependent variables, inability to judge excess in variable addition). Mathematics is a descriptive system possessing only a lower bound (consistency) without an upper bound (bandwidth constraint), and this asymmetry is shown to be the obverse of projection theory's bandwidth-constraint argument. A hierarchy of binding is described — from the space of consistent structures (the deepest level) through the determination of physical constants, measurement, and civilizational practices — and it is argued that the descriptive reach of mathematics exceeds R-space. The core thesis of this paper is that the vast scope and the blind spots of mathematics are two consequences of a single structural condition: the absence of binding. The paper self-diagnoses the limitations of the term "binding," which fails to express the voice distinction at the level of measurement and lacks descriptive power at the civilizational level, and defers the examination of an alternative descriptive language to subsequent work.