An Anchor Theory of Sayability: Three Axes of Symmetry and the Geometry of What Can Be Said

This paper addresses the dichotomy between “what can be said” and “what cannot be said” in Wittgenstein’s Tractatus Logico-Philosophicus. I argue that the Tractatus does not explain why scientific propositions can be said; it merely presents a criterion without grounding it. I propose an alternative framework in which sayability is determined by the symmetry of an anchor—the segmented part carrying the highest subjective value for the analyst. An anchor can be placed on any proposition, and the question of sayability is not whether an anchor exists but whether it survives symmetry operations. Each of the three axes—time, space, and perspective—takes the value 1 (symmetry preserved) or 0 (symmetry broken), and value can be shared, and hence the proposition can be said, only while all three axes remain at (1, 1, 1). Whether a proposition can be said is decided, at minimum, by whether a single symmetry operation breaks the anchor. The three axes correspond by nature to three value components—credibility, narrativity, and importance—but historical attribution is not one-to-one: coarse-graining allows a breakdown to be attributed primarily to one axis, while fine-grained analysis may reveal the joint operation of several axes. Scientific propositions are sayable at the coarse-grained level because all three value components are preserved under repeated operations, although individual theories can lose symmetry and suffer the same fate as phlogiston. The same framework classifies why the lives of great figures can be said while those of ordinary persons cannot. This paper is a proposal for a direction of research rather than a completed theory, and its limitations are explicitly stated.