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—under transformations of time, space, and perspective. These three symmetries are independent, like the axes of a coordinate space, and the combination of their values determines the range of populations in which a proposition can be said. Scientific propositions are a special case in which all three symmetries are high. This paper is a proposal for a direction of research rather than a completed theory, and its limitations are explicitly stated.