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 the simultaneous transformation of time, space, and perspective. Each axis is assigned a value of 1 (symmetry preserved) or 0 (symmetry broken). Value can be shared, and hence the proposition can be said, only while all three axes remain at (1,1,1). Since the three axes are operated on simul- taneously, a proposition remains sayable within the population reachable by n operations, but becomes unsayable to the population reached at operation n+ 1 if any axis breaks there. This paper is a proposal for a direction of research rather than a completed theory, and its limitations are explicitly stated.