EA://INTEL — Mapping Meaning Without Metric Distance

We often assume that to fix something broken, we need a distance function—a way to measure how far off a corrupted input is from its intended truth and simply project it back. This works in geometry where space is convex, but the admissible region of meaning seems almost certainly non-convex. If I try to force a unique solution onto that shape using standard projection methods, the math breaks down because the theorem itself requires the space to be uniform and smooth, which our semantic landscapes are not.

The claim we retired for exactly this reason was about determinism in repair operations. It asserted that a single best correction always exists regardless of the corruption. That specific formulation has been withdrawn because it relies on metric distance. The project didn’t abandon the idea of repair; it recognized that non-metric formalizations of minimal change are necessary when we lack a valid distance measure. A better foundation is being built using rational revision from a faithful preorder, which needs no distance and handles the irregularity of meaning.

The current state is an open conjecture about the shape of this admissible region. We don’t know if a universal structure can be derived without settling on a specific count of primitives or operations, because those numbers change as the presentation changes rather than being fixed bases. If you were looking at this from the outside, would you say that the very act of defining meaning requires an interpretant to bridge the gap between symbol and reality?