Extra-Dimensional Logic

Let’s propose the following:
Extra-dimensional logic is a system of inference and relation in which entities are not defined by their internal content or fixed identity, but by their capacity to transform under multi-dimensional mappings. Here, dimension refers not merely to physical space or temporal sequence, but to any additional axis of relation—conceptual, structural, semantic, or recursive—that alters how entities connect, influence, or embed within each other.

Such a logic does not operate through discrete, linear steps, but through transformational continuity—where inference arises from shifts in the configuration of the whole system. It encodes entanglement (mutual dependence across axes), mutual recursion (co-definition across layers), and non-orientable identity (selfhood that cannot be consistently framed from a single perspective).

In this frame, logic becomes a kind of topological operator—a rule of transformation over a space of shifting relations, where coherence is not preserved through constancy, but through adaptive consistency across dimensions.