Kang-Sin Choi

We formalize how learning produces origination and control. A system understands a domain relative to an evaluator if it can modify its own program in response to that feedback, such that the modified program generalizes over the domain. An evaluator is a source of feedback, which is consistent in the sense that it gives the same judgment for the same input. We show that when understanding is realized through a learning rule applied to procedural traces (here, gradient descent), organized knowledge emerges. Primitive circuits are individually learnable, the trace teaches decomposition and iteration, credit assignment separates factors into distinct weight regions, and a shared confluence orchestrates them into a hierarchical structure of shared and domain-specific factors. The same mechanism scales from integer multiplication to natural-language reasoning, with mechanistic interpretability confirming the decomposition in transformers. From this organization, two capacities emerge. Origination: cross-composition of learned factors produces new programs absent from training. Control: the same primitives that compute outputs produce halts and goal-directed acts as emergent structure, not as a separate faculty. The framework is constructive so that it identifies the mechanism at each step.

We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence density of a system is the ratio of the logarithm of its independent outputs to its total description length. A system memorizes if its description length grows with its output count; it knows if its description length remains fixed while its output count diverges. The criterion for knowing is generalization. A system knows its domain if a single finite mechanism can produce correct outputs across an unbounded range of inputs, rather than storing each answer individually. The definition places intelligence on a substrate-independent continuum from logic gates to brains. We then argue that meaning over a domain is a selection and ordering of functions that produces correct outputs where correctness is specifiable. We also define a measure of contextuality of an output as the inverse of its conditional Kolmogorov complexity given the context of prior outputs, which unifies correctness and independence into a single condition. Together, these refute Searle's third premise, that syntax is insufficient for semantics, over any domain where correctness is specifiable.