Properties of Intelligence Arising from Learning

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.