Structural causal models acquire the ability to answer teleological questions --- not just “what caused this?” but “what was this for?” --- through a new operator called the intentional intervention. Unlike standard do-interventions, which model external manipulations without regard to purpose, intentional interventions produce structural final models that interpret observed outcomes as consequences of goal-directed action by state-aware agents. The structural final model links observed states to counterfactual baselines absent the intentional intervention, enabling both agent detection and intention discovery from observational data.
The gap between causal and teleological reasoning has been one of the clean separations in formal epistemology: Pearl's do-calculus answers causal questions, but purpose is excluded by design. Adding a time-independent intentional operator that respects the SCM framework without abandoning its formal guarantees means the separation was never ontological --- it was a limitation of the operator vocabulary. The key structural insight is that teleological inference requires comparing not two causal worlds but a causal world and an intentional world, and the SCM formalism already contains the machinery for that comparison once the right intervention type is defined.
Every formal system has a boundary between what it can express and what it excludes, and that boundary is usually mistaken for a boundary in reality. The intentional intervention demonstrates that the exclusion of purpose from causal models was an artifact of operator design, not a fundamental incompatibility. The general pattern: when a framework appears to lack the capacity for a certain kind of question, the deficit is more likely in the vocabulary of operations than in the structure of the framework itself.
(arXiv:2603.18968)