Hume's Representational Conditions for Causal Judgment: What Bayesian Formalization Abstracted Away

Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural properties of representational systems: operability, consistency, structural preservation, and compositionality. These properties are demanded to different degrees by different forms of reasoning, from induction through analogy and causal inference to deduction and formal logic. Each property excludes a distinct class of reasoning failure. The analysis reveals a principal structural boundary: reasoning types below it can operate on associative, probabilistic representations, while those above it require all four properties to be fully satisfied. Scaling statistical learning without structural reorganization is insufficient to cross this boundary, because the structural guarantees required by deductive reasoning cannot be approximated through probabilistic means. Converging evidence from AI evaluation, developmental psychology, and cognitive neuroscience supports the framework at different levels of directness. Three testable predictions are derived, including compounding degradation, selective vulnerability to targeted structural disruption, and irreducibility under scaling. The framework is a necessary-condition account, agnostic about representational format, that aims to reorganize existing debates rather than close them.

Causal Bayesian networks are often described as causal because they support reasoning about interventions. Yet interventions are defined in the mathematical model, whereas the resulting model predictions concern the effects of actions in the real world. Consequently, whether and how a causal model makes falsifiable predictions about the effects of actions depends on how actions are interpreted as interventions. This requires specifying which actions correspond to which interventions, a step that is frequently left implicit. We develop a formal framework that separates a causal model from the data-generating process it aims to describe and formalizes interpretations connecting actions to interventions. Within this framework, we prove an impossibility result: no interpretation can simultaneously satisfy a collection of desirable properties while remaining non-circular. Under a circular interpretation, every model that fits the observational distribution is interventionally valid, so no experiment can falsify it. We analyze several non-circular alternatives and discuss implications for falsification, causal discovery, causal representation learning, and causal abstraction. More broadly, our framework provides a way to make assumptions about the connections between actions and interventions explicit and to reason formally about the empirical content of causal models.

Performing causal reasoning akin to humans is fundamental to achieving strong artificial intelligence. However, existing studies on causal reasoning and large language models (LLMs) often underestimate the role of human causal cognition. Human causal reasoning is far more than recognizing causes and effects. Humans often factor in many other considerations when establishing a causal link between two events, such as norm violations, intentionality, morality, counterfactual scenarios, etc. To simulate such reasoning, it is intuitive to identify cause-effect pairs using token causality formalisms while modeling the factors that influence human causal judgment using findings from cognitive science experiments. To support the evaluation and modeling of human-like causal reasoning in LLMs, we introduce HCR-Bench, a challenging benchmark with 1,093 instances and detailed human causal reasoning step annotations, and HCR-Reasoner, an approach that systematically integrates theories of token causality and cognitive science into LLMs for human-like causal reasoning. Results suggest that HCR-Reasoner consistently improves LLMs' causal alignment with humans, and that theory-guided reasoning is highly effective.