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

Yiling Wu

cs.AIApr 3, 2026

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

Authors: Yiling Wu

Organizations: BridgeM, Inc. · Department of Philosophy, University of Massachusetts Amherst

Abstract

Hume's account of causal judgment presupposes three representational conditions: experiential grounding (ideas must trace to impressions), structured retrieval (association must operate through organized networks exceeding pairwise connection), and vivacity transfer (inference must produce felt conviction, not merely updated probability). This paper extracts these conditions from Hume's texts and argues that they are integral to his causal psychology. It then traces their fate through the formalization trajectory from Hume to Bayesian epistemology and predictive processing, showing that later frameworks preserve the updating structure of Hume's insight while abstracting away these further representational conditions. Large language models serve as an illustrative contemporary case: they exhibit a form of statistical updating without satisfying the three conditions, thereby making visible requirements that were previously background assumptions in Hume's framework.

Figures & tables

Figure 1: Hume’s dual-layer model of mental representation, illustrating the distinction between inference-level processing (lively ideas, force and vivacity, basic belief) and judgment-level processing (abstract ideas, exemplars, revival sets) that underwrites the extraction of RC-2.

Figure 2: Hume’s account of causal inference, showing the pathway from perception through custom/habit to belief (lively idea). The impression of determination (an impression of reflection) accompanies this transition and provides the experiential basis for RC-3 (vivacity transfer).

Figure 3: Hume’s model of how the idea of necessary connection arises. The impression of determination is internal (an impression of reflection), not derived from external observation, illustrating why RC-3 requires a system capable of distinguishing external perceptions from internal reflective states.

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The Reasoning Error About Reasoning: Why Different Types of Reasoning Require Different Representational Structures

Yiling Wu

BridgeM, Inc. · Department of Philosophy, University of Massachusetts Amherst

Structured Reasoning Logical Reasoning Cognitive Modeling

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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.

Abstract

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