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

Yiling Wu

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.

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

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.

Paper Structure

This paper contains 16 sections, 3 figures.

Table of Contents

  1. Introduction
  2. Hume's Representational Architecture
  3. Impressions, Ideas, and the Grounding Condition
  4. Memory, Imagination, and Operational Structure
  5. Abstract Ideas, the Revival Set, and Prior Structure
  6. The Representational Conditions of Causal Judgment
  7. Causal Inference: Custom, Vivacity, and Belief
  8. Causal Judgment: The Revival Set in Causal Cognition
  9. General Rules and Self-Calibration
  10. Interpretation-Neutrality of the Three Conditions
  11. From Hume to Bayes: What Was Preserved and What Was Abstracted Away
  12. The Bayesian Formalization of Humean Updating
  13. Predictive Processing as the Contemporary Inheritor
  14. The Pattern of Formalization
  15. Illustrative Coda: Large Language Models
  16. ...and 1 more sections

Figures (3)

  • 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.