This is Part 6 of the seven-part Logic and Reasoning field guide. The previous five parts were largely static — they described what reasoning is, what its limits are, how multi-agent reasoning works, what makes a thinking system healthy. Part VI puts time back in. Reasoning systems learn. They forget. They revise. They occasionally undergo wholesale paradigm shifts where the framework underneath changes and most of the previously-settled questions have to be reopened. The dynamics matter.
The natural companions are the Generalization & Transfer field guide (where the dynamics show up as learning curves) and the HITL series (where belief revision under human gating is the central pattern).
What it covers
About twenty-two minutes of careful reading.
Belief revision. The AGM framework (Alchourrón, Gärdenfors, Makinson). The three operations — expansion, contraction, revision — and the rationality postulates that constrain them. Why “rational belief change” is a much richer notion than Bayesian updating alone.
Bayesian dynamics. The narrower case where the prior is well-defined and the posterior just updates. Why this is the right framework for some reasoning dynamics and the wrong framework for others (notably: when the question itself changes).
Learning curves. Power-law learning. The forgetting curve. The spacing effect. The empirical regularities about how humans and machines acquire skill over time. Implications for how to design a long-running reasoning system.
Paradigm shifts. Kuhn’s framework. Normal science / crisis / revolution / normal science. The pattern in which a reasoning community works under a shared framework, accumulates anomalies, the framework eventually fails, and a new framework replaces it. The companion question: when should a reasoning system have a paradigm shift?
The dynamics of disagreement. How two reasoning systems with the same evidence can end up with different conclusions. The Aumann agreement theorem and its conditions. Why those conditions almost never hold in practice — and what happens instead.
Designing for change. The architectural choices that make a reasoning system durable over time. Versioned beliefs. Audit logs. Explicit checkpoints for paradigm revision. The disciplines that turn a fragile reasoning system into a long-running one.
Read it
The series
This is Part 6 of 7:
- The Foundations and the Human Mind
- Limits, Machines, and Problem-Solving
- A Multi-Agent Problem-Solver
- From a Mind to a Society of Minds
- The Health of a Thinking System
- The Dynamics of Thinking — (this post)
- Understanding and Comprehension
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