15:13 → [[MIT/Thesis/Dual/SDM]] two candidates →
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learning as epistomological composition

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knowledge can be represented as relationships between categories of concepts

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potential structure

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Thesis: Understanding Learning as Epistemological Composition and Abstraction

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Claim: Learning is not just information accumulation but a structured, layered process of composing knowledge fragments and abstracting over them; category theory offers a formal language for modeling these nested, compositional epistemic transformations.

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Gap

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Most learning theories are either cognitive (mental models) or statistical (Bayesian update), and rarely formalize how knowledge transforms across abstraction layers.

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Few frameworks exist for representing recursive belief structures, cross-domain analogies, or meta-level learning (learning how to learn).

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There’s little alignment between formal epistemology and applied system learning (design, AI, planning).

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Hypothesis

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Learning can be modeled as composition over structured belief morphisms, with abstraction corresponding to movement up layers of epistemic categories.

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This structure enables analysis of learning loops, reflection, generalization, and design insight.

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Theoretical Foundations

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Category theory: functors, fibrations, 2-categories, composition, pullbacks, abstraction as higher morphisms

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Epistemology: nested belief, revision, speculative reasoning, conceptual change

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Learning theory: curriculum design, analogical transfer, reflection

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System design: modular abstraction, interface design, learning-by-design

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Method Overview

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Define core learning operations (composition, abstraction, analogy) as categorical structures

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Model examples of real-world learning trajectories (e.g. concept maps, planning sequences, reflective practice) using these structures

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Use visual and algebraic tools to reveal where epistemic composition succeeds or breaks

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Optionally build tooling to track or simulate epistemic composition (e.g. a learning graph based on Logseq or Omnicat-style representation)

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Apply the model to system design or planning problems to demonstrate usefulness

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Expected Contributions

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A formal model of learning as epistemic composition across abstraction layers

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Bridging epistemology, design, and cognitive systems

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A novel theoretical foundation for modular, reflective, and cross-domain learning

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