🔭 Methodeutics

Methodeutics is the logic of active inquiry: how to choose the next operation that can discriminate among live hypotheses. A trial may perturb a program, randomize a treatment, reproduce a component failure, or search wreckage for a trace. The operation changes with the conditions of exposure; the demand that it risk a verdict does not.

Statistics formalizes induction: how observations warrant generalization. Methodeutics begins one step earlier and continues one step later. It asks where hypotheses come from, which one to expose next, what exposure is available, and how the verdict restructures the inquiry.

Peirce named the field in 1902. Its unit is not an isolated inference but the self-correcting traversal: abduction proposes, deduction exposes, induction judges, and the verdict names the next question. This is the textbook.

The field inherits the old problem of scientific discovery. Peirce's abductive schema can test whether a conceived explanation would resolve a surprise, but the explanation already appears in the schema. Reichenbach and Popper separated this context of discovery from the logic of justification; Hanson, then Simon, tried to recover a logic for it. The problem remains open. In a closed space, inquiry can enumerate hypotheses and search them. Analogy can carry an existing relation from one represented domain into another. Neither explains conceptual novelty: how inquiry invents the variable, mechanism, or representation that makes a previously inexpressible hypothesis available. This book formalizes what can be placed around that leap: how inquiry constructs a surprise, constrains what would explain it, selects an exposure, reads the verdict, and makes failure provoke the next hypothesis. It is machinery for generation, not yet a theory that generates.

Modes of reasoning

Methodeutics conducts the traversal. It selects the next discriminating operation under the inquiry's available time, money, access, observability, and tolerance for harm. Everyone does part of it. Doctors call it diagnosis. Engineers call it debugging. Detectives call it deduction (wrong, but Doyle didn't read Peirce). The pieces have always existed across philosophy, cognitive science, program analysis, causal inference, and sequential testing.

How to read this book

Prerequisites: comfort reading short Python programs, and one encounter with probability at the level of a fair coin. Everything else the book uses (separation logic, martingales, type constructors) is taught where it is first needed.

The chapters are a single argument and read best in order, but there are three doors:

• From software or engineering: start at Chapter 4. The mechanic will feel like debugging because it is debugging. Circle back to Part I when you want to know what the operation is called and why it took a century to name.
• From statistics or data science: start at Chapter 10, where your field's snapshot habit fails three times in public. Then read Part II to see where the hypotheses come from.
• From philosophy: start at Chapter 1 and the appendices, which include the primary Peirce texts in full.

Each chapter ends with five exercises: a warm-up, two worked problems, a computer exploration (💻), and an open-ended field problem (★) that points the chapter's tool at a system you already own.

Chapters

Each chapter opens with a system that breaks under the previous chapter's tools. The breakage motivates the new concept. The shape of the failure names the next chapter.

Part I: The trichotomy

Ground-clearing. What abduction is, why it trades certainty for fertility, and the evidence that six fields keep rediscovering it under different names. No mathematics yet; the object of study has to exist before it can be measured.

Part II: The primitives

The mechanical core around the abductive leap. A diff constructs the surprise, bi- and tri-abduction constrain what would explain it, framing decides what the diff runs over, and economy decides which candidate to test first. By the end of Part II you can provoke, constrain, and rank hypotheses. You cannot compute their invention in an open space, and you cannot yet score a test.

Part III: The evidence

What comes back from the experiment depends on what a trial costs. Cheap trials produce trajectories and running bets. Singular, destructive trials produce differential traces. Both feed the four bins, the hypothesis graph, and its convergence rule.

Part IV: The machine

Assembly. The generate-test-update loop hardened against self-deception, validators that accept proofs and counterexamples alongside data, the full pipeline, and one real system taken apart in public.

Appendix: Primary Sources

between vision and root
blooms branches and shoots

prune the duds
thence more buds

clues for felling
perfuse its telling

do trees need an arbor
in light, soil and water?

Peirce's vocabulary

Terms coined or repurposed by Charles Sanders Peirce (1839–1914) that do work in this textbook.

Status & citation

Draft. All 19 chapters written, with exercises. Last revised August 2026. Corrections welcome: kimjune01@gmail.com.

Companion package: pip install methodeutics — the Chapter 11 e-value bankroll as a library (source).

@misc{kim2026methodeutics,
  author = {Kim, June},
  title  = {Methodeutics: The Logic of Inquiry},
  year   = {2026},
  url    = {https://june.kim/reading/methodeutics/},
  note   = {Online textbook, draft}
}