π Methodeutics
The logic of inquiry. Statistics formalizes induction: how to generalize from observations. Methodeutics formalizes abduction: how to generate the next question. Peirce named both the mode (1878) and the field (1902). This is the textbook.
Modes of reasoning
| Mode | Edge | Field | Status |
|---|---|---|---|
| Deduction | Theory β Experiment | Logic, mathematics | Formalized (Aristotle β Frege β GΓΆdel) |
| Induction | Experiment β Observation | Statistics | Formalized (Fisher β Neyman β Ramdas) |
| Abduction | Observation β Theory | Methodeutics | This textbook |
Everyone does abduction. Doctors call it diagnosis. Engineers call it debugging. Detectives call it deduction (wrong, but Doyle didn't read Peirce). The pieces have always existed: philosophy, cognitive science, program analysis, causal inference, sequential testing.
between vision and root
blooms branches and shootsprune the duds
thence more budsclues for felling
perfuse its tellingdo trees need an arbor
in light, soil and water?
Chapters
Each chapter opens with a system that breaks under the previous chapter's tools. The breakage motivates the new concept. The textbook's structure embodies the method it teaches: the shape of the failure names the next chapter.
Part I: The trichotomy
| Chapter | |||
|---|---|---|---|
| 1. | Three modes | Holmes and the dog that didn't bark. Doyle called it deduction. It isn't. | π |
| 2. | Security and uberty | Popper says discovery has no logic. Peirce says it does, but admits it's insecure. | π |
| 3. | Eight names, one operation | Bi-abduction, figure-ground, equilibration, intervention. Six fields, zero cross-citation. | π |
Part II: The primitive
| Chapter | |||
|---|---|---|---|
| 4. | Diff | A mechanic taps the alternator. The engine stalls. Two hypotheses fire. Where did they come from? | π |
| 5. | Bi-abduction | Infer runs on millions of lines. It infers the frame automatically. But bi-abduction is one path. | π |
| 6. | Tri-abduction | The program branches. Each branch changes different state. Bi-abduction can't handle the fork. | π |
| 7. | Economy of research | Ten hypotheses, budget for three experiments. Which three? | π |
Part III: The evidence
| Chapter | |||
|---|---|---|---|
| 8. | Evidence has a trajectory | An A/B test says B is better. You ship. Six months later, B is worse. The snapshot lied. | π |
| 9. | Four bins | The trajectory oscillates. Is the system fighting itself, or is your measurement noisy? | π |
| 10. | The hypothesis graph | A monotone trend test fires but curvature is indeterminate. The failure mode is the next hypothesis. | π |
| 11. | Convergence | Five sensor streams, each individually undetectable. Composed e-values classify the forcing pattern. | π |
Part IV: The machine
| Chapter | |||
|---|---|---|---|
| 12. | Protecting the loop | An agent confirms every hypothesis. It abduced from the data and tested on the same data. | π |
| 13. | Validators | Four validator types, one interface. Empirical, structural, proof, counterexample. | π |
| 14. | The pipeline | Three witnesses (Infer, Voyager, IRM), each closing the loop in a different domain. None cite each other. | π |
| 15. | Case study | A system that searches without reasoning. It can perturb and observe but never asks why. | π |
Appendix: Primary Sources
| Appendix | |||
|---|---|---|---|
| A. | Deduction, Induction, and Hypothesis | The bean syllogism. The 1878 origin of the trichotomy (Ch 1). | π |
| B. | A Neglected Argument | Musement and the three stages of inquiry. Foundations for Ch 2. | π |
Peirce's vocabulary
Terms coined or repurposed by Charles Sanders Peirce (1839β1914) that do work in this textbook.
| Term | Meaning |
|---|---|
| Abduction | Inference from a surprising fact to an explanatory hypothesis. The only mode that introduces new ideas. |
| Retroduction | Synonym. Leading backward, from effect to cause. |
| Methodeutic | The third branch of logic: the study of methods of inquiry. (After speculative grammar and critical logic.) |
| Uberty | The productive richness of a reasoning mode. Abduction: highest. Deduction: lowest. From Latin ubertas (fruitfulness). |
| Security | The certainty of a reasoning mode. Inverse of uberty. Deduction: highest. Abduction: lowest. |
| Economy of research | Hypothesis selection guided by cost-benefit: which experiment gives the most information per dollar? |
| Musement | Free, purposeless contemplation: "antipodal to vacancy and dreaminess." The pre-logical state from which abductive hypotheses emerge. |
| Pragmaticism | The meaning of a concept is its conceivable practical effects. Renamed from pragmatism: "ugly enough to be safe from kidnappers." |
Status
All 15 chapters drafted and copyedited. Codex-reviewed to convergence.