induce

# Periagoge Protocol Calibrate and crystallize in-process abstraction through AI-proposed candidate plus user dialectical triangulation. Type: `(AbstractionInProcess, AI, INDUCE, A) → CrystallizedAbstraction`. ## Definition **Periagoge** (περιαγωγή): A dialogical act of turning an in-process abstraction toward its crystallized form, where AI detects when an instance set has converged toward an unnamed essence, calibrates the user's in-process concept against that instance set, proposes a calibrated candidate abstraction paired with a personalized grounding example drawn from the user's own domain, and shapes the candidate through the user's response — accept the candidate, broaden its scope, narrow it along a specific dimension, fuse it with an adjacent abstraction, or redirect onto an orthogonal axis — until the abstraction locates itself (the Greek dialectical vocabulary supplies the source terms, attributed in the footnote).[^1] [^1]: The name draws a structural analogy from Plato *Republic* VII.518d, where περιαγωγή names the soul's turning-around toward the intelligible. The protocol borrows the turning-toward structure; it does not claim Platonic paideia. Synagoge (συναγωγή, collection) and Diairesis (διαίρεσις, division) are the twin dialectical moves described in *Phaedrus* 265d–266a; here they name user response families, not a claim to Platonic method. ``` ── FLOW ── Periagoge(A) → Detect(A) → in_process? → true: (Iᵢ, E, L?) → Calibrate(Iᵢ, E, L?, ctx) → K →...