Symbolization

Philosophy, made executable

Symbolization is Axioma's reason for being — turning meaning, natural language and philosophy into formal logic you can run. Here Epictetus' Stoic handbook becomes concepts, partitions, defeasible rules and graded proof. Every example runs right here in the page.

▶ Edit any example and press Run — or /Ctrl+Enter. Same WebAssembly interpreter as the playground; nothing leaves your browser. interpreter: loading…
EPICTETUS · c. 125 CE

The Enchiridion, formalized

Epictetus dictated the Enchiridion — the “handbook” — around 125 CE. Here its core moves are symbolized: not described, but executed. The dichotomy of control becomes a partition; disturbance, a defeasible inference; the therapy, belief revision; and the sage’s tranquility, a theorem that cannot be argued away. (Distilled from the full synthesis.)

The dichotomy of control — Ench. 1

“Of things, some are up to us and some are not.” Modeled as a genuine partition — provably disjoint and exhaustive, with membership queryable.

ench1.axOpen in Playground ↗

Disturbance follows judgment — Ench. 5

“Men are disturbed not by things, but by their judgments about things.” Disturbance is a defeasible consequence of a judgment — so it derives as the weakest, revisable tier: a conjecture.

ench5.axOpen in Playground ↗

The Stoic therapy — the cure

Treat the cause, not the symptom: forget_cascade retracts the judgment and every conclusion resting on it (a truth-maintenance system) — and the disturbance lifts on its own.

therapy.axOpen in Playground ↗

The indifferents — adiaphora

Wealth, health, reputation are indifferents — positively judged neither-good-nor-bad, which is not the same as a fact never valued at all (indifferentneutral).

adiaphora.axOpen in Playground ↗

The two handles — Ench. 11

“Never say of anything ‘I have lost it’, but ‘I have given it back’.” One fact, gripped by two qua framings — and the consequences diverge. The same fact appears in both result sets.

twohandles.axOpen in Playground ↗

Grounding is the therapy — the asymmetry

The novice’s disturbance is a conjecture (defeasible — it can be talked away). The sage’s tranquility is a theorem (a strict consequence) — and cancel refuses to defeat it. “Anytus and Meletus can kill me, but they cannot harm me.”

grounding.axOpen in Playground ↗

Meaning, made executable.

That is what symbolization is for: a 1,900-year-old text rendered as concepts, partitions, defeasible rules and graded proof — and runnable. For pure computation, see the Algorithms.