Reading guide
The fourth cell of a genuine matrix
Confirmed by reading all four discourses of this run side by side: SN 45.14 (arising / Buddha's appearance), SN 45.15 (arising / the training), SN 45.16 (purification / Buddha's appearance), and this discourse (purification / the training) exhaust all four combinations of the two variables, with no combination repeated and none skipped.
Why the matrix matters, not just its own completeness
Together, these four discourses assert that neither the mere existence nor the quality of the eightfold path's own factors is available through the training system alone without a Buddha's own historical appearance, and also that neither is available through a Buddha's own presence alone without the structured training — both conditions, tested independently across both variables, are shown necessary rather than either one being merely sufficient on its own.
Key terms
The text
§1At Sāvatthī. “Mendicants, these eight things don’t arise to be purified, bright, flawless, and rid of corruptions apart from the Holy One’s training. What eight? They are: right view, right purpose, right speech, right action, right livelihood, right effort, right mindfulness, and right immersion. These eight things don’t arise to be purified, bright, flawless, and rid of corruptions apart from the Holy One’s training.”
Self-check quiz
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