Aristotle: cuts, contacts and consecutive points
Source: On Generation and Corruption, Book I, H. H. Joachim translation, Internet Classics Archive. Selected passages read 2026-09-10, chapter 2, especially the discussion around Bekker 317a. This is a passage digest, not a transcription of the whole chapter.
Passages read
Earlier in the division argument Aristotle asks what remains besides a contact, division or point. Joachim renders the relational premise:
every contact is always a contact of two somethings
Later Aristotle examines the inference from divisibility at any chosen point to division at all points simultaneously. He raises the supposed division immediately next to a division at the centre and rejects the assumption of consecutive points. Joachim renders the conclusion:
division is not ‘immediately-next’ to division, nor composition to composition.
Both excerpts occur in chapter 2. They locate the ancient question behind the project’s distinction between possible cuts and jointly realised divisions. The chapter first presents an argument for indivisible magnitudes, then examines its faulty inference; that proposed atomic conclusion belongs to the argument under examination.
Edition comparison and coverage
The stored Barthélemy-Saint-Hilaire translation has the corresponding discussion in paragraphs 20–21 and earlier contact discussion in paragraph 14. Its editorial notes acknowledge substantial interpretive difficulty. Its paragraph 21 uses “instant” where Joachim uses “position”; a direct inference about inserted time instants requires Greek collation rather than choosing the convenient translation.
Read the English chapter’s selected contact, potential/actual division and consecutive-point paragraphs, and the corresponding stored French paragraphs and notes. No new Greek manuscript/edition collation or historical influence claim was completed. The provenance note separates these passages from the modern mechanical extension.