The Ladder of the Sciences Part 5: Necessity, Possibility, and the Shapes of an Argument

Part 5 of 6. A complete reading of Sullam al-ʿUlūm, "The Ladder of the Sciences", the logic primer by Muḥibb Allāh al-Bihārī (d. 1119/1707) that became a standard text of the madrasa curriculum of the subcontinent, read phrase by phrase with the glosses Ḍiyāʾ al-Nujūm, "The Light of the Stars", by Muḥammad Ibrāhīm al-Balyāwī of Dār al-ʿUlūm Deoband (d. 1387/1967). Technical terms are explained in plain English as they come. The Arabic is on screen throughout, with real pages of the book. This part covers the text from the modalities to the end of contraposition, just before the chapter on argument. Part 4 asked what a proposition is. Part 5 asks how strongly it holds, and how it can be turned around. First the modalities: necessary, permanent, actual, possible, and the "compound" propositions built from them, with the puzzles of "man exists", the phoenix, the eclipsed moon and the Active Intellect. Then conditional propositions, "if … then" and "either … or", Ibn Sīnā on the little word in, entailment without any cause, and whether the impossible can entail anything. Then contradiction, with the paradox of "all concepts" and the eight unities; conversion, with Zayd's mount, al-Rāzī's writer, and "can anyone doubt that motion cannot stay still?"; and contraposition, with two doubts the author calls "slippery for the feet". Chapters 0:00 How Strongly? 0:55 Matter and Mode 1:54 Is Logic's "Necessary" the Philosopher's? 2:48 Twelve Out of Infinitely Many 3:45 "As Long as He Writes" 4:39 The Sphere That Never Stops 5:29 Actually and Possibly 6:25 "Not Always", and Alexander's Absolute 7:22 "Man Exists, Necessarily"? 8:19 Not Held Hostage by Conditions 9:08 The Phoenix 10:01 "This Objection Occurred to Me" 10:56 The Tree Tells of Its Fruit 11:56 Two Kinds of "As Long As" 12:47 Is "Possibly" a Statement at All? 13:39 What "Not Always" Hides 14:35 At First Glance 15:34 "If" and "Either" 16:25 Denying a Link, and Its Quantifiers 17:17 Ibn Sīnā and the Little Word "In" 18:12 Two Things Tied Without a Cause 19:04 If Five Were Even 19:52 The Intellect Rules in the Real World 20:47 If the Horse Were a Man 21:34 Coincidences 22:23 Exactly Two 23:28 Is Everything Tied to Everything? 24:25 All the Concepts There Are 25:22 Eight Unities, or Three, or One 26:20 The Denial of a Denial 27:16 The Contradictories of the Modals 28:10 Contradicting a Compound 29:02 Turning a Statement Around 29:57 Affirmation Is a Meeting 30:48 Does "Necessarily" Survive the Turn? 31:41 Zayd's Mount 32:29 Al-Rāzī's Writer, and Motion That Cannot Stay 33:24 The Earth and the Moon 34:20 Contraposition, Old and New 35:12 Two Slippery Doubts 36:14 The Shapes of a Judgment