Source: https://pages.ceres.rub.de/ayn-al-nazar/
Timestamp: 2019-04-19 04:34:50+00:00

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As for the ʿAyn al-Naẓar, this very succinct, three-part treatise is a distillation of the three logical relationships—quintessential to a valid, truth-seeking dialectic—found, in the same order, at the start of al-Nasafī’s Muqaddima / Fuṣūl.7 They are: (1) necessary implication (talāzum / mulāzama), (2) mutual negation (tanāfin / munāfā), and (3) causal concomitance (dawarān / mudāwara); and for each of these relationships al-Samarqandī provides definitions, logical and methodological theories and rules, illustrations, and practical observations—all of obvious benefit to the aspiring dialectician.8 This, in effect, is logic in action—a premodern dialogical logic for living disputation praxis—and its influence upon the rational sciences of Islam could only have been augmented by its incorporation into, and continued evolution within, the ādāb al-baḥth wa’l-munāẓara. Somewhere between the juristic dialectic of al-Nasafī’s Muqaddima / Fuṣūl and al-Samarqandī’s universalist Risāla, the ʿAyn al-Naẓar marks a developmental staging post, and may be considered a species of proto-ādāb al-baḥth.
1 For bio-bibliographical entries, see: Ibn al-Akfānī, Irshād al-Qāṣid, pp. 129-30, 161; Ṭāshkubrī Zādah, Miftāḥ al-Saʿāda, vol. 1, pp. 280-281, vol. 2, p. 160; Ḥājjī Khalīfa, Kashf al-Ẓunūn, vol. 1, cols. 38-41, 105, vol. 2, cols. 1074, 1075, 1272, 1326, 1595, 1799, 1803; al-Qannawjī, Abjad al-ʿUlūm, pp. 255, 550-551; Brockelmann, Geschichte, vol. 1, pp. 615-17 [orig. ed. p. 468], suppl. 1, pp. 849-850; al-Baghdādī, Hadiyyat al-ʿĀrifīn, vol. 2, p. 106; Kaḥḥāla, Muʿjam, vol. 9, p. 63; al-Ziriklī, Aʿlām, vol. 6, p. 39; Sarkīs, Muʿjam al-Maṭbūʿāt, vol. 2, pp. 999-1000, 1046. For encyclopedia entries, see: Miller, al-Samarḳandī ; Kutluer, Semerkandî ; Fazlıoğlu, Samarqandī ; De Young, Samarqandī ; Dilgan, Al-Samarqandī ; O’Connor and Robertson, Shams al-Din ibn Ashraf Al-Samarqandi . For more detailed studies, see: Dadkhah, Pers. Intro. to al-Samarqandī, ʿIlm al-Āfāq, pp. 1-82 (and Engl. Intro, pp. 1-13); Eichner, Post-Avicennian Philosophical Tradition, Chapter XIII: Shams al-Dīn al-Samarqandī and 13th Century Māturīdite Kalām; Muhaddis, Pers. Intro. to al-Samarqandī, Sharḥ al-Qaṣīda al-Rūḥāniyya; al-ʿAzzāwī, al-Samarqandī ; Şeşen, Majmūʿatān ; and Young, Protocol, (Intro).
2 See Dadkhah, Pers. Intro. to al-Samarqandī, ʿIlm al-Āfāq; Young, Protocol, (Intro).
3 See Miller, Islamic Disputation Theory, pp. 148-162.
4 Brockelmann, Geschichte, vol. 1, p. 615 [orig. ed. pp. 467-468], suppl. 1, p. 849. Edited by Pehlivan and Ceylan in Ādābu’l-Baḥs̱ , and by al-ʿImrān and Shams in (Ibn Taymiyya ?), Tanbīh al-Rajul al-ʿĀqil.
5 See Young, Concomitance to Causation ; al-Samarqandī, Sharḥ Fuṣūl al-Nasafī, Süleymaniye Kütüphanesi, Esad Efendi 3034; and al-Samarqandī, Sharḥ Fuṣūl al-Nasafī, British Library, Or. 11183.
6 See Belhaj, Ādāb Al-Baḥth Wa-al-Munāẓara ; Wisnovsky, Nature and Scope , pp. 169-173; Young, Dialectic in the Religious Sciences ; Young, Protocol, (Intro).
7 On this fact alone, there is little reason not to attribute the ʿAyn al-Naẓar to al-Samarqandī, as indeed the scribes of our manuscript witnesses have done. It should be clarified, however, while acknowledging the paucity of premodern bio-bibliographical material on al-Samarqandī, that (to the editor’s current knowledge) no pre-modern source besides these manuscripts attribute a Kitāb ʿAyn al-Naẓar to him. As far as bio-bibliographical sources are concerned, attribution of the ʿAyn al-Naẓar to al-Samarqandī seems to be found only in a few modern works; these in turn draw for the most part on Brockelmann, (Geschichte, vol. 1, p. 617 [orig. ed. p. 468], suppl. 1, p. 850), who himself references only the two manuscript witnesses collated in this current edition.
8 Miller offers expositions and analyses of all three logical relations, citing the ʿAyn al-Naẓar at some points (Miller, Islamic Disputation Theory, 149-159). See also: Young, Mulāzama in Action ; Young, Concomitance to Causation ; al-Samarqandī, al-Risāla, in Protocol, §§10-12; al-Samarqandī, al-Risāla, in Muʿjam, pp. 125-126; al-Kīlānī, Sharḥ, in Protocol, §§10.1-12.4.
9 Rieu, Supplement, No. 1124, v., foll. 72-76; no. 1227, i., foll. 1-5. Belhaj ( Ādāb Al-Baḥth Wa-al-Munāẓara , p. 295, n.11) notes a witness of the ʿAyn al-Naẓar in the Dār al-Kutub al-Miṣriyya; and indeed there is an entry in the Fihris al-Kutub al-ʿArabiyya al-Mawjūda bi’l-Dār li-Ghāyat Sannat 1921 (vol. 1, p. 229), for [عين النظر في علم الجدل في آداب البحث — تأليف العلامة الشيخ شمس الدين السمرقندي], in a majmūʿa codex shelf-marked [١٩٧ مجاميع م]. At the time of writing I have not been able to access this witness.
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———. Islamic Disputation Theory: A Study of the Development of Dialectic in Islam from the Tenth Through Fourteenth Centuries. Ph.D. Diss, Princeton University, 1984.
Muhaddis, Ali. Persian Introduction to Shams al-Dīn Muḥammad al-Samarqandī, Sharḥ al-Qaṣīda al-Rūḥāniyya . In Twenty Philosophical-Mystical Texts in Persian and Arabic, edited by Ali Muhaddis, 215–226. Acta Bibliothecae R. Universitates Upsaliensis, XLI, 2008.
al-Nasafī, Burhān al-Dīn. Al-Fuṣūl. In Pehlivan, Necmettin, and Hadi Ensar Ceylan, Ādābu’l-Baḥs̱ Devrimine Doğru Son Evrim: Burhānuddīn en-Nesefī’nin el-Fuṣūl’ü . Ankara Üniversitesi İlahiyat Fakültesi Dergisi 56, no. 2 (2015): 1–76.
al-Nasafī, Burhān al-Dīn. Al-Fuṣūl fi’l-Jadal . In Ibn Taymiyya, Taqī al-Dīn Aḥmad (?), Tanbīh al-Rajul al-ʿĀqil ʿalā Tamwīh al-Jadal al-Bāṭil, edited by ʿAlī b. Muḥammad al-ʿImrān and Muḥammad ʿUzayr Shams, pp. 639–668. Makkah: Dār ʿĀlam al-Fawā’id li'l-Nashr wa'l-Tawzīʿ, 2004.
al-Qannawjī, Ṣiddīq b. Ḥasan. Abjad al-ʿUlūm. Edited by ʿAbd al-Jabbār Zakkār. 2 vols. Damascus: Manshūrāt Wizārat al-Thaqāfa wa’l-Irshād al-Qawmī, 1978.
Rieu, Charles. Supplement of the Catalogue of the Arabic Manuscripts in the British Museum. London: Longmans, Green and co., 1894.
al-Samarqandī, Shams al-Dīn Muḥammad. Al-Risāla fī Ādāb al-Baḥth. In On the Protocol for Dialectical Inquiry (Ādāb al-Baḥth): A Critical Edition and Parallel Translation of the Sharḥ al-Risāla al-Samarqandiyya by Quṭb al-Dīn al-Kīlānī (fl. ca. 830/1427), Prefaced by a Critical Edition and Parallel Translation of its Grundtext: the Risāla fī Ādāb al-Baḥth by Shams al-Dīn al-Samarqandī (d.722/1322), edited and translated by Walter Edward Young, forthcoming.
———. Ādāb al-Ḥakīm Shams al-Dīn al-Samarqandī [= Al-Risāla fī Ādāb al-Baḥth]. In Majmūʿa Mushtamila ʿalā al-Ātī Bayānuhu : al-Awwal: al-Badr al-ʿIllāt fī Kashf Ghawāmiḍ al-Maqūlāt, wa-huwa Sharḥ al-ʿAllāma al-Muḥaqqiq… al-Shaykh ʿUmar al-Mashhūr bi-Ibn al-Qarah Dāghī… ʿalā Risālat al-Maqūlāt li'l-ʿAllāma… Mullā ʿAlī al-Qiziljī ; wa-Talīhi … (Etc.), edited by Maḥmūd al-Imām al-Manṣūr, pp. 125–132. Cairo: Maṭbaʿat al-Saʿāda, 1353 H. http://dar.bibalex.org/webpages/mainpage.jsf?PID=DAF-Job:192923.
———. Kitāb ʿAyn al-Naẓar fī ʿIlm al-Jadal. MS London, British Library, Or. 3730, foll. 72a-76a (completed 1173 H).
———. Kitāb ʿAyn al-Naẓar fī ʿIlm al-Jadal. MS London, British Library, Or. 3908, foll. 1a-5b (completed 876 H).
———. Sharḥ Fuṣūl al-Nasafī. MS Istanbul, Süleymaniye Kütüphanesi, Esad Efendi 3034, foll. 1a–46b.
———. Sharḥ Fuṣūl al-Nasafī. MS London, British Library, Or. 11183, foll. 2b–35a.
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Şeşen, Ramazan. Majmūʿatān min Mu’allafāt Athīr al-Dīn al-Abharī wa Shams al-Dīn al-Samarqandī . Presented at the Mu’tamar al-Makhṭūṭāt al-Mawaqqaʿa (Conference for Signed Manuscripts), of the Tanẓīm Maktabat al-Iskandriyya, April 26–28, 2005. http://wadod.net/bookshelf/book/1868.
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———. Dialectic in the Religious Sciences . In Encyclopaedia of Islam Three, forthcoming.
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———. On the Protocol for Dialectical Inquiry (Ādāb al-Baḥth): A Critical Edition and Parallel Translation of the Sharḥ al-Risāla al-Samarqandiyya by Quṭb al-Dīn al-Kīlānī (fl. ca. 830/1427), Prefaced by a Critical Edition and Parallel Translation of its Grundtext: the Risāla fī Ādāb al-Baḥth by Shams al-Dīn al-Samarqandī (d.722/1322), forthcoming.
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Being an abridgment of the Chief Sheikh, Shams al-Dīn al-Samarqandī, may God see to his recompense, Amen.
Being an abridgment of the Chief Sheikh, Mawlānā Shams al-Dīn al-Samarqandī, may God see to his recompense, for the sake of Muḥammad and his family. Praise belongs to God alone; bless and save, oh Lord, Muḥammad and his family. And praise belongs to God in every circumstance, and His blessings upon our master Muḥammad and his family, the best family.
In the name of God, Most Compassionate, Most Merciful. Praise belongs to God, Lord of the worlds. And blessings upon His messenger Muḥammad, and upon his family, all of them.
The First Inquiry: On the Talāzum (Necessary Implication) Between Two Things. And it is [also] called Mulāzama; such being an expression denoting the impossibility of the realization of one of the two [things] except upon realization of the other. Like the impossibility of knowledge without life. And what is impossible of the two1 is called a malzūm (implicans), and the other2 a lāzim (implicatum).
Furthermore: if the impossibility pertains to both sides, it is called coequal necessary implication (mulāzama musāwiya). But if it pertains [only] to one side, it is called general [necessary implication] ([mulāzama] ʿāmma). Its sign is that one of the two [things] is always realized upon assumption of the other. As in His saying, Most High: «If there were, in [heaven and earth], gods besides God, then [heaven and earth] would have been corrupted» [Q.21:22].1 And that which is determinatively assumed of the two2 is a malzūm (implicans), and what is realized3 is a lāzim (implicatum).
1 Cf. al-Kīlānī, Sharḥ (Protocol, §10.28).
3 I.e., the corruption of heaven and earth.
1 Meaning: the term malzūmiyya is attached as genitive construct to the malzūm, and the prepositional lām added to the lāzim. Presumably, one would say: “the malzūmiyya of knowledge for life” (ملزومية العلم للحيوة).
1 That is, neither the lāzim (corruption) nor the malzūm (other gods) actually exist, but the necessary implication (mulāzama) between them exists nevertheless.
Section. And the rule (ḥukm) for mulāzama is that there necessarily follows from the existence of the malzūm the existence of the lāzim, for certain, and from the nonexistence of the lāzim the nonexistence of the malzūm, likewise [for certain]. Otherwise, the malzūm would be something realized without the lāzim; and it is absurd that it be so, since the malzūm is [by definition] such as is impossible without it.
And, for that reason, denial (manʿ) of the lāzim is invalid upon existence of the malzūm,1 even if the malzūm is impossible in its essence—that is, belonging to such as whose existence is inconceivable, like “the [other] gods.” Likewise regarding nonexistence of the malzūm upon nonexistence of the lāzim,2 even if the lāzim is necessary [of existence]—that is, belonging to such as whose nonexistence is inconceivable, like [God] the Necessary by way of Essence (wājib bi’l-dhāt). For He is a lāzim for the existence of the possible thing (mumkin).
1 NB: this constitutes an affirmation of the modus ponens: p→q; p; ∴ q.
2 That is, denial (manʿ) of the malzūm’s nonexistence when the lāzim is nonexistent is likewise invalid; which constitutes an affirmation of the modus tollens: p→q; ¬q; ∴ ¬p.
1 NB: assuming (1) that the malzūm exists because the lāzim exists, or (2) the lāzim doesn’t exist because the malzūm doesn’t exist, would constitute the formal fallacies of (1) affirming the consequent (p→q; q; ∴ p), and (2) denying the antecedent (p→q; ¬p; ∴ ¬q).
2 NB: in modern propositional logic, neither assuming affirmation of antecedent upon affirmation of consequent nor denial of consequent upon denial of antecedent is fallacious for the material equivalence of the biconditional.
Section. And, pertaining to the rule (ḥukm) for mulāzama, is that one of two things follows necessarily from its entailment (luzūm), such being either the existence of the lāzim or the contradictory (naqīḍ) of the malzūm.1 Otherwise, the disaccompaniment (takhalluf) of the lāzim from the malzūm follows of necessity, or uncertainty with regard to the lāzim or the contradictory (naqīḍ) of the malzūm.
1 NB: this is consonant with the rule of equivalence called material implication in modern propositional logic: (p→q) :: (¬p ∨ q).
Section. And the converse (ʿaks) of mulāzama is among its implicata (lawāzim); which is that the nonexistence of the lāzim be made a malzūm for the nonexistence of the malzūm.1 As when it is said that “human” is a malzūm for “animal,” so nonexistence of “animal” is a malzūm for the nonexistence of “human.” Just as we have said: From the nonexistence of the lāzim there necessarily follows the nonexistence of the malzūm.
1 NB: this rule, identified elsewhere as ʿaks al-naqīḍ, is consonant with the rule of equivalence called transposition in modern propositional logic: (p→q) :: (¬q→¬p).
Section. The malzūm of the malzūm is a malzūm, even if it multiplies further.1 Like, for example, the "rationally-articulate" (nāṭiq). For just as it is a malzūm for “human,” and “human” is a malzūm for “animal,” so does it necessarily follow that “rationally-articulate” be a malzūm for “animal.” Since “animal” must always be realized upon realization of “rationally-articulate,” via intermediacy of the realization of “human” upon its realization, likewise [always].
1 NB: this constitutes an affirmation of the hypothetical syllogism: (p→q); (q→r); ∴ (p→r).
1 That is, it is not the case that: (p→r); (q→r); ∴ (p→q).
Section. Furthermore, the negator (al-munāfī) of the lāzim is a negator of the malzūm.1 And “the negator” of something is an expression denoting such as never at all combines with that thing—be it a contradictory (naqīḍ) or a contrary (ḍidd). For the two contradictories are such as never combine, and are never together removed. Like existence and nonexistence. And as for the two contraries, they are such as never combine, but might be together removed. Like blackness and whiteness.
1 That is, if it is the case that (p→q), then whatever should result in the negation of q (e.g., the presence of its contradictory) must result also in the negation of p, in consonance with the modus tollens.
1 That is to say: neither lāzim nor malzūm are negated.
2 That is, by operation of the modus tollens.
1 NB: assuming negation of the lāzim due to negation of the malzūm would constitute the fallacy of denying the antecedent p→q; ¬p; ∴ ¬q.
1 As explained in §§13-14.
Section. Nor is it possible that something be a malzūm for both something and for what negates it, whether such is a contradictory (naqīḍ) or a contrary (ḍidd).1 Otherwise, it would be a negator of the malzūm—since the negator of the lāzim is a negator of the malzūm.
1 In other words, if it is the case that (r→¬q), then it cannot be the case that both (p→q) and (p→r), since this would result in both q and ¬q being simultaneously the case upon assumption of p.
1 In other words, if it is the case that (r→¬p), then it is indeed possible that both (p→q) and (r→q) be the case, so long as r is not the contradictory of p. Note that blackness and whiteness are contraries, not contradictories, as explained in §13.
1 It cannot be that both (p→q) and (¬p→q) are the case, because, by the rule of transposition, (p→q) is equivalent to (¬q→¬p), and (¬p→q) is equivalent to (¬q→p), which would result in both p and ¬p being simultaneously the case upon assumption of ¬q. In other words, ¬q would be a malzūm for both p and its contradictory ¬p, which, as made explicit in §18, is not possible.
1 This description is consonant with the modus tollendo ponens: [(p ∨ q); ¬p; ∴ q] or [(p ∨ q); ¬q; ∴ p]. That is, when it is the case that (p ∨ q), then the negation of p will be a malzūm for the affirmation of q—i.e., (¬p→q)—and the negation of q will be a malzūm for the affirmation of p—i.e., (¬q→p).
1 That is, adherence to one rule or the other is comprehensive, thus constituting a consensus (in fact a composite consensus, or ijmāʿ murakkab) that there is no third option (and that this is a true disjunction). Cf. §26, below, where disjunction is confirmed by way of immediate necessity (ḍarūra), rather than via consensus.
2 Which is to say, either W (zakāt is obliged for Women’s jewelry) or C (zakāt is obliged for Children’s property) is a lāzim, since if it is the case that (W ∨ C), then it is the case that either (¬W→C) or (¬C→W).
1 In other words, ¬W is impossible without realization of C, and ¬C is impossible without realization of W; and when something is impossible without realization of something else, it means (by immediate necessity) that that something is a malzūm for that something else, which is its lāzim—thus: (¬W→C) or (¬C→W) must be the case.
1 In other words, if (¬W ∨ ¬C) is unqualifiedly the case, then either C (i.e., ¬¬C) is confirmed upon confirmation of ¬W, or W (i.e., ¬¬W) is confirmed upon confirmation of ¬C. Alternately, we may read §24 as describing the implications of (¬p ∨ ¬q), which we know, by way of De Morgan’s Law, to be equivalent to ¬(p ∧ q). Thus §24 would be the counterpart to §21, i.e., consonant with the modus ponendo tollens: ¬(p ∧ q); p; ∴ ¬q. Or, as indicated in §24: [(¬p ∨ ¬q); p; ∴ ¬q] or [(¬p ∨ ¬q); q; ∴ ¬p]. That is, when it is the case that (¬p ∨ ¬q), then the negation of ¬p (equivalent to the affirmation of p) will be a malzūm for the affirmation of ¬q, and the negation of ¬q (equivalent to the affirmation of q) will be a malzūm for the affirmation of ¬p.
1 In other words, use of the descriptor “unqualifiedly” (muṭlaqan) assures exclusion of one disjunct (p) when the other (q) is already known to be confirmed; for in such a case, it could not be that the negation of p is a malzūm for the affirmation of the presumed lāzim q. Rather, since q is already confirmed, it would, presumably, be a malzūm for the negation of p. Describing the confirmation of one of the two disjuncts as “unqualified” preempts this problem.
1 That is, if it is the case that (p ∨ q ∨ r) unqualifiedly, then ¬p→(q ∨ r); and ¬q→(p ∨ r); and ¬r→(p ∨ q).
1 Meaning, negation of universal inclusion of nonexistence would be a malzūm for either existential separation or universal inclusion of existence. The claim in §27 is that, for any two things (at any one time), it must be that either (1) one exists while the other does not; (2) they both exist together; or (3) they are both nonexistent together. And this is a true, tripartite disjunction.
And likewise: negation of the first and the second is a malzūm for realization of the third; and negation of the second and third a malzūm for realization of the first; and negation of the first and third a malzūm for realization of the second, just as we have determined.1 And so we would say with regard to one of four things, and more.
1 That is, if it is the case that (p ∨ q ∨ r) unqualifiedly, then (¬p ∧ ¬q)→r; and (¬q ∧ ¬r)→p; and (¬p ∧ ¬r)→q.
1 That is, when the realization of p entails the negation of q, it cannot be that p is the malzūm of q, since implication requires that p and q be inseparable. Any observed or consequent separation of malzūm from lāzim (or madār from dā’ir) is called takhalluf. Cf. other instances of takhalluf in §§9, 54, and 56.
The Second Inquiry: On the Tanāfin (Mutual Negation) Between Two Things. And it is [also] called Munāfā; such being an expression denoting the nonexistence of conjunction between the two [things] in a single receptacle at a single time.
1 That is, neither the existence nor the nonexistence of two contradictories can coincide in the same thing at the same time.
1 That is, the existence of two contraries cannot coincide in the same thing at the same time, whereas their nonexistence can.
1 In other words, when there is the first type of tanāfin between x and y, exactly one of either x or y must be nonexistent—otherwise they would coincide in existence, which is the very contradictory of tanāfin in existence. The same holds true for the second type.
1 In other words, when there is the first type of tanāfin between x and y, exactly one of either x or y must be existent—otherwise they would coincide in nonexistence, which is the very contradictory of tanāfin in nonexistence. The same holds true for the third type.
1 It can never be that there exist both gods besides God and corruption of heaven and earth, simply because both are negated.
2 “The possible thing” being the realization of one of the two rulings. In brief, this mode of non-specified negation of one of the two rulings entails a necessary implication (talāzum), just as we saw in §22 with the “unqualified” confirmation of one of two rulings. Here, the specific realization of W (zakāt is obliged for Women’s jewelry) would become a malzūm for negation of C (zakāt is obliged for Children’s property)—i.e., (W→¬C); and specific realization of C would be a malzūm for the negation of W—i.e., (C→¬W). But W and C can never coincide, due to the composite consensus that there is no zakāt on the young girl’s jewelry.
And this is because when it is not known which one is negated, it is possible that “this” [p] be realized due to the allowance that “that” [q] is the one negated, and likewise [for] “that” [q]1 —as opposed to the first two modes,2 wherein such does not follow necessarily for either.
1 I.e., it is possible that q be realized due to the allowance that p is the one negated.
2 I.e., those described in §§36-37.
1 In other words, in the first mode described in §36, it is not possible that which is realized and which negated remain ambiguous—there is no “possibly this” or “possibly that” because both “this” and “that” are already known to be negated, and so realization of either would be absurd, and that absurdity would entail another: realization of its known-to-be-negated disjunct.
1 In the second mode described in §37, it is not possible that which is realized and which negated remain ambiguous, since one is already known to be negated, and its realization would therefore be absurd.
1 In the third mode described in §38, it is indeed possible that which is realized and which negated remain ambiguous, since either one is confirmed along with the negation of its counterpart.
2 A possible reading of this closing sentence is that when there are three mutual negators the third mode is not safe from absurdity, for there would be no simultaneous elimination of the possibility that two mutual negators conjoin upon confirmation that a third is negated.
1 Such being the ownership (milk) of the example.
2 Such being the unconditional sale (bayʿ muṭlaq) of the example.
Section. And the madāriyya might be in existence and in nonexistence, in that the dā’ir always exists upon existence of the madār, and it likewise [always] does not exist upon its nonexistence. Like the madāriyya of illicit sexual activity (zinā) by one with licit sexual access (al-muḥṣan) for obligation of the stoning penalty (rajm).1 And this sort of madāriyya is called generating (ījād).
1 That is, obligation of stoning always exists whenever zinā of the muḥṣan exists, and obligation of stoning is always nonexistent whenever zinā of the muḥṣan does not exist.
1 That is, ownership always exists whenever sale exists, but ownership is not always nonexistent whenever sale does not exist (since ownership may be occasioned by other things besides sale).
And [the madāriyya] might be in nonexistence but not in existence, in that it is the opposite way around.1 Like the madāriyya of ritual purity (ṭahāra) for the allowance of the prescribed prayer (ṣalāt).2 This sort of madāriyya is called "conditional" (sharṭiyya), and its madār and its dā’ir a condition (sharṭ) and a conditioned thing (mashrūṭ).
1 That is, the dā’ir always does not exist upon nonexistence of the madār, but it does not always exist upon its existence.
2 That is, allowance of prayer always does not exist whenever ritual purity does not exist, while allowance of prayer does not always exist whenever ritual purity does exist (since some other condition besides ritual purity might be lacking).
Section. And what you have learned of rules (aḥkām) for talāzum, such run the same course in this domain, since the madār in the first [type of] madāriyya is [both] a malzūm and a lāzim.1 And in the second [type]: a malzūm.2 And in the third [type]: a lāzim.3 So know this.
1 In the example (§44) for the first type of madāriyya (in existence and in nonexistence), the madār O (Obligation of stoning) is both a malzūm and a lāzim for the dā’ir Z (Zinā of the muḥṣan); i.e., it is necessarily the case that (O→Z) and (Z→O).
2 In the example (§45) for the second type of madāriyya (in existence not in nonexistence), the madār S (Sale) is a malzūm for the dā’ir O (Ownership); i.e., it is necessarily the case that (S→O), but it is not necessarily the case that (O→S).
3 In the example (§46) for the third type of madāriyya (in nonexistence not in existence), the madār R (Ritual purity) is a lāzim for the dā’ir A (Allowance of prayer); i.e., it is necessarily the case that (A→R), but it is not necessarily the case that (R→A).
Section. It is not possible that the madār be multiple in the first [type of] madāriyya—unless one of the two madārs is a madār for its companion, in existence and in nonexistence.
That is because when it is multiple and there is no madāriyya between the two [madārs], there necessarily follows a conjunction of two contradictories (ijtimāʿ al-naqīḍayn)—such being [both] the existence and nonexistence of the dā’ir.
And this is because when one of the two is not a madār for its companion, in existence and in nonexistence, existential separation (iftirāq) between the two things is realized—just as negation of the existential separation between two things is a malzūm for the madāriyya. And when it is thus, existence of the dā’ir necessarily follows due to realization of one of the two madārs, and its nonexistence [also necessarily follows] due to nonexistence of the other—as opposed to when one of the two [madārs] is a madār for the other.
For [in this latter case] it is possible that [the madār] be multiple, since it is not possible that one of the two be realized without its companion, and thus no absurdity (muḥāl) is entailed.
Likewise, it is possible that [the madār] be multiple in the second and third [types of madāriyya], unqualifiedly (muṭlaqan). Like [the madāriyya of both] gift and sale for ownership, and [the madāriyya of both] ritual purity and facing the qibla for the allowance of prayer.
Section. Furthermore, when something [x] is not a madār for something [y] in [both] existence and in nonexistence, but might be a madār for it in either existence or in nonexistence, disaccompaniment (takhalluf) necessarily follows in nonexistence. That is, it follows necessarily that the dā’ir [y] be realized upon nonexistence of the madār [x], overall.
Otherwise, it [x] would be a madār in [both] existence and nonexistence, while the operative assumption is the opposite. And when it is thus, the dā’ir is realized in reality (fi’l-wāqiʿ)—due to its realization upon both assuming the existence of the madār and its nonexistence—in the realization of one of the two operative assumptions in reality.
But as for when it is a madār in nonexistence, (takhalluf) necessarily follows in existence. For in such a case nonexistence of the dā’ir is realized in reality, as we have determined.
It was completed, in praise of God and by His grace, on Tuesday forenoon, 28 Jumādā I, one of the months of the year 1173 (17 Jan. 1760) of the Prophetic Hijra—upon its originator [Muḥammad] be the most excellent peace and blessings—in the hand of the one most desperately in need of his Mawlā, Aḥmad b. Muḥammad b. ʿAbd al-Hādī Qāṭin, may God forgive them.1 Amen.
1 Aḥmad b. Muḥammad b. ʿAbd al-Hādī, known as Ibn Qāṭin (1118-1199 / 1706-1785) was a famed Yemeni scholar: biographer, traditionist, and qāḍī. Ziriklī lists some of his works, and provides a sample ownership statement in his hand (Aʿlām, vol. 1, p. 244, s.v. “ابن قاطن”).
It was collated with the original from which it was transcribed.
And so this writing is completed, by the grace of God, the Almighty, the All Giving. The completion of its copying was on Wednesday, 27 Rabīʿ I, of the months of the year 876, in accordance with the Sunna (22 Sept. 1471). And may [God’s] peace and blessings be upon our master Muḥammad and his family.
It was collated with the original.
It was collated a second time (?), and glosses added (?), and [???]. And the praise is due to God, Lord of the Worlds, on 27 Rabīʿ II of the year 879, in accordance with the Sunna (10 Sept. 1474). Oh God forgive me and have mercy on me, oh Lord.

References: §10
 §13
 §18
 §26
 §24
 §24
 §21
 §24
 §27
 §22
 §36
 §37
 §38