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Argumentation and Arabic Philosophy of Language

On the Logical Machinery of Post-Classical Dialectic: The Kitāb ʿAyn al-Naẓar of Shams al-Dīn al-Samarqandī (d. 722/1322)

Sur la machinerie logique de la dialectique postclassique : le Kitāb ʿAyn al-Naẓar de Shams al-Dīn al-Samarqandī (m. 722/1322)
Walter Edward Young

Résumés

Le genre post-classique (ou post-Avicennien, post-Rāzien) des « protocoles pour l'enquête et la discussion dialectiques » (ādāb al-baḥth wa-l-munāẓara) détient ses origines plus proches dans la célèbre Risāla de Shams al-Dīn al-Samarqandī (m. 722/1322). L'essentiel de ses conceptions et de sa méthodologie consiste cependant à rationaliser et à universaliser la dialectique plus strictement juridique (jadal / khilāf) de son maître Burhān al-Dīn al-Nasafī (m. 687/1288) ; et s'appuie à son tour, sur la dialectique hautement logicisée de Rukn al-Dīn al-ʿAmīdī (m. 615/1218) et de son maître Raḍī al-Dīn al-Nīsābūrī (m. 617/1220). Au cœur des méthodes de cette lignée, et reportées par al-Samarqandī dans l'ādāb al-baḥth universel, se trouvent trois relations logiques préservant la vérité, essentielles à l'entreprise dialectique de recherche de la vérité : l'implication (talāzum / mulāzama), la négation mutuelle ou exclusion (tanāfin / munāfā), et la concomitance causale (dawarān). L'élaboration pratique de ces relations révèle une logique en action, ou une logique dialogique prémoderne pour vivre la praxis de la dispute. En réalité, ces relations étaient si critiques pour l'entreprise dialectique qu'al-Samarqandī a consacré tout un traité spécialisé à résumer leurs caractéristiques et règles déterminantes, le nommant à juste titre ʿAyn al-Naẓar, ou « puits de l'investigation rationnelle ». Dans cet article, et en m'appuyant sur une édition critique numérique récemment publiée, je présenterai un aperçu analytique de ces relations logiques fondamentales telles que présentées dans le ʿAyn al-Naẓar. Par la suite, j'aborderai un certain nombre de points d'intérêt dans ce texte, regroupés sous six thèmes : le potentiel d'avancement transdisciplinaire ; les notions en développement discursif ; les formulations significatives ou uniquement contributives ; particularités du contenu ; les signes d'un agenda universaliste en évolution ; et la preuve que le ʿAyn al-Naẓar a été conçu comme un aide-mémoire pour le contestataire actif.

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Texte intégral

A summary version of this paper was first presented at the Islamic Philosophy Conference, Harvard University, 20-21 April 2019, organized by Aaron Spevack, where it received a number of helpful comments. A significant amount of contributing research (including the inception of the digital critical edition-translation of the ʿAyn al-Naẓar) was completed as a visiting fellow at the Käte Hamburger Kolleg: Dynamics in the History of Religions Between Asia and Europe (Volkhard Krech, PI), 2015-2016, Ruhr-Universität Bochum. Special thanks are due to Frederik Elwert (Digital Humanities Coordinator, Center for Religious Studies, RUB) for patiently seeing the digital edition through to completion in 2019. Thanks are also due to the British Library for providing access to its two manuscript witnesses of the ʿAyn al-Naẓar, and allowing me to take images of MS Or. 3730. My sincere gratitude goes to Shahid Rahman for improving this study through numerous suggestions, and for solving a number of difficult questions. Sincere thanks are especially due to Reviewer A and Reviewer B, whose comments and debates have greatly enriched my understanding of al-Samarqandī’s notion of talāzum and how best to approach it. Finally, I am much obliged to my wife, Saïs Mandjee, for helping translate the abstract into French, and for patiently encouraging me through yet another interminable project.

Introduction

  • 1 For (unfortunately brief) bio-bibliographical entries on al-Samarqandī, see: Muḥammad b. Ibrāhīm Ib (...)
  • 2 See Wilferd Madelung (1989), “Borhān al-Dīn Nasafī,” in Encyclopaedia Iranica, IV/4, 371, Available (...)

1Shams al-Dīn Muḥammad b. Ashraf al-Ḥusaynī al-Samarqandī (d. 722/1322) was a polymath known for his works in philosophized theology, logic, geometry, and astronomy. His greatest impact by far, however, was in planting the seeds of that post-classical—or, more accurately, post-Avicennan, post-Rāzian—genre of dialectical disputation theory known as the “protocols for dialectical inquiry and disputation” (ādāb al-baḥth wa-l-munāẓara).1 Too little is known of his life and career, though from clues hidden in his own writings and the marginalia of extant manuscripts, we gather that various stages unfolded in Khujand (and Transoxiana more broadly), Tabriz, and Mārdīn; from such internal indicants we know also that he was a student of the influential Ḥanafī jurist, theologian, and dialectician, Burhān al-Dīn al-Nasafī (d. 687/1288).2

  • 3 On this eastern school of juristic dialectic, see Larry Benjamin Miller (2020), Islamic Disputation (...)
  • 4 Carl Brockelmann (1996), Geschichte, vol. 1, p. 615 [orig. ed. p. 467-468], suppl. 1, p. 849. Editi (...)
  • 5 See Walter Edward Young (2019), Concomitance to Causation: Arguing Dawarān in the Proto-Ādāb al-Ba (...)

2Al-Nasafī was himself famed for continuing to develop that logicized theory of juridical dialectic (jadal, or khilāf) which appears to have emerged from the circle of Raḍī al-Dīn al-Nīsābūrī (d. 617/1220), and to have been elaborated by his students—most notably in the method of Rukn al-Dīn al-ʿAmīdī (d. 615/1218).3 Al-Nasafī’s most famed treatise in this dialectical tradition is variously titled the Muqaddima (Introduction) or Fuṣūl (Sections) fī ʿIlm al-Jadal (on the Science of Dialectic);4 and, importantly, this text was in turn the subject of a commentary (sharḥ) by Shams al-Dīn al-Samarqandī.5

  • 6 See Abdessamad Belhaj (2016), “Ādāb Al-Baḥth Wa-al-Munāẓara: The Neglected Art Of Disputation In La (...)

3Familiarity with al-Nasafī’s dialectical method (and with the logicized tradition from which it emerged) is as plain in our subject text, the ʿAyn al-Naẓar (Wellspring of Rational Investigation), as it is in al-Samarqandī’s most important and impactful contribution, the Risāla fī Ādāb al-Baḥth wa-l-Munāẓara (Treatise on the Protocols of Dialectical Inquiry and Disputation). The streamlined and universalized theory of the Risāla was the launching point for a revolution in Islamic dialectics: the birth of a new genre thereafter named the ādāb al-baḥth wa-l-munāẓara, or “protocols for dialectical inquiry and disputation.” The ādāb al-baḥth—as subsequent primary works and hosts of commentaries and glosses attest—quickly outgrew its predecessor theories, persevered as a standard madrasa discipline, and continued to develop well into modern times.6

  • 7 The same three are found, in the same order, at the start of al-Nasafī’s Muqaddima / Fuṣūl; and the (...)
  • 8 Miller offers expositions and analyses of all three logical relations, citing the ʿAyn al-Naẓar at (...)

4As for the ʿAyn al-Naẓar, it is a very succinct distillation of three logical relationships which dialecticians in this logicized tradition (going back at least to al-Nīsābūrī) deemed quintessential to a valid, truth-seeking disputation. They are: (1) entailment (talāzum / mulāzama), (2) mutual negation or exclusion (tanāfin / munāfā), and (3) causal concomitance (dawarān / mudāwara);7 and for each of these relationships al-Samarqandī provides definitions, rules and corollaries with short justificatory arguments, illustrations, and explanations—all of obvious benefit to the aspiring dialectician.8

5The ʿAyn al-Naẓar, in effect, is a blueprint for logical reasoning in dialectical action—a premodern dialogical logic for living disputation praxis. Its impact on the rational sciences of Islam—or, rather, the impact of the methodological current to which it belongs—has yet to be properly assessed; but it could only have been augmented by 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 as belonging to a species of “proto-” ādāb al-baḥth.

  • 9 The digital edition: Shams al-Dīn Muḥammad al-Samarqandī (2019), Kitāb ʿAyn al-Naẓar fī ʿIlm al-Jad (...)

6In this study, I will draw upon a digital edition of the ʿAyn al-Naẓar published in 2019 in fruitful technical collaboration with Dr. Frederik Elwert, Digital Humanities at the Center for Religious Studies, Ruhr-Universität Bochum.9 The quintessential logical relations presented in the ʿAyn al-Naẓar will first be outlined and analyzed. I will then review a number of points of interest: observations, implications, avenues for exploration, etc., under a set of six themes. These include the text’s potential for cross-disciplinary advancement; its signs that certain notions were in discursive development; its significant or uniquely contributive formulations; its peculiarities of content; its testimony to an evolving, universalist agenda; and its evident design as an aide-mémoire for the active disputant.

  • 10 See our brief comparison with a section from Ibn Sīnā’s Najāt below in the fourth theme of section (...)

7Before proceeding, there are at least two disclaimers which should be stated here. The first is that, for the most part, this is not a comparative study, though it is acknowledged that a number of outstanding questions raised during my analytical review of the ʿAyn al-Naẓar might be answered by bringing it into conversation with other texts. Projects which ought next to be undertaken include comparing the ʿAyn al-Naẓar’s formulations with those of: (1) al-Samarqandī’s own logical magnum opus the Qisṭās al-Afkār; (2) the “Samarqandian” ādāb al-baḥth—that is, al-Samarqandī’s Risāla along with its numerous commentaries and glosses; (3) the jadal / khilāf works of Burhān al-Dīn al-Nasafī and his intellectual predecessors; (4) Ibn Sīnā in various relevant works (e.g., the Jadal of the Shifāʾ);10 and (5) classics of post-Avicennan logic, like al-Kātibī al-Qazwīnī’s Shamsiyya.

8The second is that my use of modern logic symbols (here and elsewhere) should be considered an adaptation—in fact, merely a kind of shorthand for the text—not a modern analysis or back-projecting of modern logical conceptions. For example, in this study the symbol should be understood as whichever kind of conditional / implication / entailment al-Samarqandī meant by the relation of talāzum, the true nature of which is currently debated (see below) and will have to be worked out in separate and more extensive studies. That is to say, in the contexts of this study, “PQ” means only “P is an entailer (malzūm) of Q,” or “the existence of P is something which entails the existence of Q,” not “if the proposition ‘P exists’ is true, then the proposition ‘Q exists’ is true.”

The Kitāb ʿAyn al-Naẓar11

  • 11 In what follows, all references and quotations with regard to the ʿAyn al-Naẓar derive from the dig (...)

9At least so far as structure is concerned, the ʿAyn al-Naẓar is an exceedingly simple text. It is short (ca. 1,370 words), with neither preface nor conclusion, consisting only of three “inquiries” (buḥūth, s. baḥth) subdivided into “sections” (fuṣūl, s. faṣl), each simply labeled “faṣl.” The first and longest inquiry, on entailment (talāzum / mulāzama), contains about 800 words in thirteen sections; the second and shortest inquiry, on mutual negation or exclusion (tanāfin / munāfā), contains only 233 words in two sections; and the third, on causal concomitance (dawarān / mudāwara), contains 325 words in four sections.

10After an exceedingly brief and unornamented doxology (khuṭba), al-Samarqandī omits a preface entirely and launches directly into the first inquiry. This, and each subsequent inquiry, is expository in a most concise manner (as the above word-counts suggest), laying out a series of logical rules whose justificatory arguments and explanations are sometimes so brief and precise as to appear elliptical to the non-initiated. Certainly, the author presumed his audience to have already obtained a reasonable training in the rational, as well as the transmitted, Islamic sciences.

11This concision and lack of preface, in fact, obscure the author’s intentions in composing the ʿAyn al-Naẓar. However, as a simple outline of definitions and practical rules (with only the shortest of justifications and explanations), it was evidently designed for quick and ready use, perhaps even to be memorized by students and aspiring dialecticians—a premodern cheat sheet for logical disputation. In form and function, we might consider the ʿAyn al-Naẓar akin to the folding, laminated reference sheets for logic, grammar, algebra, etc., which we find in today’s university bookshops. This does not mean, however, that the ʿAyn al-Naẓar lacks innovation. On the contrary, al-Samarqandī here introduces a number of observations and rules which are found in few other treatises, if they are found at all.

The First Inquiry: On Entailment (talāzum / mulāzama)

At the start of the first inquiry, the author introduces the technical term for entailment (talāzum), along with: a synonym (mulāzama), a concise definition, its component terms, a primary typological distinction, and illustrative examples. As for the remainder of the first inquiry: although there are no headers beyond the word faṣl, and the majority of subsequent logical forms are unnamed, an underlying organizational system is evident. Supported throughout with concise justificatory arguments (invariably reductios in the modus tollens), corollary rules, illustrations, and explanations, the first inquiry proceeds from linguistic concerns to ontology-based rules of entailment (where components are treated in terms of existence and nonexistence), to rules paralleling material implication and transposition, the hypothetical syllogism, negation-based rules (where components are subjected to a negator [al-munāfī]), rules of disjunction—including tripartite disjunction—and, finally, detachment (takhalluf), which is the contradictory of entailment.

The Nature of al-Samarqandī’s Talāzum: An Ongoing Debate

  • 12 Miller also observes that talāzum is not material implication. Citing the example of talāzum provid (...)

12Before proceeding, it is important to relate an ongoing debate between two reviewers of this study, let us call them A and B, both trained logicians, which reflects the fact that pinpointing the precise nature of al-Samarqandī’s talāzum remains a matter of significant interest (and difficulty). In brief, Reviewer A holds that al-Samarqandī’s talāzum (and, more obviously, dawarān) does not express propositional relations. Talāzum holds between concepts and things, not propositions and judgments (although, of course, the former can usually be expressed as the latter). Moreover, certain of the peculiarities and absences which I have drawn attention to in a later section are in fact signs of this. That al-Samarqandī speaks in terms of the existence and nonexistence of malzūm and lāzim (and madār and dāʾir) shows that talāzum (and dawarān) are not propositional; likewise, the absence of treatment of categorical propositions or syllogisms, and of the traditional manṭiq technical terms for conditional and disjunctive propositions, mixed hypothetical syllogisms, etc., are simply because talāzum is not for propositional relations. And in consequence, talāzum should not be formulated in terms of material conditionality; it is not what modern logic calls material implication, but is in fact much closer to relevant implication.12

13Reviewer B, on the other hand, recognizing the problems of converting relations between concepts into connectives, and of formulating talāzum in terms of material conditionality, has developed a novel view on implication in the Arabic logical tradition (and in ancient and medieval logic more broadly). In his opinion, employing relevant logics, which changes structural rules in its quest to both capture content and maintain truth-functional connectives, is simply not a good idea. Rather, what Reviewer B sees in such premodern logics are functions between sets or types, which can certainly be seen as propositions; and from such functions, “relevance” yielding implications and quantifications can be produced. In this way, then, it is problematic to always take at face value al-Samarqandī’s simple expression of terms such as “human” and “horse,” which do not by themselves constitute propositions—i.e., one does not say: “If horse, then animal,” but, rather: “If something is a horse, then it is an animal.” Therefore, when al-Samarqandī says “human is a malzūm for animal” we should understand “[being a] human is a malzūm for [being an] animal” or “if it is a human, then it is an animal.”

14After further discussion with Reviewer B, I have come to agree that al-Samarqandī certainly employs different levels of analysis, switching from one to another: in one place talāzum is a relation between concepts and in another between propositions. I also agree that the question of whether his talāzum is a kind of relevance/relevant logic, or connexive logic, or something else entirely, should be left open pending further investigation. Moreover, it is generally not a good idea to start with what we have in terms of modern logic, but instead to first observe closely what we find in the works of premodern logicians and dialecticians in their own terms, and then to generate a new logic more perfectly suited to what we see.

15Not being a logician myself, my own, far simpler, understanding falls currently somewhere in between that of Reviewer A and Reviewer B. At the very least, I agree al-Samarqandī’s talāzum is primarily (if not entirely) non-propositional, and certainly not a material implication, but I wouldn’t (at this time) go so far as to consider it a precursor to relevant or type/set function implications (even if it may be profitably analyzed through these lenses). At this stage of research, therefore, I thought it best to convey the gist of both reviewers’ comments—and indeed to invite further comment—while simply rendering al-Samarqandī’s formulations as literally as possible. Similarities of form and function (with, e.g., modus ponens and modus tollens) will be addressed as “parallels,” not identities; and, as mentioned above, logic symbols are employed merely as a kind of shorthand—they are not modern analyses or back-projections of modern conceptions. Overall, this ongoing debate is an important one; considering al-Samarqandī’s mastery of several disciplines, bringing his dialectical talāzum into finer resolution should help us considerably in our quest to better understand post-classical implication-theory in logic, dialectic, theology, and legal theory alike.

Opening (§§2-3): terms, definitions, general typology

  • 13 NB: Reviewer B cautions that talāzum is more general than mere entailment, as it also includes pres (...)

16Returning to the ʿAyn al-Naẓar, its first inquiry opens (§2) by introducing the primary technical term talāzum for its subject logical relation: “the entailment between two things.”13 Its technical synonym is mulāzama—a verbal noun of the third form, implying reciprocity or mutuality—and its technical definition is: “the impossibility of the realization of one of the two [things] except upon realization of the other.” This is exemplified by “the impossibility of knowledge without life,” which further illustrates the component terms of talāzum: “what is impossible of the two” (“knowledge,” in the example) is the malzūm, or entailer; the other component (“life,” in the example) is the lāzim, or entailed. We may therefore recognize talāzum as paralleling the logical entailment expressed in modern textbooks with the conditional “if p, then q.” If there is knowledge, then there is life (p→q); if there is no life, then there is no knowledge (¬q→¬p). “Knowledge” is the malzūm, or entailer (p) and “life” is the lāzim, or entailed (q). The realization of knowledge entails the realization of life, and the realization of knowledge is impossible without the realization of life.

  • 14 Cf. Burhān al-Dīn al-Nasafī (2015), Al-Fuṣūl, in Necmettin Pehlivan and Hadi Ensar Ceylan, “Ādābu’l (...)
  • 15 This verse’s formula might be described as an enthymemic modus tollens, where the minor premise (th (...)

17The author now introduces an important typological distinction (§3): coequal entailment (mulāzama musāwiya), wherein “the impossibility pertains to both sides” (p is impossible without q, and q is impossible without p), is to be distinguished from general entailment (mulāzama ʿāmma), wherein the impossibility pertains to only one side (p is impossible without q).14 We may recognized the former as paralleling the biconditional, and the latter the conditional. A hallmark of the latter “is that one of the two [things] is always realized upon assumption (ʿalā taqdīr) of the other.” By way of example, al-Samarqandī brings God’s saying (Q.21:22): “If there were, in [heaven and earth], gods besides God, then [heaven and earth] would have been corrupted.”15 He now explains the components of general entailment in light of this hallmark quality: the malzūm (entailer) is “that which is assumed of the two” (i.e., “gods besides God”), while the lāzim (entailed) is “what is realized” (i.e., “corruption” in heaven and earth).

  • 16 On al-Fārābī and the biconditional, see Saloua Chatti (2019), Arabic Logic from al-Fārābī to Averro (...)
  • 17 See Walter Edward Young (2016), “Mulāzama in Action,” 346, 352-3, passim.
  • 18 See Walter Edward Young (2021), “The Formal Evolution of Islamic Juridical Dialectic: A Brief Glimp (...)

18Before moving on, two items are worthy of pointing out. The first is that the broader typology introduced here is an encouraging prompt for future investigations into post-classical distinctions between conditionality and biconditionality: how were they formulated and how were they understood?16 The second is that al-Samarqandī, as he does elsewhere, here links a notion of hypothetical or determinative “assumption” (taqdīr) to that of entailment.17 General entailment (mulāzama ʿāmma) is when the lāzim is always realized “upon assumption” (ʿalā taqdīr) of the malzūm; and the malzūm in general entailment is “what is assumed” (mā yuqaddaru). Notably, al-Samarqandī affords the notion of taqdīr no individual treatment or comment; and it seems evident (from a similar lack of exposition elsewhere) that taqdīr was something he expected his audience to readily understand.18

First Faṣl (§4): proper usage of entailment-relevant terms

19The first faṣl (§4) is simply a linguistic directive for properly formulating certain terms of the entailment relation, as exemplified by components of the life-knowledge illustration. In short, we learn that one should say “the entailment (mulāzama), or entailed-ness (lāzimiyya), of life for knowledge” (attaching mulāzama or lāzimiyya to the lāzim in a genitive construction [iḍāfa], and marking the malzūm with the preposition li-), and “the entailer-ness (malzūmiyya) of knowledge for life” (attaching malzūmiyya to the malzūm in a genitive construction [iḍāfa], and marking the lāzim with the preposition li-). That is, with the standard modern variables, the entailment or entailed-ness of q for p, and the entailer-ness of p for q.

Second and Third Fuṣūl (§§5-8): ontology-based rules

20In the second and third fuṣūl, however, al-Samarqandī begins laying down the foundational norms of implicative inference. These are what might be called “ontology-based” rules of entailment. That is, the valid forms of inference to be employed (and the invalid forms to be avoided and critiqued), along with their justificatory arguments, are all formulated in terms of the existence (wujūd) and nonexistence (ʿadam) of malzūm (entailer) and lāzim (entailed).

21The first and most general rule betrays the subtlety of epistemological and ontological theorizing which produced it. “The existence of mulāzama,” al-Samarqandī tells us, “considered in abstraction, as in itself it is (min ḥaythu hiya hiya), requires neither the existence of the lāzim nor the existence of the malzūm.” Like many other rules in the ʿAyn al-Naẓar, this rule is next supported by an argument in the form of a reductio, expressed as an enthymemic modus tollens; and, unsurprisingly, it refers back to the Qurʾānic example from §3. Were it not so, the author tells us, mulāzama would not be realized without its lāzim and malzūm—and yet it has been, as in the entailment of (q) the corruption of heaven and earth from (p) gods besides God. In other words, neither the entailed “corruption” nor the entailer “other gods” actually exist, but the entailment between them, considered in abstraction, exists nonetheless (and on the highest authority).

  • 19 On a related controversy (including al-Samarqandī’s input, from his Qisṭās) see Khaled El-Rouayheb (...)
  • 20 I suspect this indicates that this sort of unreal mulāzama exists “in the thing-itself” (fī nafs al (...)

22This section is of some interest as an interface between dialectical theory and philosophical discourse. At stake is just how hypothetical a mixed hypothetical can be, and whether or not valid inferences can be made with unreal propositions of the sort which do not—or even cannot—exist.19 Al-Samarqandī’s answer, grounded in an authoritative—indeed, divinely dictated—example, is that they can. Just what kind of existence such a mulāzama enjoys is not stated directly, but al-Samarqandī provides a hint by specifying it is mulāzama “considered in abstraction, as in itself it is” (min ḥaythu hiya hiya).20

23Broader ontology aside, it is in the third faṣl that al-Samarqandī begins to express what we would recognize as the familiar forms of propositional logical inference—though maintaining throughout the vocabulary of entailment (talāzum, mulāzama, malzūm, lāzim, etc.) Notably, neither here, nor elsewhere in the ʿAyn al-Naẓar or the Risāla fī Ādāb al-Baḥth, do we encounter the technical terms with which these relations, forms, and rules are usually expressed in the logic texts. And this is despite the fact that al-Samarqandī was an established logician, a fact amply demonstrated in his logical magnum opus, the Qisṭās al-Afkār fī Taḥqīq al-Asrār, and his self-commentary on the same. Significant further investigation is required before any positive pronouncement may be made as to why this is so. We may safely conjecture, however, that it is simply a mark of the disciplinary contexts in which al-Samarqandī developed his dialectical theory. He was expanding and refining the primarily juristic dialectic expounded by his teacher Burhān al-Dīn al-Nasafī, which emanated ultimately from the circle of Raḍī al-Dīn al-Nīsābūrī; and it is in terms of talāzum / mulāzama that this theory is expressed, not the conjunctive / disjunctive conditional (sharṭiyya muttaṣila / munfaṣila), or the repetitive syllogism (qiyās istithnāʾī), or the antecedent (muqaddim) and consequent (tālī), etc., of Avicennan and post-Avicennan logic texts. Al-Samarqandī’s mastery of these logic-text terms is not to be questioned, and amply demonstrated in the Qisṭās; but, for whatever reason, he eschews them in his works on dialectical theory.

  • 21 That is, if it is not the case that existence of the malzūm entails existence of the lāzim and none (...)

24Thus, maintaining an ontological focus on existence (wujūd) and nonexistence (ʿadam), and an implicative vocabulary of entailer (malzūm) and entailed (lāzim), al-Samarqandī brings in §6 a set of rules paralleling the modus (ponendo) ponens (p→q; p; q) and modus (tollendo) tollens (p→q; ¬q; ¬p), but expressed as follows: “the rule (ḥukm) for mulāzama is that from the existence of the malzūm [p] the existence of the lāzim [q] is entailed, with certainty (qaṭʿan), and from the nonexistence of the lāzim [¬q] the nonexistence of the malzūm [¬p] likewise [is entailed with certainty].” By way of brief justification, he argues: “Otherwise, the malzūm would be something realized without the lāzim; and it is absurd that it be so, since the malzūm is what is impossible without [the lāzim].” Note this argument is itself in the modus tollens (like all the ʿAyn al-Naẓar’s justifications), and its minor premise (negating the consequent of its major premise) is supported by the definition of malzūm from §2.21

  • 22 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, Albany, State University of New (...)
  • 23 “Other gods” being the malzūm for “corruption” in the Qurʾānic example. Thus, even though the exist (...)

25Working from the implications of this definition, al-Samarqandī next (§7) tackles a series of invalid forms—fallacies we may easily match to their parallels in propositional logic. Due to the impossibility of the malzūm without the lāzim, he says, “denial (manʿ) of the lāzim is invalid upon existence of the malzūm”—which parallels the fallacy of ponendo tollens (p→q; p; ¬q).22 This is fortified by an ontological expansion, being the case “even if the malzūm [p] is impossible in its essence (dhāt)—that is, belonging to such as whose existence is impossible, like ‘[other] gods.’”23 Put differently, the fallacy of ponendo tollens remains fallacious even when the antecedent is in essence impossible—the hypothetical assumption of that impossible antecedent’s existence will nevertheless assure that the denial of its consequent is fallacious.

  • 24 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 376, Table 28.1.
  • 25 Thus, even though the nonexistence of God is in reality impossible, it is nevertheless incorrect to (...)

26There immediately follows a parallel to the fallacy of tollendo ponens (p→q; ¬q; p),24 whereby denying nonexistence of the malzūm when the lāzim does not exist is also invalid. This, too, has its ontological expansion, being the case “even if the lāzim [q] is necessary [of existence]—that is, belonging to such as whose nonexistence is impossible, like [God] the Necessary by Essence (wājib bi-l-dhāt), for He is a lāzim for existence of [the malzūm, p] the possible thing (mumkin).”25 Again put differently, the fallacy of tollendo ponens remains fallacious even when the consequence is in essence necessary—the hypothetical assumption of that necessary consequent’s nonexistence will nevertheless assure that the denial of its antecedent’s nonexistence is fallacious.

  • 26 Khaled El-Rouayheb (2009), “Impossible Antecedents.”

27These ontological expansions constitute further interfacings between dialectical and logical-philosophical theory. Al-Samarqandī’s insistence that the ponendo tollens remains fallacious “even if the malzūm is impossible in its essence” relates to the “impossible antecedents” discourse explored by Khaled El-Rouayheb in an important study,26 and the principle that “it is possible that the absurd (muḥāl) entail the absurd” (see §40 at the end of the second inquiry, below). The illustration of Q.21:22 persists as an example of this rule precisely because, for the ʿAyn al-Naẓar’s intended audience, the existence of other gods is a clear absurdity the hypothetical assumption of which is nevertheless entertained (for the sake of arguing against it) by no less an authority than God Himself. At the very least, these ontological expansions or corollary rules in §7 extend the §5 rule that “the existence of mulāzama, considered in abstraction, as in itself it is, requires neither the existence of the lāzim nor the existence of the malzūm.” For saying “even if the malzūm is impossible in its essence” and “even if the lāzim is necessary [of existence]” is asserting that mulāzama still holds when one employs purely hypothetical malzūms (e.g., existence of other gods) and lāzims (e.g., nonexistence of God the Necessary), which cannot occur in reality.

28Al-Samarqandī closes the third faṣl (§8) with what may easily be matched with the fallacies of affirming the consequent (p→q; q; p) and denying the antecedent (p→q; ¬p; ¬q), saying: “existence of the malzūm is not entailed from existence of the lāzim, nor is nonexistence of the lāzim entailed from nonexistence of the malzūm.” It is important, however, that he marks an exception to both of these: “coequal entailment” (mulāzama musāwiya), which we will recall was opposed to “general entailment” (mulāzama ʿāmma) at the start of the first inquiry. Coequal entailment is exempt from these fallacies “since in it the lāzim is like the malzūm.” Again, al-Samarqandī provides material for investigating premodern formulations of biconditionality. Notably, 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.

Fourth and Fifth Fuṣūl (§§9-10): rules paralleling equivalence rules of material implication and transposition

  • 27 Thanks to Reviewer B for pointing out that al-Samarqandī’s formulae here do not parallel full equiv (...)
  • 28 Irving M. Copi, Carl Cohen, & K. D. McMahon (2016), Introduction to Logic, 14th ed., London, Routle (...)
  • 29 In short, if I understand correctly: (1) if p exists q necessarily exists, (2) if p does not exist (...)

29The fourth and fifth fuṣūl (§§9-10) lay out rules which parallel—in part, if not in full—what are known in propositional logic as rules of equivalence, along with justifications and illustrations.27 Al-Samarqandī first (§9) parallels the equivalence rule of material implication, indeed linking implication to disjunction, by saying: “From the entailment (luzūm) [of mulāzama], one of two things is entailed: either the existence of the lāzim or the contradictory (naqīḍ) of the malzūm.” Couched as the entailment of an entailment (p→q)→(q ¬p), this clearly parallels the equivalence rule of material implication, but falls short of the full equivalence rule of implication (p→q) :: (¬p q)28 by not expressing the complementary (q ¬p)→(p→q). Regardless, al-Samarqandī justifies this rule with a reductio, for if it were not so, “a detachment (takhalluf) of the lāzim from the malzūm would be entailed, or an uncertainty (taraddud) with regard to the lāzim or with regard to the contradictory of the malzūm.”29

  • 30 Irving M. Copi, Carl Cohen, & K. D. McMahon (2016), Introduction to Logic, p. 389; Galen A. Foresma (...)
  • 31 See Shams al-Dīn Muḥammad al-Samarqandī (2014), Qisṭās al-Afkār fī Taḥqīq al-Asrār [= Kıstâsu'l-Efk (...)

30Similarly, we may recognize a parallel to the equivalence rule of transposition when al-Samarqandī notes (§10): “the converse (ʿaks) [of mulāzama] is among its entailments (lawāzim); namely, that the nonexistence of the lāzim be made a malzūm for the nonexistence of the malzūm.” Again, phrased as the entailment of an entailment (p→q)→(¬q→¬p), this clearly parallels transposition, but falls short of the full equivalence rule of transposition (p→q) :: (¬q→¬p)30 by not expressing the complementary (¬q→¬p)→(p→q). Note that here he uses the simple term “converse” (ʿaks) to convey transposition; and below (§20) he uses the passive form VII verbal-noun inʿikās to express the same. Elsewhere, however, this rule is normally more completely identified as “converse of the contradictory” (ʿaks al-naqīḍ).31 Whatever the reason for abbreviation, he does here provide illustration. It is like when one says “human is a malzūm for animal, so the nonexistence of animal is a malzūm for the nonexistence of human.” Put differently, if it is the case that “if it is a human, then it is an animal” (p→q), then it is the case that “if it is not an animal, then it is not a human” (¬q→¬p). Ultimately, al-Samarqandī justifies this transposition by linking it back to the modus tollens rule in §6, for just as he said there: “from nonexistence of the lāzim is entailed nonexistence of the malzūm.” Thus, the very least which may be said of these sections is that they provide material for investigating early formulations, or even prefigurations, of the rules of equivalence known today as material implication and transposition.

Sixth Faṣl (§§11-12): pure hypothetical syllogisms

  • 32 The pure hypothetical is typically formulated today as (p→q), (q→r) (p→r).
  • 33 That is: if it is rationally articulate, then it is a human; and if it is a human, then it is an an (...)

31Though again without naming them as such, in the sixth faṣl al-Samarqandī parallels the pure hypothetical syllogism and a related fallacy. First (§11), he notes that “the malzūm of the malzūm is a malzūm, even if it multiplies [further],” thus asserting the validity of something like pure hypothetical syllogisms of any length.32 He illustrates this with “what is rationally articulate” (nāṭiq), which, being a malzūm for human, and human being a malzūm for animal, must also be a malzūm for animal.33 This is supported by further explanation, in that “animal must always be realized upon realization of what is rationally articulate, via the intermediacy (wāsiṭa) of the realization of human—likewise always—upon realization of [what is rationally articulate].”

  • 34 That is, it is fallacious to argue: If it is a horse, then it is an animal; and if it is a human, t (...)

32He proceeds (§12) to an interesting fallacy which is not only unnamed here, but, to my knowledge, has never received a name in traditional logic. Reviewer B, however, has identified it as a variant on the fallacy of affirming the consequent. Al-Samarqandī notes that, unlike the malzūm of the malzūm above, the malzūm of the lāzim is not a malzūm for the malzūm; that is, it is not the case that: (p→r), (q→r) (p→q). Horse, like human, is a malzūm for animal, but obviously not a malzūm for human.34 According to Reviewer B’s helpful explanation (the following is a paraphrase): this fallacy can occur when the arguer first commits the fallacy of the consequent with regard to the second premise, and then draws his conclusion from the result. That is, he argues: “If it is a horse, then it is an animal; and if it is a human, then it is an animal—thus (fallaciously) if it is an animal, then it is a human—therefore, if it is a horse, then it is a human.” That is: If A, then C; if B, then C—thus (fallaciously) if C, then B—therefore, if A then B.

33This sixth faṣl thus offers material for investigating fallacy types not commonly treated in premodern or modern logic traditions. One might ask what compelled al-Samarqandī to include it in his very concise, ultimately pragmatic outline. Was it a fallacy of common occurrence in his contexts of debate? Reviewer B again offers a cogent explanation. In paraphrase: it is plausible that a disputant could indeed, during a dialectical exchange, commit the fallacy of the consequent in the second premise and so erroneously conclude that A entails B. Moreover, if the second premise is a biconditional, then the fallacy drops away, and the conclusion (if A then B) is valid. This makes the commission of the fallacy in real dialectic all the more plausible, as a disputant would simply have to mistake the second premise as a biconditional rather than just a conditional.

Seventh through Tenth Fuṣūl (§§13-20): negation-based rules

34Throughout the seventh to tenth fuṣūl al-Samarqandī sets out a series of what might be called negation-based rules—that is, a range of valid and invalid operations, along with justificatory arguments and illustrations, all formulated in terms of negation (intifāʾ), and the negator (al-munāfī) of entailer (malzūm) and entailed (lāzim). This, we may note, represents a different approach to the preceding ontology-based rules, where these two components of entailment were formulated in terms of their existence (wujūd) and nonexistence (ʿadam). Rather, the key role in the seventh through tenth fuṣūl is played by the negator (al-munāfī), its application to malzūm or lāzim, and the overall impact this has on the mulāzama between them. In effect, al-Samarqandī is bringing the logical relation of mutual negation or exclusion (tanāfin / munāfā)—as we will see it below in the second inquiry—together with the entailment (talāzum / mulāzama) of the first inquiry, in a series of combined operations.

35He begins in the seventh faṣl by stating (§13) “the negator (al-munāfī) of the lāzim is a negator of the malzūm,” which we might express, using r as the negator, by (p→q), (r→¬q) (r→¬p). He then defines “the negator of something” (al-munāfī lil-shayʾ) as what “never at all comes together with that thing—be it a contradictory (naqīḍ) or a contrary (ḍidd)”—a definition in perfect consonance with the relation of tanāfin / munāfā as expounded in the second inquiry. Mutual negation or exclusion thus manifests in two ways: “two contradictories are such as never come together, and are never together removed,” like existence vs. nonexistence; and two contraries “are such as never come together, but might be together removed,” like blackness vs. whiteness.

  • 35 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 396-397.

36His justificatory argument (§14) for the rule formulated in §13 is not, for once, a reductio in the modus tollens, but a complex constructive dilemma in which the antecedents of the major premise are contradictories.35 In brief, either the negator of the lāzim is realized or it is not (¬r r). If not, then—as is obvious (ẓāhir)—the lāzim remains (¬r q) and nothing whatever is entailed for the malzūm. If the negator is realized, however, then negation of the lāzim occurs (r ¬q), triggering negation of the malzūm (¬q→¬p)—as is likewise obvious (by operation of the modus tollens).

37Al-Samarqandī next (§15) shows that the converse of this rule does not work, thus expressing an apparent corollary to the fallacy of denying the antecedent. That is to say, though the negator of the lāzim is a negator of the malzūm, the negator of the malzūm is not a negator of the lāzim; it is not the case that: (p→q), (r→¬p) (r→¬q). This is justified in that “negation (intifāʾ) of the lāzim is not entailed from negation of the malzūm” which compares favorably to the ontology-based expression of the fallacy of denying the antecedent we saw in §8: “nor is nonexistence of the lāzim entailed from nonexistence of the malzūm.”

38Note that a number of questions are raised by the very existence of these negation-based rules. Why is al-Samarqandī introducing them as distinct from, though obviously related to, the rules we find in the ontology-based mulāzama sections (§§5-12)? Is it that the ontology-based are more primary or axiomatic, and the negation-based secondary or corollary? What is the operative difference between nonexistence (ʿadam) of the lāzim and negation (intifāʾ) of the lāzim? Is it simply that negation of the lāzim denotes an action resulting in nonexistence of the lāzim? If so, what is the significance of shifting emphasis to that action?

39Whatever the answer to these questions, al-Samarqandī delves deeper into the implications of negation for entailment in the eighth faṣl. First (§16) he formulates a fallacy rule whereby it is impossible that the lāzim be the negator of the malzūm; that is, it cannot be the case that both (p→q) and (q→¬p). The justifying reductio is that “otherwise, the malzūm would likewise be [the lāzim’s] negator, since mutual negation / exclusion (munāfā) is from both extremes.” In other words, the munāfā of p and q (as in the definition of negator in §13, and in the second inquiry, below) is such that p and q can never come together, and so their repulsion is mutual. Likewise (§17), it is impossible that the malzūm be a negator of the lāzim; that is, it cannot be the case that both (p→q) and (p→¬q)—the justifying reductio for this parallel fallacy rule being: “otherwise, it would be a negator of itself, since the negator of the lāzim is a negator of the malzūm” (this final clause being the rule in §13, verbatim).

40The ninth faṣl (§18) presents another fallacy rule whereby “it is impossible that something be a malzūm for something [else] and what negates it, whether [the negator] is a contradictory (naqīḍ) or contrary (ḍidd).” Put differently, it cannot be that p is a malzūm for q and r [(p→q) Λ (p→r)] when r is a negating contradictory or contrary of q (r→¬q). By way of justifying reductio, al-Samarqandī notes: “otherwise, it [r] would be a negator of the malzūm [p],” supporting this with another verbatim citation of the rule in §13 (“the negator of the lāzim is a negator of the malzūm”).

41The ninth faṣl’s impossibility, however, does not necessarily hold for the lāzim in like context. In the tenth faṣl, al-Samarqandī first (§19) introduces and illustrates a parallel rule which escapes this fallacy; for it is indeed “possible that something be a lāzim for something [else] and what negates it, when [the negator] is not a contradictory (naqīḍ).” That is, it can be that q is a lāzim for p and r [(p→q) Λ (r→q)] when r as negator of p (r→¬p) is merely a contrary, not a contradictory. This is illustrated by color, which is a lāzim of both blackness and its negator: whiteness (since whiteness is not the contradictory of blackness, but merely its contrary).

  • 36 Reviewer A considers this an indication that talāzum should not be rendered as material conditional (...)
  • 37 Via the equivalence rule of transposition half-expressed in §10, it would be the case that (p→q) :: (...)

42But the fallacy holds, as is next confirmed (§20), when the negator is a contradictory. For it is “impossible that something [q] be a lāzim for something [else] [p] and its contradictory [r] only because”—and here is the justifying reductio—“if it were a lāzim, then the nonexistence of something would be a malzūm for something and its contradictory, as a proposition resulting from conversion (inʿikās), but this is not possible.” In other words, it cannot be that q is a lāzim for p and r [(p→q) Λ (r→q)] when r as negator of p (r→¬p) is a full contradictory;36 and this is because q being a lāzim for both p and r means that, via transposition (here: “conversion” [inʿikās]), not-q would be a malzūm for the contradictories not-p and not-r, and we have already seen in §18 that nothing can be a malzūm for both a thing and its negator.37

Eleventh and Twelfth Fuṣūl (§§21-28): inclusive (?) disjunction rules

  • 38 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 387, Table 29.1 (first colum (...)

43The eleventh faṣl of the ʿAyn al-Naẓar’s first inquiry tackles, with some very interesting (and challenging) explanations and illustrations, certain basic rules of disjunction, while the twelfth faṣl deals with tripartite (and larger) disjunctions. To begin with (§21), al-Samarqandī offers up a detailed rule for what we might recognize as the disjunctive modus tollendo ponens (in its two figures),38 saying:

  • 39 Note this as the solitary instance in the ʿAyn al-Naẓar of a term from the Arabic logic tradition’s (...)

If [either] one of two things is true, in an unqualified way (ṣādiqan muṭlaqan)39—in that which is affirmed (thābit) is not known, but [merely] possible—then there necessarily follows that the negation (intifāʾ) of each one, specifically designated (ʿalā al-taʿyīn), is a malzūm for the realization of its counterpart.

  • 40 That is, either figure 1: (p q); ¬p; q or figure 2: (p q); ¬q; p of the modus tollendo pone (...)

Put differently, when either p or q is truly the case (p q), then p’s negation will be a malzūm for q’s realization (¬p→q), and q’s negation will be a malzūm for p’s realization (¬q→p).40 By way of illustration, al-Samarqandī next brings (§22) a juristic example:

  • 41 In fact, the basis for this disjunction is a versatile case (we will encounter it again in §38) of (...)

It is like when one says: “One of two obligations is entailed (lāzim): either [J] the obligation of alms tax (zakāt) for women’s jewelry, or [C] the obligation [of alms tax] for children’s property; and this is by virtue of consensus (ijmāʿ).” For which of the two is affirmed is not known, based on [the principle] that every qualified legal specialist (mujtahid) both errs and hits the mark. And when it is thus, it will necessarily follow that nonexistence [of obligation of alms tax] for jewelry is a malzūm for the obligation [of alms tax] for children’s property; and nonexistence [of obligation of alms tax] for children’s property is likewise a malzūm for the obligation [of alms tax] for jewelry.41

In other words, either J or C must be the case by virtue of a compound consensus (J C), so it follows that negation / nonexistence of J would be a malzūm for the affirmation / existence of C (¬J→C), and negation / nonexistence of C would be a malzūm for the affirmation / existence of J (¬C→J). Thus, either C is a lāzim (with ¬J as malzūm), or J is a lāzim (with ¬C as malzūm), and the relation between this kind of suspended-knowledge disjunction and entailment becomes clear.

44Note that the negation (intifāʾ) in §21’s rule has been switched for nonexistence (ʿadam) in §22’s illustration. This indicates that they were deemed interchangeable—or, again, that nonexistence is simply the consequence of negation. Note also the sort of Schrödinger’s cat indeterminacy which is implied by one of two things being “true in an unqualified way” (ṣādiqan muṭlaqan), with affirmation not known (maʿlūm) but merely possible (muḥtamal). We will encounter similar contexts of suspended knowledge, along with their related disjunctive consequences, in the second and third inquiries. In the current example it results from the combination of compound consensus (limiting the range of possible rulings to either J or C) with the non-relativist principle “every mujtahid both errs and hits the mark” (assuring equal indeterminacy between them, on our part). This constitutes a noteworthy interface between legal, philosophical, and logical-dialectical theories.

45Al-Samarqandī now (§23) justifies his expression of the rule in §21. In this unqualified state of affirmation—knowing the affirmed must be one of two, but not which—negation of the first [¬p] is impossible (mumtaniʿ) without realization of the second [q], and vice versa. And, by intuitive necessity (bi-l-ḍarūra), if it is impossible (i.e., without the realization of the other), it is a malzūm. Note this also matches the very definition of mulāzama presented in §2.

  • 42 It may also be noted that by De Morgan’s Law, (¬p ¬q) is equivalent to ¬(p q). In the terse pre (...)

46Al-Samarqandī continues this concise exposition (§24) with something which may be interpreted as either a conclusion to the justification in §23, a corollary to the rule in §21, or merely a different formulation of that rule. He says: “And if nonexistence of one of the two is affirmed, in an unqualified way (thābitan muṭlaqan), then it necessarily follows that [the] other is affirmed.” We may recall that the rule in §21 was: “If [either] one of two things is true, in an unqualified way (ṣādiqan muṭlaqan)… the negation of each one… is a malzūm for the realization of its counterpart.” Thus, in §21, knowledge is suspended with regard to which disjunct is true / affirmed, whereas in §24 knowledge is suspended with regard to which is affirmed not to exist. Perhaps the latter may be considered a later state of the former, in that it subsists in a moment after an assumption of negation has been brought to §21 (but before the specific designation), and so the suspended knowledge has transformed from “which of the two exists / is true / is affirmed” to “which of the two does not exist / is false / is negated.” Whatever his purpose, al-Samarqandī seems to be saying that if the nonexistence of either J or C is the case in an unqualified way (¬J ¬C), then either the affirmation / existence of C (i.e., ¬ ¬C) will be affirmed upon affirmation of the nonexistence of J—that is: (¬J ¬C); ¬J ¬ ¬C [= C]—or the affirmation / existence of J (i.e., ¬¬J) will be affirmed upon affirmation of the nonexistence of C—that is: (¬J ¬C); ¬C; ¬ ¬J [= J]. More in consonance with §21’s formulation, we might say that when it is the case that (¬p ¬q), then the affirmation of ¬p will be a malzūm for the affirmation of q (equivalent to the negation of ¬q), and the affirmation of ¬q will be a malzūm for the affirmation of p (equivalent to the negation of ¬p).42

47There follows (§25), concluding this particular exposition, a definitional justification regarding §21’s rule.

By virtue of our saying “in an unqualified way” (muṭlaqan), there is removed [from consideration] the case of mulāzama between “one of two things” wherein it is not possible that negation of one be a malzūm for the realization of its counterpart—whether a lāzim or a malzūm—because what is affirmed of the two is known in reality, and such [i.e., “what is affirmed of the two”] is the lāzim.

In other words, al-Samarqandī’s stipulation that one of the two disjuncts be true / affirmed “in an unqualified way” (muṭlaqan) was intended to limit his treatment of disjunctive mulāzama here to the suspended knowledge type. It achieves this by excluding that kind of mulāzama wherein the affirmed disjunct—which, being “what is affirmed,” plays the role of lāzim—is already “known in reality” (as opposed to “not known, but [merely] possible” in §21). This assures that its counterpart’s negation can no longer function as a malzūm for its realization whether or not it—i.e., “what is affirmed”—was a lāzim or malzūm, as is the case in the properly unqualified disjunctive mulāzama.

  • 43 Questions to pursue include: (1) whether or not this excluded type is a corollary to the fallacy of (...)

48If we don’t know, e.g., whether J or C is the lāzim (J C), then negation of J becomes a malzūm for affirmation of C (¬J→C), and negation of C becomes a malzūm for affirmation of J (¬C→J). But if we know, e.g., that J is “what is affirmed” (and hence, the lāzim), then it can no longer be the case that negation of C becomes a malzūm for affirmation of J no matter whether J was a lāzim or malzūm. Unfortunately, al-Samarqandī does not provide us an example of this excluded type. At the time of writing it remains unclear to me how or in what contexts this would have played out, or why al-Samarqandī felt the need to justify the stipulation of “in an unqualified way” (muṭlaqan).43

  • 44 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 389, Table 29.2.

49Whether or not al-Samarqandī’s formulations in the ʿAyn al-Naẓar can yield definitive answers, this exposition in the eleventh faṣl provides an avenue for investigating whether or not he entertained any distinction between inclusive and exclusive disjunctions. At the time of writing, the evidence seems to point away from this, and towards his only entertaining exclusive disjunctions. It is true, on the one hand, that here in the first inquiry his discussion parallels only the modus tollendo ponens [(p q); ¬p; q], and not the modus ponendo tollens [(p q); p; ¬q], the latter being valid only in exclusive disjunctions;44 and it is true that the entire second inquiry is devoted to mutual negation / exclusion (with kinds of exclusive disjunction, including ponendo tollens)—opening the possibility that here in the first inquiry only inclusive disjunction is intended. On the other hand, however, al-Samarqandī never states that it is possible that both disjuncts be true / affirmed / existent as in an inclusive disjunction. Moreover, the illustrative example he selects in §22 cannot possibly be an inclusive disjunction: its suspended knowledge is the result of a “composite consensus” (ijmāʿ murakkab) that there is no alms tax for young girls’ jewelry—thus it cannot be that an inclusive “tax for jewelry or tax for minor’s property, or both” is meant, but only an exclusive “either tax for jewelry or tax for minor’s property, but not both.” We will see that the same example from §22 reappears in §38 of the second inquiry, along with a clear formulation of the disjunctive ponendo tollens (which, again, is valid only in exclusive disjunctions).

50Whatever the case may be, in the twelfth faṣl al-Samarqandī moves on, now setting out rules for tripartite disjunctions. He begins (§26) by stating a rule that if one of three things is affirmed in an unqualified way (muṭlaqan), then the negation (intifāʾ) of each [individually] is a malzūm for the realization of one of the other two. That is, if it is the case that (p q r), in an unqualified way, then ¬p→(q r); and ¬q→(p r); and ¬r→(p q). He illustrates this (§27) with a fascinating—and, it turns out, very practical—example which appears to hail, ultimately, from the juristic theory of dialectic (khilāf / jadal) in the line of Burhān al-Dīn al-Nasafī and predecessors. In brief: either “existential separation (iftirāq) between two things, or universal inclusion of existence (shumūl al-wujūd) for both, or universal inclusion of nonexistence (shumūl al-ʿadam) [for both]” is a lāzim, by intuitive necessity (bi-l-ḍarūra). Such being the case, the negation of existential separation is a malzūm for one of the two inclusions, and negation of inclusion of existence is a malzūm for either separation or inclusion of nonexistence, and inclusion of nonexistence is a malzūm for either separation or inclusion of existence.

  • 45 For an example of this tripartite distinction between iftirāq and the two shumūls in dialectical ac (...)

51Put differently, for any two things (at any one time), it must be that either (1) one exists while the other does not; (2) they are both, together, existent; or (3) they are both, together, nonexistent. And this is a true, tripartite disjunction. Note that this has a particular application in law, where it may be argued whether a ruling (ḥukm) belongs to both from a pair of correlated cases (shumūl al-wujūd), or to neither (shumūl al-ʿadam), or to one and not the other (iftirāq). That ruling (ḥukm), however, can just as easily be a judgment-assertion (also ḥukm) belonging to both, neither, or one and not the other of a pair of correlated things. Thus, we have in this shumūl-iftirāq disjunction a path for inquiring into the impact of legal reasoning on the methodology of kalām and ḥikma; and this becomes all the more promising due to the fact that this shumūl-iftirāq disjunction is encoded into the Samarqandian ādāb al-baḥth.45

52Returning to his elaboration on tripartite disjunction, al-Samarqandī (§28) posits a corollary rule that “negation (intifāʾ) of the first and the second [disjunct] is a malzūm for realization of the third; and negation of the second and third is a malzūm for realization of the first; and negation of the first and third is a malzūm for realization of the second.” That is, if it is the case that (p q r), in an unqualified way, then (¬p ¬q)→r, and (¬q ¬r)→p, and (¬p ¬r)→q. Finally, al-Samarqandī caps the discussion by affirming that these same rules also apply to quadripartite and even larger disjunctions.

Thirteenth Faṣl (§29): detachment (takhalluf)

  • 46 Cf. instances of takhalluf in §§9, 54, and 56. In §§54-55, we will encounter al-takhalluf ʿadaman, (...)

53The thirteenth faṣl, last in the first inquiry on entailment, treats takhalluf, or “detachment,” the very contradictory of entailment. Al-Samarqandī provides a formulaic expression: takhalluf is that one says “this [p] is not a malzūm for that [q] while this [p] might be realized and thus entail the negation (intifāʾ) of that [q], overall (fī l-jumla); otherwise this [p] would be a malzūm for that [q], but the operative assumption (taqdīr) was the opposite.” That is, when the realization of p entails the negation of q, it cannot be that p is the malzūm of q, since entailment requires that q (the lāzim) be inseparable from p (the malzūm). Any observed or consequent separation of lāzim from malzūm (or, as we will see in the third inquiry, of concomitant presumed effect [dāʾir] from concomitant presumed cause [madār]) is called takhalluf, detachment.46 Note that the formulaic manner in which al-Samarqandī presents takhalluf here indicates its utility as a dialectical objection. That is, we might read the above as a blueprint for how to articulate a specific kind of objection in real disputation.

54Alternately, al-Samarqandī might be saying that takhalluf is when p could be the malzūm of q, but the hypothetical assumption (taqdīr) is that either p or q must be the case (p q), which means—in exclusive disjunction only—that realization of p entails negation of q, “overall.” And, of course, when assuming if p then q (pq), p cannot be the malzūm for both q and ¬q; this would be the fallacy of ponendo tollens paralleled in §7. Therefore, once (p q) is assumed, p cannot be the malzūm of q; i.e., it cannot be that if p then q (pq). Thus, al-Samarqandī’s point may be that assuming an exclusive disjunction between the presumed malzūm and lāzim—i.e., (p q)—entails a kind of takhalluf, detachment, vis-à-vis the mulāzama between p and q.

55Table 1: Summary Outline of the First Inquiry: On Entailment (talāzum / mulāzama).

Opening (terms, definitions, general typology)

  • §2: technical term: talāzum; synonym: mulāzama; definition: “the impossibility of the realization of one of the two things except upon realization of the other;” illustration (life and knowledge); component terms: entailer (malzūm) and entailed (lāzim)

  • §3: typological distinction: coequal (musāwiya) vs. general (ʿāmma) mulāzama; hallmark of general mulāzama: “one of the two [the lāzim] is always realized upon assumption of the other [the malzūm];” illustration (Q.21:22)

First Faṣl (proper usage of entailment-relevant terms)

  • §4: proper formulations: “the mulāzama / lāzimiyya of life for knowledge;” “the malzūmiyya of knowledge for life”

Second and Third Fuṣūl (ontology-based rules)

  • §5: rule: mulāzama, considered in abstraction, can exist without existence of lāzim or malzūm; justificatory argument (exemplified by Q.21:22)

  • §6: rule: modus ponendo ponens; rule: modus tollendo tollens; justificatory argument for both

  • §7: rule: fallacy of ponendo tollens; corollary rule (even when the malzūm is in essence impossible of existence); illustration (Q.21:22); rule: fallacy of tollendo ponens; corollary rule (even when the lāzim is in essence necessary of existence); illustration (God the Necessary by essence = lāzim for existence of the possible by essence)

  • §8: rule: fallacy of affirming the consequent; rule: fallacy of denying the antecedent; exception to both: coequal mulāzama (biconditional); explanation: “the lāzim is like the malzūm

Fourth and Fifth Fuṣūl (rules paralleling material implication and transposition)

  • §9: rule: material implication; justificatory argument

  • §10: rule: transposition; illustration (human and animal); justification (§6, modus tollens)

Sixth Faṣl (pure hypothetical syllogisms)

  • §11: rule: pure hypothetical syllogism, any length; illustration (rationally articulate, human, animal); explanation

  • §12: rule: fallacy (p→r); (q→r); (p→q) [= variant on the fallacy of affirming the consequent]; illustration (horse, animal, human)

Seventh through Tenth Fuṣūl (negation-based rules)

  • §13: rule: (p→q); (r→¬q); (r→¬p); definition: the negator (al-munāfī) of something is “what never at all comes together with that thing, whether a contradictory or a contrary; definition of contradictory (naqīḍ) and illustration (existence and nonexistence); definition of contrary (ḍidd) and illustration (blackness and whiteness)

  • §14: justificatory argument for rule in §13

  • §15: rule: it is impossible that (p→q), (r→¬p) (r→¬q) (= correlate to denying the antecedent); justification (second rule of §8)

  • §16: rule: it is impossible that (p→q) Λ (q→¬p); justification via appeal to definition of mutual negation / exclusion (munāfā)

  • §17: rule: it is impossible that (p→q) Λ (p→¬q); justification via rule in §13

  • §18: rule: it is impossible that [(p→q) Λ (p→r)] Λ (r→¬q); justification via rule in §13

  • §19: rule: it is possible that [(p→q) Λ (r→q)] Λ (r→¬p) [when r and p are only contraries]; illustration (color, blackness, whiteness)

  • §20: rule: it is impossible that [(p→q) Λ (r→q)] Λ (r→¬p) [when r and p are contradictories]; justificatory argument via transposition and rule in §18

Eleventh and Twelfth Fuṣūl ((inclusive?) disjunction rules)

  • §21: rule: disjunctive modus tollendo ponens

  • §22: illustration for rule in §21 (alms tax for either women’s jewelry or children’s property) with explanation

  • §23: justificatory argument for rule in §21

  • §24: rule: corollary to / variant formulation of rule in §21

  • §25: definitional explanation for rule in §21 (reason for incorporating muṭlaqan)

  • §26: rule: tripartite disjunction

  • §27: illustrative example for rule in §26 (between any two things there is either existential separation [iftirāq], inclusion of existence [shumūl al-wujūd], or inclusion of nonexistence [shumūl al-ʿadam]).

  • §28: rule: corollary to tripartite disjunction; general rule: same rules for quadripartite disjunctions and larger

Thirteenth Faṣl (detachment (takhalluf))

  • §29: formula: expression of takhalluf, the contradictory of entailment

The Second Inquiry: On Mutual Negation / Exclusion (tanāfin / munāfā)

56At the start of the second inquiry, just as he did for the first, al-Samarqandī introduces the subject relation’s technical term—tanāfin (mutual negation / exclusion)—along with a synonym and concise definition. He then, even before the first faṣl, presents and illustrates an ontology-based typology for this logical relation. Thereafter, in the two fuṣūl of this shortest of the three inquiries, he lays out and justifies a pair of corollary rules which draw upon the law of non-contradiction, then proffers and illustrates a negation-based typology, accompanying this with several explanations.

Opening (§§30-33): terms, definition, ontology-based tanāfin typology

57The second inquiry opens (§30) by introducing a primary technical term for its subject logical relation: “the mutual negation / exclusion (al-tanāfī) between two things.” Its technical synonym is munāfā—again a verbal noun of the third form, implying reciprocity or mutuality—and this is followed by a concise technical definition: it is “the nonexistence of conjunction of two [things] in a single receptacle at a single time.” Thus it appears from the start that (generally speaking) tanāfin might constitute a parallel to exclusive disjunction; the total absence of p and q conjoining in the same thing at the same time means that they cannot both hold true of the same thing at the same time as they could in an inclusive disjunction.

58Al-Samarqandī proceeds immediately to an ontology-based typology for the subject relation. Tanāfin may be (§31) both in existence and in nonexistence—that is, the two things can neither both exist, nor both not exist. This first type (we will label it E&N tanāfin) is illustrated by the mutual negation / exclusion between two contradictories (naqīḍayn), as we are left to understand that two contradictories can neither both exist, nor both not exist. Exactly one must exist and exactly one must not. Neither their existence nor their nonexistence can coincide in the same thing at the same time. This is as much an identification as an illustration, then; E&N tanāfin is, at the very least, consonant with the oppositional relation of contradiction.

59Tanāfin may also be (§32) in existence but not in nonexistence, in that the two things cannot both exist, but they can both not exist. This second type (E-not-N tanāfin) is illustrated by the mutual negation / exclusion between two contraries (ḍiddayn) which, as we are again left to understand, cannot both exist but can both not exist. Their existence cannot coincide in the same thing at the same time, but their nonexistence can. Again, illustration borders on identification; E-not-N tanāfin parallels the oppositional relation of contrariety.

60Finally, tanāfin may also be (§33) in nonexistence but not in existence, in that the two things cannot both not exist, but they can both exist. This third type (N-not-E tanāfin) is illustrated by the mutual negation / exclusion between the lāzim [q] and the contradictory (naqīḍ) of the malzūm [¬p] (cf. the parallel to the equivalence rule of material implication in §9). Their conjoining in nonexistence is impossible, al-Samarqandī explains, but not so in existence, “due to the possibility of the lāzim’s existence without the malzūm.” That is, if we assume “if p then q” (p→q), then it is not possible that both not-q (¬q, nonexistence of the lāzim) and not-not-p (¬ ¬p, nonexistence of the contradictory of the malzūm), which is the equivalent of p, are simultaneously the case because (by way of the modus tollens) nonexistence of the lāzim (¬q) necessarily entails nonexistence of the malzūm (¬p). It is possible, however, that both q (the lāzim) and ¬p (contradictory of the malzūm) simultaneously exist. Were we to assume otherwise, we would commit the fallacy of denying the antecedent (paralleled in §8). As E-not-N tanāfin was illustrated by two contraries, we might have expected N-not-E tanāfin to have been illustrated by two subcontraries (which can both exist but cannot both not exist), rather than al-Samarqandī’s lāzim and contradictory of malzūm example. We may nevertheless recognize N-not-E tanāfin as paralleling the oppositional relation of subcontrariety.

61Note that the consonance of E&N, E-not-N, and N-not-E tanāfin with the oppositional relations of contradiction, contrariety, and subcontrariety opens yet another avenue for philosophical- and juridical-dialectical comparison. We might, for instance, ask where else oppositional relations are formulated in such terms of mutual negation / exclusion, and where else subcontrariety is exemplified by the impossible joining of lāzim and contradictory of malzūm in nonexistence.

First Faṣl (§§34-35): corollary rules (based on non-contradiction)

62The first faṣl of the second inquiry brings a pair of rules for the ontology-based types of tanāfin just introduced, both of which draw upon the law of non-contradiction. Al-Samarqandī begins (§34) with a rule for the first two types (E&N, E-not-N), whereby “nonexistence of one of its two parts is entailed with absolute certainty.” His justificatory reductio is that “otherwise, a conjunction between the two in existence would be entailed—and such is absurd (muḥāl).” In other words, when there is E&N tanāfin between p and q, exactly one of either p or q must be nonexistent. Were it not so, then p and q would coincide in existence—the very contradictory of tanāfin in existence, which is of course absurd, since we had already assumed tanāfin in existence. The same holds true for E-not-N tanāfin. Put differently, it is entailed for pairs of contradictories and contraries that exactly one of the pair not exist; otherwise, both parts of the pair would exist simultaneously and so not be contradictories or contraries.

63The second rule brought by al-Samarqandī (§35) applies to the first and third types of tanāfin (E&N, N-not-E), and states that “existence of one of its two parts is entailed likewise [i.e., with absolute certainty];” and its justificatory reductio is that “otherwise, a conjunction between the two in nonexistence would be entailed.” In other words, when there is E&N tanāfin between p and q, exactly one of either p or q must be existent. If such were not the case, then p and q would coincide in nonexistence—the very contradictory of tanāfin in nonexistence, though we had already assumed tanāfin in nonexistence. Here, the same holds true for N-not-E tanāfin. Again put differently, it is entailed for pairs of contradictories and subcontraries that exactly one of the pair exist; otherwise, both parts of the pair would simultaneously not exist and so not be contradictories or subcontraries.

Second Faṣl (§§36-42): negation-based tanāfin typology

64In the second faṣl, al-Samarqandī introduces and explains a negation-based typology for tanāfin, whereby the non-conjunction (ʿadam al-ijtimāʿ) of the mutual negation / exclusion is analyzed in terms of which components are negated, rather than whether they are disjoined in existence, nonexistence, or both. Being that, in the course of explaining one of them he calls it a wajh (way, manner, mode) we will refer to these types as “modes.”

65The first mode (§36; we will label it mode A tanāfin) is when the non-conjunction is by virtue of the negation of each one of the two parts; they can never conjoin (in existence only, presumably) because both are negated. In illustrating this, reference is again made to the now familiar Qurʾānic example. Mode A tanāfin is “like the non-conjunction between ‘the [other] gods’ and ‘the corruption [of heaven and earth].’” In other words, it can never be that “gods besides God” conjoins (in existence) with “corruption of heaven and earth,” simply because both are negated from the start. We are reminded here of the utility of Q.21:22, with its purely hypothetical malzūm and lāzim, in illustrating the principle (in §5) that entailment requires the existence of neither lāzim nor malzūm. Similarly, it seems, tanāfin can come about (in mode A, and, presumably, in existence only) simply because neither of its non-conjoining terms exist in the first place.

66The second mode (§37; mode B tanāfin) consists of two sub-modes. In its larger sense, it is when the non-conjunction is by virtue of the negation of (only) one of the two parts; they can never conjoin (in either existence or nonexistence, presumably) because one of them is negated. In such a case, there are two possibilities: either the negated part is specifically designated (mode B1), or it is not (mode B2). Note that by this distinction we are immediately reminded of the suspended-knowledge type of disjunction introduced in §21.

  • 47 Cf. the example of counter-indication (muʿāraḍa) in Quṭb al-Dīn al-Kīlānī (Forthcoming), Sharḥ al-R (...)

67Al-Samarqandī illustrates the first mode—B1, wherein the negated component is specifically designated—by a claim of non-conjunction between obligation of alms tax (zakāt) for a poor person and obligation of alms tax for a debtor. We are left to understand that such obligations can never conjoin; it cannot be that alms tax must be paid by both poor person and debtor because we know, by juristic consensus, that alms tax for the poor person is negated. Note that in this manner, the negated component is “specifically designated” (muʿayyan).47

  • 48 Cf. §22, above, and the example of contradicting (munāqaḍa) in Quṭb al-Dīn al-Kīlānī (Forthcoming), (...)
  • 49 Recall that this stems from a compound consensus that no alms tax is obliged for young girls’ jewel (...)
  • 50 Cf. §21, above, where: “there necessarily follows that the negation of each one, specifically desig (...)

68The second mode—B2, wherein the negated component is not specifically designated (thus generating a state of suspended-knowledge)—is illustrated (§38) by a claim of non-conjunction between obligation of alms tax for jewelry and obligation of alms tax for children’s property.48 We may recognize this as the same pair of cases from §22 in the eleventh faṣl of the first inquiry on talāzum, above, which reads: “One of two obligations is entailed: either [J] the obligation of alms tax for women’s jewelry, or [C] the obligation [of alms tax] for children’s property; and this is by virtue of consensus.”49 In that case (i.e., in the talāzum disjunction of §22), knowledge of which is the affirmed ruling was suspended—thus, (J C)—due to the principle “every mujtahid both errs and hits the mark;” and, by consequence, the nonexistence of one was a malzūm for the affirmation of the other (¬J→C), and vice versa (¬C→J). In this case, however (i.e., in the tanāfin disjunction of §38), knowledge of which is the negated ruling is suspended—that is, the negated component is not specifically designated (muʿayyan); and al-Samarqandī now explains that “in this mode (wajh), there necessarily follows that the realization of one of the two, specifically designated (ʿalā al-taʿyīn), is a malzūm for the negation of its counterpart—no matter whether it is the first or the second.”50 In other words, when the negated component is not specifically designated—again, (J C)—by consequence the realization of one is a malzūm for the negation of the other (J→¬C), and vice versa (C→¬J); and so we have a parallel to the disjunctive ponendo tollens [(p q); p; ¬q].

  • 51 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 387, Table 29.1; p. 389, Tab (...)

69As we now expect, al-Samarqandī follows up with a justificatory reductio: “Otherwise, an absurdity (muḥāl) would be entailed; namely, a conjunction between them upon assumption (ʿalā taqdīr) of something possible (mumkin).” But before proceeding to his explanation in §39 for that “something possible,” there are a number of observations to be made with regard to §38. First, the suspended-knowledge context of §§37-38, wherein the negated component is not specifically designated (muʿayyan), is an obvious parallel to the suspended-knowledge context of §§21-22, wherein the disjuncts are “true / affirmed in an unqualified way” (ṣādiqan / thābitan muṭlaqan); and this fact is much emphasized not only by similar formulations, but by a common juristic example. Importantly, however, we have seen that this example—viz. alms tax for either jewelry or children’s property—is differently employed in the two inquiries. Though their discourse surely ties suspended-knowledge tanāfin to suspended-knowledge disjunctive talāzum, §21 of the first inquiry clearly expresses the disjunctive tollendo ponens [(p q); ¬p; q], while §38 of the second inquiry clearly expresses the disjunctive ponendo tollens [(p q); p; ¬q]—and this latter is valid only in exclusive disjunctions.51 The two discussions thus appear opposite sides of the same coin, with opposite approaches to the same example. This, taken with their separation in two different inquiries, supports an interpretation that the first inquiry’s suspended-knowledge talāzum-disjunction is primarily inclusive, while the second inquiry’s suspended-knowledge tanāfin-disjunction is wholly exclusive.

70Returning to al-Samarqandī’s justification for mode B2 (a parallel, as we noted, to the disjunctive ponendo tollens), we saw him argue that specific singling out of one component’s realization is a malzūm for the other’s negation because, were it otherwise, an absurd conjunction of the two would follow “upon assumption of something possible (mumkin).” Now he explains why (§39): when which is the negated component (manfī) is “not the subject of knowledge,” then it is possible (yumkinu) that one be realized due to allowance that the other is the negated, and vice versa; but this is not entailed for the first two modes (A and B1). Note that the phrase “not the subject of knowledge” again ties this mode of tanāfin to the disjunctive talāzum whose component is “true / affirmed in an unqualified way.” Both express a state of suspended knowledge, but for disjunctive talāzum the affirmed becomes known through negation of its counterpart (tollendo ponens), and for mode B2 tanāfin the negated becomes known through affirmation of its counterpart (ponendo tollens).

71With characteristic thoroughness, al-Samarqandī now explains why mode B2’s possibility (i.e., of one component’s realization due to the other’s negation, and vice versa) does not hold for the other modes. For mode A (§40) it is because realization of what is negated (manfī), as pertains to either of the two components, is absurd (muḥāl), “and it is possible that the absurd entail the absurd.” Put differently, in mode A it cannot be that either component is realized via allowance that the other is the negated one. Why not? Because in mode A the existence of both is ab initio negated (hence they can never conjoin [in existence]); realization of either is absurd simply because both are already negated from the start. Moreover, the absurd (muḥāl M1: realization of already-negated component 1) can possibly entail the absurd (muḥāl M2: realization of already-negated component 2)—and, thus, both would be realized, not just one or the other (which tanāfin requires), and not because negation of one entails realization of the other (as in mode B2). This may be seen more easily if we refer back to the Q.21:22 illustration of §36. ‘The [other] gods’ and ‘the corruption [of heaven and earth]’ cannot conjoin because both are ab initio negated. Realization of either is therefore absurd; and, what is more, one of these absurdities (realization of ‘the [other] gods’) can entail the other (realization of ‘the corruption [of heaven and earth]’), as per the talāzum rules of the first inquiry (e.g., §5).

  • 52 See Shams al-Dīn Muḥammad al-Samarqandī (Forthcoming), Risāla fī Ādāb al-Baḥth, §50 (wa-l-muḥāl jāz (...)
  • 53 See Khaled El-Rouayheb (2009), “Impossible Antecedents.” In response to my query during a conferenc (...)

72This could be read as a double impediment, or a doubly untenable consequence. Note also how the formula “and it is possible that the absurd entail the absurd” (wa-l-muḥāl jāza an yakūna mustalziman li-l-muḥāl) opens another avenue for investigating the impact of contemporaneous philosophical discourse on juridical-dialectical theory. A similar formula appears near the end of al-Samarqandī’s third illustrative problem-question (masʾala) in his Risāla fī Ādāb al-Baḥth, and there are other indicants it was relatively common.52 The discussions from which this principle emerged go back at least to Ibn Sīnā and the post-Avicennan “impossible antecedents” studied by El-Rouayheb.53

73Returning to al-Samarqandī, he next explains (§41) why mode B2’s possibility does not hold for mode B1. Unsurprisingly, it is because realization of the (known-to-be) negated component in this second mode is also absurd. In other words, in mode B1 it again cannot be that either component is realized via allowance that the other is the negated one, because in mode B1 what is negated has been specifically designated (hence the components can never conjoin); realization of what is (already) negated is absurd.

74Finally, al-Samarqandī confirms (§42) why the possibility does in fact hold for mode B2. It is because here the affirmation of one component is simultaneous with (maʿa) the other’s negation. Put differently, in mode B2 it can be that either component can be realized via allowance that the other is negated, because in mode B2 what is negated has not been specifically designated. That is, what is negated is not yet known to be negated—its negation is simultaneous with its counterpart’s affirmation. Note that this negation of one “simultaneously with” (maʿa) affirmation of the other is an avenue for exploring notions of temporal simultaneity, anteriority, and posteriority in implicative (and causal) relations, especially in disjunctive contexts of suspended knowledge.

75The second inquiry comes to an end with a very brief assertion that “no mulāzama is entailed between three things.” Note this is the opposite of what we learned of disjunctive talāzum, with its tripartite disjunction rules in §§26-28. It seems that due to the mutually negating / exclusive nature of tanāfin the same considerations are impossible, as is perhaps best illustrated by mode B2 tanāfin (for which this might constitute a corollary rule). That is, the possibility that either component can be realized via allowance that the other is negated would no longer hold true for mode B2 if it had three disjuncts. When there are three mutual negators / excluders, mode B2 tanāfin is not safe from absurdity, for upon affirmation that one is negated there would be no simultaneous elimination of the possibility that the remaining two mutual negators / excluders conjoin. If we can imagine a tripartite tanāfin as (p q r), confirming negation of p would entail the absurdity that q and r must conjoin in existence (despite their mutual negation / exclusion), because otherwise we would have the absurdity of one of them conjoining with p in nonexistence (despite their mutual negation / exclusion).

76Table 2: Outline of the Second Inquiry: on mutual negation (tanāfin / munāfā).

Opening (terms, definition, ontology-based tanāfin typology)

  • §30: technical term (al-tanāfī bayna al-shayʾayn); synonym (munāfā); definition: “the nonexistence of conjunction of two [things] in a single receptacle at a single time”

  • §31: type 1 (E&N): tanāfin in existence and in nonexistence; illustration (two contradictories)

  • §32: type 2 (E-not-N): tanāfin in existence not in nonexistence); illustration (two contraries)

  • §33: type 3 (N-not-E): tanāfin in nonexistence not in existence); illustration (lāzim and contradictory of malzūm); explanation (cf. rules in §§8-9)

First Faṣl (corollary rules [based on non-contradiction])

  • §34: rule (for types 1 and 2): nonexistence of one of the two parts is entailed with certainty; justificatory argument

  • §35: rule (for types 1 and 3): existence of one of the two parts is entailed with certainty; justificatory argument

Second Faṣl (negation-based tanāfin typology)

  • §36: mode A: non-conjunction by negation of both parts; illustration (Q.21:22)

  • §37: mode B: non-conjunction by negation of one part; mode B1: which is negated is specifically designated; illustration (alms tax for poor person and debtor)

  • §38: mode B2: which is negated is not specifically designated; illustration (alms tax for jewelry and children’s property); explanation: expression of the disjunctive ponendo tollens; justificatory argument

  • §39: general explanation of §38 justificatory argument: possibility that either component can be realized via allowance that the other is negated

  • §40: explanation: why §39 possibility does not hold for mode A

  • §41: explanation: why §39 possibility does not hold for mode B1

  • §42: explanation: why §39 possibility holds for B2; corollary rule (for mode B2?): no mulāzama entailed between three (mutually negating / exclusive) things

The Third Inquiry: On Causal Concomitance (dawarān / mudāwara)

77At the start of the third inquiry, as with the first and second, al-Samarqandī introduces the subject relation’s technical term—dawarān ([presumably causal] concomitance)—along with a synonym, concise definition, illustration, and component terms. Having then addressed the relation’s proper linguistic formulation, he lays out, in four fuṣūl, all of the following: an ontology-based typology for dawarān, with explanations and illustrations; a general rule tying dawarān to the rules of talāzum; rules and justificatory arguments for cases with more than one concomitant presumed cause (madār); and rules, justifications, and implications for yet another context of suspended knowledge: one we might call “disjunctive madāriyya.”

Opening (§§43-44): terms, definitions, linguistic formulations

  • 54 See, for example, among many others, Imām al-Ḥaramayn al-Juwaynī (1981), Al-Burhān fī Uṣūl al-Fiqh, (...)
  • 55 Undoubtedly part of the reason lies in the more nuanced treatment of multiple madārs we see with al (...)

78Before we proceed, know that up until the appearance of the universalist ādāb al-baḥth, the discursive history around this causal test known as dawarān (or al-ṭard wa-l-ʿaks, “co-presence and co-absence”) seems to have unfolded entirely in the domain of legal theory and juristic dialectic, wherein this and several other methods for identifying the cause or occasioning factor (ʿilla) giving rise to a ruling in God’s Law—the methods of causal justification (masālik al-taʿlīl)—were developed and disputed.54 Considering al-Samarqandī’s role in establishing the ādāb al-baḥth with a patently universalist agenda, the whole of the third inquiry therefore provides an avenue by which we might assess the impact of legal theoretical method on the methodology of logic, philosophy, and theology (rather than the other way round). One area worthy of particular focus is the evident synthesis which appears to have occurred between the ʿilla-qua-occasioning-factor of juristic discourse—i.e., the “legal cause” (ʿilla sharʿiyya)—and the ʿilla-qua-cause of theological and philosophical discourse—i.e., the “intellective cause” (ʿilla ʿaqliyya). The long-held distinction has all but vanished in al-Samarqandī’s dialectic (and from that of his teacher, Burhān al-Dīn al-Nasafī), and a more sophisticated, single cause has emerged.55

79As mentioned, the third inquiry opens (§43) by introducing the primary technical term for this logical relation: dawarān, which we may understand as the “concomitance” of what are presumed to be cause and effect. Its technical synonym is mudāwara—once again a verbal noun of the third form, implying reciprocity or mutuality—and this is followed by a concise technical definition. Dawarān / mudāwara is “the effect’s following from something which has a rightness of causation (ṣalāḥ al-ʿilliyya), time after time.” This is illustrated by the juristic case of ownership following from unconditional sale. And just as the components of talāzum received technical names (viz. lāzim and malzūm) in the first inquiry, the components of dawarān are here named. Referring back to the definition, al-Samarqandī notes that the “effect” (ownership in his illustration) is called a dāʾir—that is, the concomitant which is taken to be the effect—and the “something which has a rightness of causation” (unconditional sale in his illustration) is called a madār—that is, the concomitant which is taken to be the cause.

80Finally, before launching into the first faṣl, al-Samarqandī again conveys (§44), as he did for talāzum (cf. §4 above) a short note on proper linguistic formulation. Here the terms are of course concomitance-relevant, and are exemplified by components of the same illustration in §43. In short, one should say “the concomitance (dawarān) of ownership with sale” (attaching dawarān to the dāʾir in a genitive construction [iḍāfa]) and “the concomitant presumed causation, or ‘being-a-madār’ (madāriyya) of sale for ownership” (attaching madāriyya to the madār in a genitive construction).

First Faṣl (§§45-47): ontology-based dawarān typology

81In the first faṣl of this third and final inquiry, al-Samarqandī introduces an ontology-based typology for dawarān—that is, just as he did with talāzum and tanāfin, he treats the components of dawarān (viz. the madār and the dāʾir) in terms of whether they are existent or nonexistent. In so doing, as we will see, he provides a remarkable premodern parallel to the notions of necessary and sufficient conditions.

  • 56 See Walter Edward Young (2019), Concomitance to Causation,” p. 276-7, and sources cited therein.

82In fact, rather than for dawarān proper, al-Samarqandī presents a typology for madāriyya—that is, for being-a-madār, or for concomitant presumed causation—with the ontological combinations we are familiar with from the previous inquiry (and which may again be labeled E&N, E-not-N, and N-not-E). First he explains (§45) that the madāriyya “might be in existence and in nonexistence, in that the dāʾir exists upon the madār’s existence, always, and is nonexistent upon its nonexistence, likewise [i.e., always].” That is, the madār and dāʾir are both always co-present or co-absent, which we may note as analogous to the madār being both a sufficient condition (presence of madār means presence of dāʾir) and a necessary condition (absence of madār means absence of dāʾir). This first type (we will label it E&N madāriyya) is illustrated by a juristic example: the madāriyya of the illicit sexual activity (zinā) of one who enjoys licit sexual access (e.g., in a valid marriage) for obligation of the stoning penalty. That is, the madār of adultery and the dāʾir of stoning are always both co-present and co-absent—obligation of stoning always exists whenever the zinā of one who enjoys licit sexual access exists, and it is always nonexistent whenever such zinā does not exist. Finally, in a too-rare instance of naming his ontological types, al-Samarqandī tells us that this sort of madāriyya is called “existentiation” (ījād). Note that E&N madāriyya thus provides an avenue for exploring the existential productivity or efficacy of various notions (and tests) of causation, such as are of interest to modern philosophers of causality like Mario Bunge.56

83Continuing to the next type (§46), al-Samarqandī tells us that madāriyya may also be “in existence but not in nonexistence, in that the dāʾir exists upon the madār’s existence, always, but is not nonexistent upon its nonexistence, likewise [always].” That is, the madār and dāʾir are always co-present but not co-absent, which we may note as analogous to the madār being a sufficient condition (presence of madār means presence of dāʾir) but not a necessary condition (absence of madār does not mean absence of dāʾir). This second type (we will label it E-not-N madāriyya) is illustrated by the juristic example familiar from the definition in §43: the madāriyya of sale for ownership. That is, the madār of sale and the dāʾir of ownership are always co-present but not always co-absent—ownership always exists whenever sale exists, but it is not always nonexistent whenever sale does not exist. Ownership, after all, may be occasioned by other things besides sale (e.g., donation or bequest).

84Finally, al-Samarqandī tells us (§47) that madāriyya may also be “in nonexistence but not in existence, in that it is the opposite way around [from the previous type].” That is, the madār and dāʾir are always co-absent but not co-present, which we may note as analogous to the madār being a necessary condition (absence of madār means absence of dāʾir) but not a sufficient condition (presence of madār does not mean presence of dāʾir). This third type (we will label it N-not-E madāriyya) is illustrated by a juristic example: the madāriyya of ritual purity (ṭahāra) for the allowance of the prescribed prayer (ṣalāt). That is, the madār of purity and the dāʾir of prayer are always co-absent but not always co-present—allowance of prayer is always nonexistent whenever ritual purity does not exist, but it does not always exist whenever ritual purity exists. After all, some other necessary condition besides ritual purity might be lacking (e.g., facing in the proper direction). It is not surprising, then, that in another rare instance of naming his ontological types, al-Samarqandī says this sort of madāriyya is called “conditional” (sharṭiyya); its madār is a “condition” (sharṭ) and its dāʾir is “what is conditioned” (mashrūṭ).

Second Faṣl (§48): causal entailment principle

85By this point a family resemblance between talāzum and dawarān is manifest; we are therefore not surprised that al-Samarqandī dedicates the second faṣl of this inquiry (§48) to a principle according to which the rules of talāzum hold true for dawarān. “What you have learned of rules for talāzum,” he says, “apply in this domain, since the madār in the first madāriyya [i.e., type 1: E&N] is a malzūm and a lāzim, in the second [i.e., type 2: E-not-N] it is a malzūm, and in the third [i.e., type 3: N-not-E] it is a lāzim—so know this.”

  • 57 A critical commentator (who may have been Ibn Taymiyya) on Burhān al-Dīn al-Nasafī’s Fuṣūl also mak (...)

86This principle is born out should we apply it to the illustrative examples al-Samarqandī brought for each of the three types. In the illustration of E&N madāriyya (§44), the madār of adultery is both a malzūm and a lāzim for the dāʾir of stoning; that is, if there is adultery, then there is stoning (a→s) and if there is stoning, then there is adultery (s→a), as the crime of adultery has but the one punishment of stoning, and that specific punishment is inflicted only for that crime. This we may recognize as the biconditional-paralleling “coequal entailment” (mulāzama musāwiya) introduced at the start of the first inquiry (§3).57

87In the illustration of E-not-N madāriyya (§45), the madār of sale is a malzūm but not a lāzim for the dāʾir of ownership; that is, if there is sale, then there is ownership (s→o), but the converse (o→s) does not necessarily follow, as ownership may have other causes besides sale. And in the illustration of N-not-E madāriyya (§46), the madār of ritual purity is a lāzim but not a malzūm for the dāʾir of allowance of prayer; that is, if there is allowance of prayer, then there is ritual purity (a→r), but the converse (r→a) does not necessarily follow, as prayer has other conditions to be met besides ritual purity. In these latter two types we may therefore recognize the first inquiry’s “general entailment” (mulāzama ʿāmma).

  • 58 See Walter Edward Young (2019), Concomitance to Causation,” p. 221-2, 274-5.

88Elsewhere, al-Samarqandī is also careful to underscore the critical difference between talāzum and dawarān. In short, by definition it is impossible to separate lāzim from malzūm. However, dāʾir can be separated from madār due to an impeding factor (māniʿ). In his commentary on al-Samarqandī’s Ādāb al-Baḥth, al-Kīlānī takes this farther, noting that both talāzum and dawarān hold true when the malzūm is a cause (ʿilla) for the lāzim, only talāzum holds true when the lāzim is an effect (maʿlūl) of the malzūm, and only dawarān holds true when the dāʾir can be separated from the madār. The commentator al-Shirwānī al-Rūmī also explores the relation between talāzum and dawarān.58

  • 59 These ideas are further developed in this current issue of Methodos, in the article “In Existence a (...)

89In this fashion, al-Samarqandī and commentators open an avenue for exploring premodern theories on the relation between causality and entailment, an issue which continues to be of interest to modern logicians and philosophers of causality. In discussing this topic, Reviewer B has suggested the need for an in-depth study of these theories—not only to ascertain how close they come to those of ancient Megarians and Stoics, but to discern the very bases of causal entailment as understood by Muslim jurists and dialecticians, along with the tools of abductive reasoning they developed for determining the link between madār and dāʾir, and formulating proofs for such links.59

Third Faṣl (§§49-53): multiple madār rules

  • 60 Such as we find in J.S. Mill’s “Four Methods of Experimental Inquiry.” Here and in his commentary o (...)

90The whole of the third inquiry’s third faṣl is dedicated to rules and justificatory arguments of special relevance to the problem of multiple madārs. The entire faṣl therefore has significance for the pursuit of greater accuracy in the philosophical and scientific determination of truly causal concomitants.60 Al-Samarqandī begins (§49) with a simple rule, and a singular exception, for E&N madārs: “It is not possible that the madār be multiple in the first [type of] madāriyya—unless, that is, one of the two madārs is a madār for its counterpart in existence and in nonexistence.” Note this as an observation of significant consequence; among other things, the fact that in any one case of E&N dawarān there can only be one madār—unless it is also an E&N madār for a fellow madār—establishes another valuable criterion for identifying true causes.

91Al-Samarqandī next justifies this rule (§50) in the now familiar form of a reductio argument: “If it is multiple but there is no madāriyya between the two [madārs], then a conjunction of two contradictories (ijtimāʿ al-naqīḍayn) will be entailed; namely, the [simultaneous] existence and nonexistence of the dāʾir.” In other words, the core problem with multiple E&N madārs having no madāriyya between them is that this generates the possibility that one madār (M1) exists without the other (M2), thus entailing that the dāʾir both exists (because M1 exists) and does not exist (because M2 does not) at the same time—an impossible “conjunction of two contradictories.” The only way this untenable consequence can be avoided is if one of the madārs also happens to be an E&N madār for the other.

92Al-Samarqandī in turn justifies this exception (§§51-2) by arguing as follows:

This is because if one of the two is not a madār for its counterpart in existence and in nonexistence, then existential separation (iftirāq) between the two things will be realized; as on the other hand, negating the existential separation between the two things constitutes a malzūm for the madāriyya [between them]. When it is thus, there necessarily follows the dāʾir’s existence due to realization of one of the two madārs and [the dāʾir’s] nonexistence due to nonexistence of the other [madār]—as opposed to when one of the two [madārs] is a madār for its counterpart. For in this case it is possible that [the madār] be multiple, since it is not possible that one of the two be realized without its counterpart, and so no absurdity (muḥāl) is entailed.

  • 61 Just as al-Samarqandī shows us (by transposition): if there is talāzum (no existential separation) (...)

Here the import of the causal entailment principle established in §48 is plain; its implications provide further tools for determining true causes. If there is no madāriyya between multiple E&N madārs, then there is no talāzum between them; this is the state of “existential separation” (iftirāq) introduced in §27—one counterpart exists while the other does not—the very contradictory of entailment.61 This state of existential separation in turn creates the absurd possibility of the dāʾir’s simultaneous existence and nonexistence. The entailment inherent to madāriyya thus plays a critical role in establishing this primary multiple-madār rule.

93Importantly, however, this rule holds only for multiple madārs in the first type of madāriyya (E&N). In fact, as al-Samarqandī next clarifies (§53), there can be multiple madārs in the second (E-not-N) and third (N-not-E) types “without qualification” (muṭlaqan)—that is, without the requirement that one be an E&N madār for the other. As for multiple E-not-N madārs, this is illustrated by the madāriyya of both gifting and sale for ownership. That is, the dāʾir-effect of ownership has two madār-causes: gifting and sale (and, in fact, a number of others); and since the dāʾir of ownership concomits with them only in existence (ownership exists when gifting / sale exists), not in nonexistence (ownership is not necessarily nonexistent when gifting / sale does not exist), then one madār can exist while the other does not without entailing the simultaneous existence-nonexistence of the dāʾir (ownership can exist in the absence of gifting and presence of sale, and vice versa). Put differently, gift and sale are both sufficient but not necessary conditions for ownership, which can therefore exist with the presence of one but absence of the other.

  • 62 Elsewhere, al-Samarqandī dives deeper and produces a more complex set of rules for multiple madārs. (...)

94And as for multiple N-not-E madārs, this is illustrated by the madāriyya of both ritual purity and facing the proper direction (qibla) for allowance of prayer. That is, the dāʾir-effect of allowance of prayer has two madār-conditions: ritual purity and facing the qibla (again, among other things); and since the dāʾir of allowance of prayer concomits with them only in nonexistence (allowance of prayer does not exist when ritual purity / facing the qibla does not exist), not in existence (allowance of prayer does not necessarily exist when ritual purity / facing the qibla exists), then again one madār can be nonexistent while the other exists without entailing the dāʾir’s simultaneous nonexistence-existence (allowance of prayer can be nonexistent in the presence of ritual purity and absence of facing the qibla, and vice versa). More simply: ritual purity and facing the qibla are both necessary but not sufficient conditions for allowance of prayer, which can therefore be nonexistent with the absence of one but presence of the other.62

  • 63 See Walter Edward Young (2019), Concomitance to Causation,” p. 268-9; Walter Edward Young (Forthco (...)
  • 64 Ahmad Hasan (1986), Analogical Reasoning in Islamic Jurisprudence: a Study of the Juridical Princip (...)

95Before proceeding to the ʿAyn al-Naẓar’s final section, there is at least one implication of multiple-madār rules which should be mentioned. Among the traditional legal-theoretical arguments of those who were opposed to treating the jurists’ “legal cause” (ʿilla sharʿiyya) like the philosophers’ and theologians’ “intellective cause” (ʿilla ʿaqliyya) is that co-absence (ʿaks) is not a necessary condition for the legal cause as it is for the intellective.63 Among other reasons for this stance was the common doctrine that a given ruling in God’s Law might have a number of causes;64 co-absence therefore cannot be a condition, as the ruling might exist with one cause in the absence of its other causes. This is of course related to the third faṣl above; and, considering this, al-Samarqandī’s rules and justifications here and elsewhere provide an entry point for exploring how later legal and dialectical theory came to synthesize the legal and intellective cause by working out viable ways to cope with multiple madārs.

Fourth Faṣl (§§54-56): disjunctive madāriyya

  • 65 This is further supported by how the line breaks in MS British Library Or. 3730 (Ms. [أ] of the edi (...)

96The fourth and final faṣl of the third inquiry, drawing the ʿAyn al-Naẓar to a close, introduces a set of what we might call “disjunctive madāriyya” rules. Before proceeding, however, there is a brief philological matter to address. In the course of deciphering al-Samarqandī’s elliptical formulations in this final section I have become convinced there is a scribal omission in both manuscript witnesses from which the current digital edition was transcribed (and thus from the edition itself). If I am correct, then the partially omitted phrase currently transcribed in §54 as [يلزم التخلّف عدماً], or “detachment is entailed in nonexistence,” should read in full [إذا كان مداراً وجوداً يلزم التخلّف عدماً], or “if it is a madār in existence, then detachment is entailed in nonexistence,” thus mirroring its counterpart in §56 [إذا كان مداراً عدماً يلزم التخلّف وجوداً], or “if it is a madār in nonexistence, then detachment is entailed in existence.”65

97Returning to this final faṣl’s subject, it provides, as mentioned, rules for what we might call “disjunctive madāriyya.” In short, al-Samarqandī here works out the implications of yet another “suspended knowledge” context; in this case, it is known that the madār must be a madār for the dāʾir either in existence but not nonexistence (E-not-N), or in nonexistence but not existence (N-not-E), but not both in existence and in nonexistence (E&N). With what I presume to be the omitted text conveyed in [[double brackets]], al-Samarqandī begins (§54) by observing:

  • 66 Note this explanation of the detachment (takhalluf) resonates with the formula for detachment in §2 (...)

If something is not a madār for something in [both] existence and in nonexistence, but it is a madār for it either in existence or in nonexistence, [[then if it is a madār in existence]], then detachment (takhalluf) will be entailed in nonexistence—that is, it will be entailed that the dāʾir will be realized upon nonexistence of the madār overall (fī l-jumla).66

  • 67 Note that this rule is in the disjunctive ponendo tollens form, which, as mentioned before, is vali (...)

If we may proceed with our label, then al-Samarqandī is describing the first form of “disjunctive madāriyya,” in which the first disjunct: “it is a madār… in existence” (i.e., it is an E-not-N madār) is the one which is affirmed. Put differently, if the madār is not an E&N madār for the dāʾir, but could be either an E-not-N or an N-not-E madār for the dāʾir, as an exclusive disjunction [(p→q) (¬p→¬q)], then if the madār is affirmed to be E-not-N (p→q), then detachment of the dāʾir from the madār in nonexistence is entailed, in that the dāʾir will exist with the madār’s nonexistence overall (¬p→q).67

98Upon examination, it would seem that it must be so, for if we affirm that the dāʾir exists when the madār exists, and, as a consequence of exclusive disjunction, we deny that the dāʾir is nonexistent when the madār does not exist, then in such a case as when the madār does not exist we can only conclude that the dāʾir exists without it (having denied their co-absence). It is not surprising, then, that al-Samarqandī’s justificatory reductio (§55) for this rule—as ever, in the implicative modus tollens—is that “otherwise, it would be a madār in [both] existence and nonexistence, but the operative assumption was the opposite (wa-l-taqdīr bi-khilāfihi).” In other words, if it were not the case that “detachment in nonexistence” would result, then it would have to be the case that the madār would be an E&N madār for the dāʾir—against the initial assumption that it is not. This is because (1) madāriyya in existence has been affirmed (the first disjunct was chosen) in this first form of “disjunctive madāriyya,” and (2) a lack of “detachment in nonexistence” would mean that madāriyya in nonexistence was also affirmed; and thus E&N madāriyya would be affirmed despite its initial denial.

99Al-Samarqandī follows through by explaining the interesting implication of this rule and its justification. “And if it is thus,” he says, “then the dāʾir will be realized in reality (fī l-wāqiʿ)—due to its realization upon both operative assumptions: of the madār’s existence and of its nonexistence—with one of the two operative assumptions’ realization in reality.” In other words, since the dāʾir will be assumed to exist no matter whether we assume existence or nonexistence of the madār, the dāʾir will actually be realized, in the real world, whichever of the two assumptions (existence or nonexistence of the madār) is realized in the real world. Altogether, then: if it is the case that the madār is a madār for the dāʾir in existence or in nonexistence, but not both, and it is affirmed that it is a madār for the dāʾir in existence, then the dāʾir will be detached from the madār in nonexistence (it will exist with the madār’s nonexistence), and, consequently, the dāʾir will be realized no matter whether the madār’s existence or nonexistence is realized. If all the conditions outlined in §§54-55 hold true, then the dāʾir is realized no matter what.

100Although al-Samarqandī does not pursue this conclusion, we can make the additional inference that if the dāʾir can be realized with or without realization of the madār, then it must be that the madār is a sufficient but not necessary condition for the dāʾir, or the dāʾir has another cause besides the madār. We might also note here that this section provides an entry for exploring the relation between purely hypothetical entailment (taqdīr) and real-world entailment (fī l-wāqiʿ). Moreover, it highlights the ʿAyn al-Naẓar’s value as a practical outline of argument strategies. Although it has yet to be verified that the theory of §§54-55 was put into practice by al-Samarqandī or others, we might attempt to envisage scenarios in which it would prove useful. Considering that the dāʾir in legal argument is the ruling (ḥukm), and the madār is presumed to be the cause (ʿilla) occasioning that ruling, there might be situations in which it is useful for a respondent to argue that their ruling exists with or without its presumed cause, or for a questioner to argue that the respondent’s presumed cause is merely sufficient but not necessary, and that the ruling has another cause.

  • 68 This phrase supplying the full model for what appears partially omitted in §54.

101Whatever the practicalities of §§54-55, al-Samarqandī brings in §56 the last rule of the third inquiry (and of the ʿAyn al-Naẓar as a whole), which we may consider the second form of “disjunctive madāriyya.” He says: “But as for if it is a madār in nonexistence, then detachment (takhalluf) is entailed in existence.”68 Here, in other words, the second disjunct: “it is a madār… in nonexistence” (i.e., it is an N-not-E madār) is the one which is affirmed, and to opposite effect. Put differently, if the madār is not an E&N madār for the dāʾir, but could be either an E-not-N or an N-not-E madār for the dāʾir, as an exclusive disjunction [(p→q) (¬p→¬q)], then if the madār is affirmed to be N-not-E (¬p→¬q), then detachment of the dāʾir from the madār in existence is entailed, in that the dāʾir will be nonexistent with the madār’s existence (p→¬q)—presumably “overall.” Al-Samarqandī avoids a repetitive explanation, but we may assume one complementary to that in §54, in that “detachment in existence” means it will be entailed that nonexistence of the dāʾir will be realized upon existence of the madār overall.

102He does, however, again alert us to an interesting implication. “In such a case,” he says, “the dāʾir’s nonexistence will be realized in reality (fī l-wāqiʿ), just as we have resolved [for the first form].” That is, if we presume to fill in what al-Samarqandī refrained from repeating, the dāʾir’s nonexistence will be realized in reality—due to realization of its nonexistence upon both operative assumptions: of the madār’s nonexistence and of its existence—with one of the two operative assumptions’ realization in reality. In other words, since the dāʾir will be assumed to not exist no matter whether we assume nonexistence or existence of the madār, the dāʾir’s nonexistence will actually be realized, in the real world, whichever of the two assumptions (nonexistence or existence of the madār) is realized in the real world. If all the conditions of this second form hold true, then the dāʾir’s nonexistence will be realized no matter what. And we can again make an additional inference: if the dāʾir’s nonexistence can be realized both without or with realization of the madār, then it must be that the madār is a necessary but not sufficient condition for the dāʾir, or the dāʾir has another condition besides the madār.

103According to this analysis, what the final faṣl of the ʿAyn al-Naẓar tells us may be summarized as follows. If we find ourselves in a situation where the ruling under consideration (the dāʾir) has a madār which can only be either an E-not-N madār (i.e., a sufficient but not necessary condition for the ruling) or an N-not-E madār (i.e., a necessary but not sufficient condition for the ruling), but not an E&N madār (i.e., not a sufficient and necessary condition for that ruling), then, if we can affirm that the madār is an E-not-N madār, we can conclude that the ruling is realized whether or not the madār is realized, and thus it must have another cause besides the madār. Likewise, if we can affirm that the madār is an N-not-E madār, we can conclude that the ruling is not realized whether the madār is not realized or it is, and thus it must have another condition besides the madār.

  • 69 In his Risāla fī Ādāb al-Baḥth, for example, he claims to have “invented” the three illustrative pr (...)

104At this stage of research, I have not come across such rules for “disjunctive madāriyya” anywhere else, and my interpretations here should be considered tentative. In the final faṣl we appear to have either an entirely novel or a relatively rare set of argument rules, and this raises far more questions than it answers. The final faṣl brings us a disjunctive pair of scenarios: one wherein the dāʾir is realized with or without the madār, and one wherein the dāʾir’s nonexistence is realized without or with the madār. What is the significance of this presentation? Why did al-Samarqandī include it here, at the end of the ʿAyn al-Naẓar? Where else and in which contexts is it discussed, or does it constitute an argumentative innovation (something for which al-Samarqandī seems to pride himself elsewhere)?69 Was knowing that the madār was not an E&N madār for the dāʾir, and contending whether it was E-not-N or N-not-E, so common an occurrence in disputation that al-Samarqandī felt the need to provide templates for it?

105This may not be as far-fetched as it seems at first glance. Consider a basic pattern revealed by our analyses of the three inquiries. In this third inquiry there is a “suspended knowledge” disjunction, with a madār either in existence or in nonexistence but not both, which parallels the “true / affirmed in an unqualified way” disjunction of the first inquiry, and the “not specifically designated / known” disjunction of the second; and these latter ought to have been common enough occurrences in dialectical exchanges. If this is true, these “suspended knowledge” disjunctive argument rules at once illuminate the ʿAyn al-Naẓar’s practicality as a quick-reference for argument method and the relative sophistication of the dialogical logic employed in 13th and 14th century CE juristic dialectic and the early ādāb al-baḥth.

106Table 3: Outline of the Third Inquiry: on causal concomitance (dawarān / mudāwara).

Opening (terms, definitions, linguistic formulations)

  • §43: technical term: dawarān; synonym: mudāwara; definition: “the effect’s following from something which has a rightness of causation, time after time;” illustration (ownership and sale); component terms: concomitant presumed cause (madār) and concomitant presumed effect (dāʾir)

  • §44: proper formulations: “the dawarān of ownership with sale” and “the madāriyya of sale for ownership”

First Faṣl (ontology-based dawarān typology)

  • §45: type 1 (E&N): madāriyya in existence and in nonexistence; explanation; illustration (zinā and stoning); technical name for type 1: “existentiation” (ījād)

  • §46: type 2 (E-not-N): madāriyya in existence not in nonexistence; explanation; illustration (sale and ownership)

  • §47: type 3 (N-not-E): madāriyya in nonexistence not in existence; explanation; illustration (ritual purity and prayer); technical name for type 3: “conditional” (sharṭiyya), madār = “condition” (sharṭ), dāʾir = “what is conditioned” (mashrūṭ)

Second Faṣl (causal entailment principle)

  • §48: principle: rules of talāzum hold for dawarān; madār types by entailment components: E&N madār is a malzūm and a lāzim; E-not-N madār is a malzūm; N-not-E madār is a lāzim

Third Faṣl (multiple madār rules)

  • §49: rule: E&N madār cannot be multiple; exception: when one madār is also an E&N madār for the other

  • §50: justificatory argument for rule in §49

  • §§51-2: justificatory argument for exception in §49

  • §53: rule: E-not-N and N-not-E madārs can be multiple without qualification; illustration for multiple E-not-N (gift and sale for ownership); illustration for multiple N-not-E (ritual purity and facing qibla for allowance of prayer)

Fourth Faṣl (“disjunctive madāriyya”)

  • §54: rule for first form (when first disjunct [it is an E-not-N madār] is affirmed); explanation

  • §55: justificatory argument for rule in §54; implication: dāʾir is realized with or without madār’s realization

  • §56: rule for second form (when second disjunct [it is an N-not-E madār] is affirmed); implication: dāʾir’s nonexistence is realized without or with madār’s realization

Points of Interest and Exploratory Themes

107Throughout this review of al-Samarqandī’s ʿAyn al-Naẓar, I have attempted to draw attention to various points of interest—avenues for exploration, historical and theoretical implications, apparent innovations, etc.—as they have occurred. It is unlikely I have managed to recognize more than a small portion of what the ʿAyn al-Naẓar has to offer to the historian and/or practitioner of logic and dialectic, and to Islamic intellectual history, and the history of ideas more broadly. Nevertheless, the present section aims to review such items as have arrested my attention during analyses of the text, gathering them under a set of six themes.

108The first theme addresses the potential for cross-disciplinary developments, whether in the background of the text, or as a result of its reception. In the text we have observed an interfacing between legal theory and dialectic on the one hand, and logical-philosophical discourse on the other. The juristic, non-relativist principle “every mujtahid both errs and hits the mark” served as the motive for “suspended knowledge” disjunctions. The tripartite disjunction consisting of either existential separation (iftirāq), or universal inclusion of existence (shumūl al-wujūd), or universal inclusion of nonexistence (shumūl al-ʿadam), need not be restricted to a dialectic on norms; as such it is a site with great potential for measuring the impact of legal reasoning on the methodologies of post-classical theology (kalām) and philosophy (ḥikma), especially through the vehicle of al-Samarqandī’s “protocols for dialectical inquiry and disputation” (ādāb al-baḥth wa-l-munāẓara).

109This potential is all the more obvious with respect to dawarān, the whole of the third inquiry, a concept born and elaborated in texts of legal theory (uṣūl al-fiqh). The incorporation of the legal theorist’s conception and elaboration of dawarān into a universal dialectical method opened wide the gate for legal methodology—that is, for argument forged in and for the normative domain—to impact the empirical and speculative methods of the theological, philosophical, and natural sciences.

110Cross-disciplinary developments in the other direction are also evident in the ontological or purely hypothetical expansions to certain rules we have seen; namely, such addenda as “even if the malzūm is impossible in its essence,” or “even if the lāzim is necessary of existence;” and connections to Avicennan “impossible antecedents;” and such principles as “it is possible that the absurd (muḥāl) entail the absurd”—with the “other gods” entailment of “corruption in heaven and earth” from Q.21:22 providing a frequent and useful example.

  • 70 The latter has been suggested by Shahid Rahman. See the postscript to Walter Edward Young (2021), “ (...)

111The second theme covers notions which appear to be in discursive, philosophical development; for even though a bare outline, the ʿAyn al-Naẓar provides a clear snapshot of evolving dialectical and logical-philosophical issues. These include individual notions, like al-Samarqandī’s use (§42) of “simultaneously with” (maʿa) in a “suspended knowledge” disjunctive context, suggesting background conversations of simultaneity, anteriority, and posteriority in implicative relations. And these include individual linkages, like the interplay between hypothetical assumption (taqdīr) and entailment (talāzum), suggesting a kind of convertibility, or proof, or even introduction rule;70 and the more particular relation between hypothetical assumption (taqdīr) and entailment or realization (taḥaqquq) “in reality” (fī l-wāqiʿ); and the interplay between “realization” (taḥaqquq) and “existence” (wujūd).

  • 71 Note that Aristotle articulates contradiction in both ways. In Met. 4.4 he says: “it will not be po (...)

112Also within this theme is the evident distinction between what we’ve called “ontology-based” and “negation-based” typologies and rules. As with other phenomena of the ʿAyn al-Naẓar, this raises far more questions than it answers. With regard to the ontology-based rules of entailment, why has al-Samarqandī formulated them as he has? Why is it “existence” (wujūd) and “nonexistence” (ʿadam) here, but “affirmed” (thābit) and “negated” (manfiyy) there, and (only once) “true” (ṣādiq), never “false” (kādhib)? Why are contradiction, contrariety, and other notions treated in terms of existence vs. nonexistence rather than true vs. false? What is the difference between saying, e.g., “the mutual negation / exclusion between two contradictories is in existence and in nonexistence” rather than “contradictories cannot both be true and cannot both be false”?71

113And what is the significance of al-Samarqandī’s dual ontology- and negation-based approaches? It is most evidently a conscious distinction, but what is the difference between negation (intifāʾ) of the lāzim and nonexistence (ʿadam) of the lāzim—or is the former simply the act producing the latter? Note the ontology-based rules come first. So are they more fundamental, and the negation-based rules corollary? And in at least one place, negation (intifāʾ) was switched for nonexistence (ʿadam) between rule and illustration. So were they interchangeable (or, again, is nonexistence simply the consequence of negation)?

114Also in this theme are dialectics-born topics of clearly ongoing development, including the problem of determining causality when there are multiple madārs. Al-Samarqandī’s detailing of where multiple madārs are possible and where they are not is in fact less elaborate here than elsewhere, and it differs from the analyses of his predecessors. Likewise, his approaches to what we’ve called “suspended knowledge” disjunctions most likely grew out of practical dialectical contexts which spurred a more refined analysis, resulting ultimately in a notable parallelism between the three inquiries’ treatments: disjuncts being “true / affirmed in an unqualified way” in the first, the negated component being “not specifically designated / known” in the second, and the madār being either in existence or in nonexistence (but not both) in the third.

115The same could be true of other parallelisms, like the family resemblance between talāzum and dawarān, with the E&N madār being both malzūm and lāzim, the E-not-N madār being a malzūm, and the N-not-E madār being a lāzim; or the manner in which the relation of tanāfin is intertwined with that of disjunctive talāzum by al-Samarqandī’s articulation of them in their respective inquiries. In fact, the very way in which the ʿAyn al-Naẓar is structured suggests how its three logical relations are related to each other—an observation which would easily arise from extensive use of these relations in dialectic. The entailment and disjunction forms of talāzum (as discussed in the first inquiry) are, after all, foundational to tanāfin and dawarān (as discussed in the second and third inquiries). Tanāfin is of course a special kind of disjunction governed by talāzum; and, with regard to dawarān, al-Samarqandī himself says: “What you have learned of rules for talāzum apply in this domain.”

  • 72 Riccardo Strobino (2018), “Ibn Sina’s Logic,” §3.2.3 notes that Ibn Sīnā treated three types of dis (...)

116Similarly, and whatever its origins, the problem of whether or not valid inferences can be made with unreal propositions of the sort in which malzūm and/or lāzim do not (or even cannot) exist must have arisen in practical dialectical contexts. This would have sparked continual reconsideration, with relevant articulations such as mulāzama per se needing neither the lāzim’s nor the malzūm’s existence, and the possibility of the absurd entailing the absurd. Here, too, we may consider the question of whether or not al-Samarqandī ever came to entertain a distinction between inclusive and exclusive disjunctions. As mentioned above, there are indicants either way, but overall they lean towards his entertaining only the exclusive.72

117The third theme pertains to significant or uniquely contributive formulations (and, possibly, prefigurations) of modern logical concepts. In the first inquiry, al-Samarqandī not only introduces coequal entailment (mulāzama musāwiya) and general entailment (mulāzama ʿāmma)—paralleling, respectively the biconditional and conditional, and thus inviting comparison with the formulations of Avicennan and post-Avicennan logic texts—but he observes that coequal entailment is exempt from the fallacies of denying the antecedent and affirming the consequent. He also brings formulations which parallel material implication and transposition, while just falling short of full expressions of their rules of equivalence. Perhaps of most interest, however, is the handful of unnamed fallacy types he reviews—fallacies which don’t seem to receive much attention in modern manuals of logic and argumentation. As infrequently as they may appear elsewhere, however, the occurrence of these fallacies in real dialectic is quite plausible, and that they are treated here in this terse, practical outline speaks volumes for the sophistication of dialectical practice in al-Samarqandī’s milieu.

118The third inquiry—on a notion of dawarān hailing ultimately from centuries of juristic deliberation, but now drawing towards application in a universal dialectic—is replete with contributions to the study of causality. Among other things, its articulation of E&N madāriyya vis-à-vis the efficacy of causation is such as would have been of interest to the late Mario Bunge; while al-Samarqandī’s ontology-based typology of dawarān not only prefigures Mill’s famous methods, but the notions of necessary and sufficient conditions (with E&N as sufficient and necessary, E-not-N as sufficient but not necessary, and N-not-E as necessary but not sufficient). The problem of multiple madārs as treated by al-Samarqandī here (and elsewhere, in greater detail) not only prefigures certain aspects of Mill’s methods, but would be of benefit to any modern, scientific pursuit of accuracy in determining truly causal concomitants. And as for what we have referred to as “disjunctive madāriyya,” it has yet to be ascertained whether anything of this sort has been formulated in works of logic and dialectic, before or since. That it concludes the third inquiry, and the ʿAyn al-Naẓar as a whole, again says something significant about the sophistication of debating causality in al-Samarqandī’s time.

  • 73 Reviewer A, in keeping with earlier opinions, suggests that the real answer is because al-Samarqand (...)

119The fourth theme attempts to cover peculiarities of the text’s contents—again leaving us with more questions than answers. The ʿAyn al-Naẓar is notable, for example, in preserving or promoting a syllogistic standard for argument; but why, we might ask, is there no treatment of categorical propositions and syllogisms, no direct explication of the square of opposition? Did they have no place in the practice of juristic dialectic (khilāf, jadal) in al-Samarqandī’s various scholarly milieus, or those of his immediate intellectual predecessors?73 And with particular regard to his entailments paralleling hypothetical syllogisms, the focus is as much on invalid as valid forms—whether common and named fallacies (e.g., the fallacy of the consequent), uncommon but named fallacies (e.g., ponendo tollens and tollendo ponens), and fallacies which are both uncommon and unnamed (e.g., the variant on the fallacy of the consequent identified by Reviewer B in §12). Again we might ask: why did al-Samarqandī include these latter types in this concise and ultimately practice-oriented outline? Were they so common in debate? And if so, what does it imply of juristic disputation at that time if they were?

  • 74 Again, Reviewer A, suggests that this is because al-Samarqandī’s talāzum and dawarān are not for pr (...)

120Perhaps the most intriguing question is why, from beginning to end, is the familiar technical jargon of the logic texts absent? Where, in the very relevant inquiry on talāzum, is the “conjunctive / disjunctive conditional” (sharṭiyya muttaṣila / munfaṣila), or the “repetitive syllogism” (qiyās istithnāʾī), or the “antecedent” (muqaddim) and “consequent” (tālī)? This seems all the more strange considering al-Samarqandī was himself a recognized master logician, more than fluent in these terms, as evident in his logical magnum opus the Qisṭās al-Afkār. Why such a restricted technical vocabulary in the ʿAyn al-Naẓar, then? Why eschew the lexicon of conditional and disjunctive propositions, mixed hypothetical syllogisms, etc.?74

  • 75 Abū ʿAlī al-Ḥusayn b. ʿAbd Allāh Ibn Sīnā (1985), Kitāb al-Najāt fī l-Ḥikma al-Manṭiqiyya wa-l-Ṭabī (...)

121In §§7-8, for example, we saw al-Samarqandī deal with a number of invalid forms, exclusively with the vocabulary of talāzum: first, [1] the invalidity of denying the lāzim despite the malzūm’s existence (paralleling the ponendo tollens fallacy), and thus affirming the modus ponens; then, [2] the invalidity of denying the malzūm’s nonexistence despite the lāzim’s nonexistence (paralleling the tollendo ponens fallacy), and thus affirming the modus tollens. Likewise, he confirms that “[3] the malzūm’s existence is not entailed from the lāzim’s existence, nor is [4] the lāzim’s nonexistence entailed from the malzūm’s nonexistence” (paralleling, respectively, the fallacies of affirming the consequent and denying the antecedent). Now let us compare this with Ibn Sīnā in the Najāt on the same subjects:75

The repetition (istithnāʾ), as pertains to a syllogism (qiyās) in which there is a conjunctive conditional (sharṭiyya muttaṣila), is either of [1] the antecedent (al-muqaddim)—in which case it must be that what is repeated (mustathnā) is identical to the antecedent, in order to yield the identical consequent (al-tālī), like our saying: “If Zayd is walking, then he is moving his two feet; but he is walking; therefore he is moving his two feet”—[2] [or the repetition is of the consequent]. And if it is of the consequent, then it must be its contradictory (naqīḍ), in order to yield the antecedent’s contradictory—like our saying: “But he is not moving his two feet” yields “therefore he is not walking.” [3] The repetition of the antecedent’s contradictory and of [4] the identical consequent yields nothing. This will be clear to you upon consideration.

  • 76 As we might expect, Reviewer A suggests that this is because qiyās istithnāʾī is for propositional (...)

Both accounts being systematic, the subjects we’ve labeled 1-4 appear in the same order; but absent from Ibn Sīnā’s account is the vocabulary of talāzum, and absent from al-Samarqandī’s account is the vocabulary of qiyās istithnāʾī.76

  • 77 Al-Samarqandī’s universalizing program is even more evident in the illustrations of his Commentary (...)

122The fifth theme treats evidence of al-Samarqandī’s universalist agenda. To be certain, the move towards a multidisciplinary dialectic is fully actualized in his Risāla fī Ādāb al-Baḥth, but it is also discernable here in the ʿAyn al-Naẓar—especially in his illustrations, which blend empirical, speculative, and normative examples. As for the empirical, we may cite, for example, the impossibility of knowledge without life, and the absence of corruption in the heavens (and thus absence of other gods); as for the speculative, we have God, the Necessary by Essence (wājib bi-l-dhāt) as a lāzim for the possible thing’s existence; and as for the normative we have several rulings, established and contested, on enduring problem-questions (masāʾil), like whether or not alms-tax is obliged for women’s jewelry.77 In a different way, though perhaps consequent to the same or similar motives, is the evident synthesis between the “legal cause,” or “occasioning factor consonant with God’s Law” (ʿilla sharʿiyya) and the “intellective cause” (ʿilla ʿaqliyya). A significant amount of research remains before we can make assertions as to what this means, and how it came about. But as conjectured above, increasingly nuanced approaches to the problem of multiple madārs most probably played a role in this.

  • 78 Cf. for example al-Nasafī’s Fuṣūl, upon which al-Samarqandī wrote a commentary, and which is most l (...)

123The sixth and final theme pertains to evidence that al-Samarqandī intended the ʿAyn al-Naẓar to be a truly pragmatic set of argument blueprints: a practical reference for real disputation. Consider first the handy structure of the text. The reduction to nothing but these three logical relations is telling:78 as earlier suggested, one gets the sense this is something like a crib sheet or aide-mémoire for the active disputant—though it would of course also have assisted the internal dialog and self-testing requisite to the preliminary stages of discovering God’s Law (ijtihād), and refining or “verifying” opinions and supporting arguments (taḥqīq). Each inquiry, after definitions and other prefatory concerns, is little more than a series of bullet points outlining the ways in which the subject relations can and cannot be—valid forms and related fallacies both—accompanied by concise justificatory arguments which themselves, through repetition in form, impress the very useful reductio-as-modus-tollens into the reader’s argumentative toolbox.

124Consider also the evidently conscious method of paralleling without identifying. For example, al-Samarqandī’s treatment of what we’ve called the “ontology-based” types of tanāfin parallels the oppositional relations of contradiction, contrariety, and subcontrariety—indeed, naming the first two as examples—yet with no categorical formulation using the familiar universal affirmative (A), universal negative (E), particular affirmative (I) and particular negative (O), nor even a nod to the square of opposition itself. I believe this makes more sense if we assume that his objective here is neither to introduce us to the square of opposition nor to theorize about it. Rather, he is intent on showing us how to do it—that is, how to produce and how to navigate the various modes of opposition in real-time debate.

  • 79 For examples of the logic of entailment and opposition in dialectical objection and response, see W (...)

125In line with this is the fact that a number of formulations—particularly those invoking negation (intifāʾ)—offer themselves neatly to a disputant’s critical activities of objection and response. In negation-based rules, we have seen a key role played by “the negator” (al-munāfī) and its application to malzūm or lāzim; this mirrors an obvious, central task of both objection and response. Knowing the valid and invalid modes for negating an opponent’s malzūm or lāzim, and gaining familiarity with the manipulation of contradictories and contraries in real-time argument, is an obvious prerequisite to one’s efficacy in debate.79 Similarly, a state of “detachment” (takhalluf), if determined by an opponent, has immediate utility as a mulāzama-destroying charge. Recall al-Samarqandī’s formulation in the thirteenth faṣl of the first inquiry (§29), which resembles a blueprint for articulating an anti-mulāzama objection: “this is not a malzūm for that while this might be realized and thus entail the negation of that, overall; otherwise this would be a malzūm for that, but the operative assumption was the opposite.”

  • 80 On denial with corroboration (manʿ maʿa mustanad), see Shams al-Dīn Muḥammad al-Samarqandī (Forthco (...)

126Note also that such rules as we see in §18: “it is impossible that something be a malzūm for something [else] and what negates it, whether [the negator] is a contradictory or a contrary” actually provide mental templates for the disputant which map onto what can happen in real-time dispute—just as the rules of a game do. If the respondent, in the course of a supporting argument, asserts at one point that if r is the case, then not-q is the case, then at another point asserts that if p is the case, then q is the case, and elsewhere asserts that if p is the case, then r is the case, the questioner can immediately bring a denial (manʿ), and furthermore bring immediate support (mustanad) to that denial with a crisp formula:80 “This is denied (mamnūʿ), because it is not possible that something be a malzūm for something [else] and what negates it.”

127Through memorization and practice, these logical formulae were something which could be imprinted in the mind’s eye, and called forth to measure an opponent’s proofs with increasing rapidity and accuracy. In a similar way, what we’ve called “disjunctive madāriyya” in the final faṣl of the ʿAyn al-Naẓar, constitutes a complex argument template which might also be considered a strategy template: finding ourselves in a context of disjunctive madāriyya, we can conclude that the ruling is realized whether or not the madār is realized, and must therefore have another cause besides the madār, so long as we can affirm that the madār is an E-not-N madār; and we can conclude that the ruling is not realized whether the madār is not realized or it is, and must therefore have another condition besides the madār, so long as we can affirm that the madār is an N-not-E madār.

128In short, the reason these formulae serve well as dialectical templates is the same reason we see so much paralleling rather than logic-text identifying: the ʿAyn al-Naẓar is truly a manual for “logic in action.” It is not identified as exactly the same logic we find in the logic texts precisely because it is not exactly the same logic. It is a true dialogical logic, formulated for disputation, not for intra-logical or meta-logical systematization and theorizing. The logical principles are the same, but they are recast through the prism of pragmatic dialogue and the exigencies of disputation. The logical details and jargon of conditionals, hypotheticals, mixed hypotheticals, disjunctions, and causal relations are reduced to the malzūm and the lāzim, the munāfī and the manfī, the madār and the dāʾir, and the valid and invalid ways that they can be. The end result is a set of blueprints for assembling valid arguments while avoiding fallacies—or objecting to them—all with a manageable range of fundamental components. Ultimately, the ʿAyn al-Naẓar might best be understood as a slim and eminently practical toolbox of key instruments for premodern, juristic, dialogical logic, concisely and systematically arranged for quick and accurate deployment in live disputation.

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Notes

1 For (unfortunately brief) bio-bibliographical entries on al-Samarqandī, see: Muḥammad b. Ibrāhīm Ibn al-Akfānī (1998), Irshād al-Qāṣid ilā Asnā l-Maqāṣid fī Anwāʿ al-ʿUlūm, eds. Muḥammad Kamāl, Maḥmūd Fākhūrī, & Ḥusayn Ṣiddīq, Beirut, Maktabat Lubnān, p. 129-30, p. 161; Aḥmad b. Muṣṭafā Ṭāshkubrī Zādah (1985), Miftāḥ al-Saʿāda wa-Miṣbāḥ al-Siyāda fī Mawḍūʿāt al-ʿUlūm, 3 vols., Beirut, Dār al-Kutub al-ʿIlmiyya, vol. 1, p. 280-281, vol. 2, p. 160; Ḥājjī Khalīfa (Kâtip Çelebi) ([199-]), Kashf al-Ẓunūn ʿan Asāmī al-Kutub wa-l-Funūn, 2 vols., eds. Muḥammad Sharaf al-Dīn Yāltaqāyā and Rifʻat Bīlgah al-Kilīsī, [intro. Shahāb al-Dīn al-Najafī al-Marʿashī], Beirut, Dār Iḥyāʼ al-Turāth al-ʿArabī, [reprint of the Istanbul edition, Istanbul, Wakālat al-Maʿārif, 1941-1943], vol. 1, cols. 38-41, 105, vol. 2, cols. 1074, 1075, 1272, 1326, 1595, 1799, 1803; Ṣiddīq b. Ḥasan al-Qannawjī (1978), Abjad al-ʿUlūm, 2 vols., ed. ʿAbd al-Jabbār Zakkār, Damascus, Manshūrāt Wizārat al-Thaqāfa wa-al-Irshād al-Qawmī, p. 255, p. 550-551; Carl Brockelmann (1996), Geschichte der arabischen Litteratur (GAL), 2 vols. & 3 Suppl., Leiden/New York, Brill, [originally published: 1898-1902; 2nd ed. 1909], vol. 1, p. 615-17 [orig. ed. p. 468], suppl. 1, p. 849-850; İsmail Paşa al-Bābānī al-Baghdādī (1951-1955), Hadiyyat al-ʿĀrifīn: Asmāʾ al-Muʾallifīn wa Āthār al-Muṣannifīn, 2 vols., Istanbul, Wakālat al-Maʿārif al-Jalīliyya fī Maṭbaʿatihā al-Bahiyya, [Reprint, Beirut, Dār Iḥyāʾ al-Turāth al-ʿArabī], vol. 2, p. 106; ʿUmar Riḍā Kaḥḥāla ([198-?]), Muʿjam al-Muʾallifīn : Tarājim Muṣannifī al-Kutub al-ʿArabiyya, 15 vols. in 8, Beirut, Dār Iḥyāʾ al-Turāth al-ʿArabī, vol. 9, p. 63; Khayr al-Dīn al-Ziriklī (2002), Al-Aʿlām : Qāmūs Tarājim li-Ashhar al-Rijāl wa-l-Nisāʾ min al-ʿArab wa-l-Mustaʿribīn wa-l-Mustashriqīn, 15th Printing, Beirut, Dār al-ʿIlm lil-Malāyīn, vol. 6, p. 39; Yūsuf Ilyān Sarkīs (1928-1931), Muʿjam al-Maṭbūʿāt al-ʿArabiyya wa-al-Muʿarraba, 2 vols., Cairo, Maṭbaʿat Sarkīs, vol. 2, p. 999-1000, p. 1046.

For encyclopedia entries, see: Larry Benjamin Miller (2012), “al-Samarḳandī, S̲H̲ams al-Dīn,” in P. Bearman, Th. Bianquis, C.E. Bosworth, E. van Donzel, and W.P. Heinrichs (eds.), Encyclopaedia of Islam, Second Edition, Leiden, Brill, Brill Online; İlhan Kutluer (1988-2013), “Semerkandî, Muhammed b. Eşref,” in Türkiye Diyanet Vakfı İslâm Ansiklopedisi, İdare Meclisi: Bekir Topaloğlu, Tayyal Altıkulaç, İsmail E. Erünsal, İstanbul, Türkiye Diyanet Vakfi, vol. 36, p. 475-77; İhsan Fazlıoğlu (2007), “Samarqandī: Shams alDīn Muḥammad ibn Ashraf alḤusaynī alSamarqandī,” in Thomas Hockey, et al. (eds.), The Biographical Encyclopedia of Astronomers, Springer Reference, New York, Springer, p. 1008; Gregg de Young (2016), “Samarqandī, Shams al-Dīn al-,” in The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam, Oxford Islamic Studies Online, http://www.oxfordislamicstudies.com/article/opr/t445/e204; Hâmit Dilgan (2008), “Al-Samarqandī, Shams al-Dīn…,” in Charles Coulston Gillispie, Frederic Lawrence Holmes, and Noretta Koertge (eds.), Complete Dictionary of Scientific Biography, Detroit, Charles Scribner's Sons.

For more detailed studies, see: Gholamreza Dadkhah (2014), [Persian and English introductions], in Shams al-Dīn Muḥammad al-Samarqandī, Science of the Cosmos and the Soul [= ʿIlm al-Āfāq wa-l-Anfus], ed. Gholamreza Dadkhah, Costa Mesa, CA, Mazda Publishers, p. 1-82 (and Engl. Intro, p. 1-13); Heidrun Eichner (2015), The Post-Avicennian Philosophical Tradition and Islamic Orthodoxy: Philosophical and Theological summae in Context, Unpublished Habilitationsschrift, Halle, “Chapter XIII: Shams al-Dīn al-Samarqandī and 13th Century Māturīdite Kalām;” Ali Muhaddis (2008), [Persian introduction], in Shams al-Dīn Muḥammad al-Samarqandī, Sharḥ al-Qaṣīda al-Rūḥāniyya, ed. Ali Muhaddis, in idem, ed., Twenty Philosophical-Mystical Texts in Persian and Arabic, Acta Bibliothecae R. Universitates Upsaliensis, vol. XLI, p. 215-226; ʿAbbās al-ʿAzzāwī (1959), “Shams al-Dīn Muḥammad al-Samarqandī,” Al-Majalla 25, p. 65-71; Ramazan Şeşen (2005), “Majmūʿatān min Muʾallafāt Athīr al-Dīn al-Abharī wa Shams al-Dīn al-Samarqandī,” Presented at the Muʾtamar al-Makhṭūṭāt al-Mawaqqaʿa (Conference for Signed Manuscripts), of the Tanẓīm Maktabat al-Iskandriyya, 26-28 April, 2005, available online at: http://wadod.net/bookshelf/book/1868; and Walter Edward Young (Forthcoming B), On the Protocols 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), (Intro).

2 See Wilferd Madelung (1989), “Borhān al-Dīn Nasafī,” in Encyclopaedia Iranica, IV/4, 371, Available online at: http://www.iranicaonline.org/articles/borhan-al-din-nasafi-abul-fazael-mohammad-b; Mustafa Sinanoğlu (1988-2013), “NESEFÎ, Burhâneddin,” in Türkiye Diyanet Vakfı İslâm Ansiklopedisi, İdare Meclisi: Bekir Topaloğlu, Tayyal Altıkulaç, İsmail E. Erünsal, İstanbul, Türkiye Diyanet Vakfi, vol. 32, p. 565-7; Gholamreza Dadkhah & Abbas Goodarznia (2015), [Persian and English introductions], in Burhān al-Dīn Muḥammad b. Muḥammad al-Nasafī, Commentary upon the Foundation of Intellectual Perspicacity: Concerning Logic, Natural Philosophy, Metaphysics and Mathematics; Sharḥ ʾAsās al-Kīyāsat [= Sharḥ Asās al-Kiyāsa fī l-ʿUlūm al-Arbaʿa al-Manṭiq wa-l-Ṭabīʿī wa-l-Ilāhī wa-l-Riyāḍī], ed. Gholamreza Dadkhah and Abbas Goodarznia, Costa Mesa, CA, Mazda Publishers; Gholamreza Dadkhah (2014), Pers. Intro. to al-Samarqandī, ʿIlm al-Āfāq; Sharīfa bint ʿAlī al-Ḥawshānī (1428 [2008]), [Arabic introduction], in Burhān al-Dīn al-Nasafī, Manshaʾ al-Naẓar fī ʿIlm al-Khilāf, ed. Sharīfa bint ʿAlī al-Ḥawshānī, Al-Ḥikmah 34, p. 409-471; Necmettin Pehlivan & Hadi Ensar Ceylan (2015), “Ādābu’l-Baḥs̱ Devrimine Doğru Son Evrim: Burhānuddīn en-Nesefī’nin el-Fuṣūl’ü,” Ankara Üniversitesi İlahiyat Fakültesi Dergisi 56(2), p. 1-75; Sharīfa bint ʿAlī al-Ḥawshānī (2012), [Arabic introduction], in Burhān al-Dīn al-Nasafī, Sharḥ al-Fuṣūl fī ʿIlm al-Jadal, ed. Sharīfa bint ʿAlī al-Ḥawshānī, Riyadh, Jāmiʿat al-Malik Suʿūd; Walter Edward Young (Forthcoming B), Protocols, (Intro).

3 On this eastern school of juristic dialectic, see Larry Benjamin Miller (2020), Islamic Disputation Theory: The Uses & Rules of Argument in Medieval Islam, Cham, Springer, p. 148-162. On Raḍī al-Dīn al-Nīsābūrī, see Ḥājjī Khalīfa ([199-]), Kashf al-Ẓunūn, 2:1113; Muḥyī al-Dīn ʿAbd al-Qādir al-Qurashī al-Ḥanafī (1978-1988), al-Jawāhir al-Muḍiyya fī Ṭabaqāt al-Ḥanafiyya, 5 vols., ed. ʿAbd al-Fattāḥ Muḥammad al-Ḥilw, Riyadh, Dār Iḥyāʾ al-Kutub al-ʿArabiyya / Dār al-ʿUlūm, 4.386-7, no 2073, and sources cited by Ḥilw. And on Rukn al-Dīn al-ʿAmīdī, see Ḥājjī Khalīfa ([199-]), Kashf al-Ẓunūn, 1:69, 2:1113, 2:1966; Muḥyī al-Dīn ʿAbd al-Qādir al-Qurashī al-Ḥanafī (1978-1988), al-Jawāhir al-Muḍiyya, 3.355-6, no 1529, 4.388, no 2075; Khayr al-Dīn al-Ziriklī (2002), Al-Aʿlām, 7.27-8.

4 Carl Brockelmann (1996), Geschichte, vol. 1, p. 615 [orig. ed. p. 467-468], suppl. 1, p. 849. Editions are in Necmettin Pehlivan & Hadi Ensar Ceylan (2015), “Ādābu’l-Baḥs̱;” and Taqī al-Dīn Aḥmad Ibn Taymiyya (?) (2004), Tanbīh al-Rajul al-ʿĀqil ʿalā Tamwīh al-Jadal al-Bāṭil, eds. ʿAlī b. Muḥammad al-ʿImrān and Muḥammad ʿUzayr Shams, Mecca, Dār ʿĀlam al-Fawāʾid li-l-Nashr wa-al-Tawzīʿ.

5 See Walter Edward Young (2019), Concomitance to Causation: Arguing Dawarān in the Proto-Ādāb al-Baḥth,” in Peter Adamson (ed.), Philosophy and Jurisprudence in the Islamic World, p. 205-281, Berlin/Boston, De Gruyter; Shams al-Dīn Muḥammad al-Samarqandī (780 [1378]?), Sharḥ Fuṣūl al-Nasafī, MS Istanbul, Süleymaniye Kütüphanesi, Esad Efendi 3034, foll. 1a-46b; and Shams al-Dīn Muḥammad al-Samarqandī (847 [1443]), Sharḥ Fuṣūl al-Nasafī, MS London, British Library, Or. 11183, foll. 2b–35a. An edition of al-Nasafī’s self-commentary on the Fuṣūl has been published: Burhān al-Dīn al-Nasafī (2012), Sharḥ al-Fuṣūl fī ʿIlm al-Jadal, ed. Sharīfa bint ʿAlī al-Ḥawshānī, Riyadh, Jāmiʿat al-Malik Suʿūd.

6 See Abdessamad Belhaj (2016), “Ādāb Al-Baḥth Wa-al-Munāẓara: The Neglected Art Of Disputation In Later Medieval Islam,” in Arabic Sciences and Philosophy 26(2), p. 291-307; Robert Wisnovsky (2004), “The Nature and Scope of Arabic Philosophical Commentary in Post-Classical (ca. 1100-1900 AD) Islamic Intellectual History: Some Preliminary Observations,” Bulletin of the Institute Of Classical Studies 47, p. 149-191 (Special Issue 83/2: Philosophy, Science and Exegesis in Greek, Arabic and Latin Commentaries, eds. P. Adamson, H. Baltussen and M.W.F. Stone), at p. 169-173; Walter Edward Young (2021), “Dialectic in the Religious Sciences,” in Kate Fleet, Gudrun Krämer, Denis Matringe, John Nawas, & Everett Rowson (eds.), Encyclopaedia of Islam Three, Leiden, Brill; Walter Edward Young (Forthcoming B), Protocols, (Intro).

7 The same three are found, in the same order, at the start of al-Nasafī’s Muqaddima / Fuṣūl; and they derive, ultimately, from that methodological lineage going back (at least) to the circle of Raḍī al-Dīn al-Nīsābūrī (see Larry Benjamin Miller (2020), Islamic Disputation Theory, p. 148-162). 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), even while acknowledging that (to my current knowledge) no pre-modern source besides these manuscripts attribute a Kitāb ʿAyn al-Naẓar to him. Other attributions of the ʿAyn al-Naẓar to al-Samarqandī are found only in a few modern bio-bibliographical works. These in turn draw on Carl Brockelmann (1996), Geschichte, vol. 1, p. 617 [orig. ed. p. 468], suppl. 1, p. 850, who himself references only the two manuscript witnesses collated in our current, digital edition (see the prefatory material to the digital edition, at https://pages.ceres.rub.de/ayn-al-nazar/).

8 Miller offers expositions and analyses of all three logical relations, citing the ʿAyn al-Naẓar at some points [Larry Benjamin Miller (2020), Islamic Disputation Theory, 149-159]. See also: Shams al-Dīn Muḥammad al-Samarqandī (Forthcoming), 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), ed. and transl. Walter Edward Young, §§10-12; Shams al-Dīn Muḥammad al-Samarqandī (1353 [1934/5]), Ādāb al-Ḥakīm Shams al-Dīn al-Samarqandī [= al-Risāla fī Ādāb al-Baḥth], ed. Maḥmūd al-Imām al-Manṣūrī, 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.), p. 125-32, Cairo, Maṭbaʿat al-Saʿāda, p. 125-126; and Shams al-Dīn Muḥammad al-Samarqandī (2014), Risāla fī Ādāb al-Baḥth, in Zakariyyāʾ b. Muḥammad al-Anṣārī, Fatḥ al-Wahhāb bi-Sharḥ al-Ādāb: wa-huwa sharḥ ʿalā al-Ādāb fī al-Baḥth wa-Munāẓara lil-Imām Muḥammad b. Ashraf al-Samarqandī; wa-yashmal masāʼil kalāmiyya wa-ḥikmiyya wa-jadaliyya wa-maʿahu Ḥāshiyat al-ʿAllāma Muḥammad b. Aḥmad b. ʿArafah al-Dasūqī, ed. ʿArafah ʿAbd al-Raḥmān Aḥmad ʿAbd al-Raḥmān al-Nādī, p. 73-94, Kuwait, Dār al-Ḍiyāʼ lil-Nashr wa-l-Tawzīʿ, at p. 76; Quṭb al-Dīn al-Kīlānī (Forthcoming), Sharḥ al-Risāla al-Samarqandiyya, 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), ed. and trans. Walter Edward Young, §§10.1-12.4; Walter Edward Young (2016), “Mulāzama in Action in the Early Ādāb al-Baḥth,” Oriens 44.3-4 [Special Issue: Major Issues and Controversies of Arabic Logic], p. 332-385; Walter Edward Young (2019), Concomitance to Causation.”

9 The digital edition: Shams al-Dīn Muḥammad al-Samarqandī (2019), Kitāb ʿAyn al-Naẓar fī ʿIlm al-Jadal, Digital critical edition, ed. and trans. Walter Edward Young; TEI Infrastructure by Frederik Elwert, Digital Humanities at the Center for Religious Studies (DH@CERES), Ruhr-Universität Bochum, https://pages.ceres.rub.de/ayn-al-nazar/ . For a brief project description, see https://dh.ceres.rub.de/en/projects/project/ayn-al-nazar/. The edition was collated from two manuscript witnesses currently held by the British Library. Descriptions may be found in Charles Rieu (1894), Supplement of the Catalogue of the Arabic Manuscripts in the British Museum, London, Longmans & [etc.], n° 1124, v., foll. 72-76; n° 1227, i., foll. 1-5. Abdessamad Belhaj (2016), “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 vol. 1, p. 239 of Dār al-Kutub al-Miṣriyya (1924), Fihris al-Kutub al-ʿArabiyya al-Mawjūda bi-l-Dār li-Ghāyat Sannat 1921, Cairo, Maṭbaʿat Dār al-Kutub al-Miṣriyya, 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, however, nor even to discover any record of it in later Dār al-Kutub catalogs.

10 See our brief comparison with a section from Ibn Sīnā’s Najāt below in the fourth theme of section three.

11 In what follows, all references and quotations with regard to the ʿAyn al-Naẓar derive from the digital edition.

12 Miller also observes that talāzum is not material implication. Citing the example of talāzum provided by al-ʿAmīdī in his Irshād, he says:

“An example of ‘implication’ would be ‘P says: If the zakāt tax were incumbent upon debtors, it would also be incumbent upon beggars’—in logical terms, if P then Q. Now in modern logic, there need not be any relationship between ‘P’ and ‘Q’ in order for the statement to be true or for the material implication to work. The statement would be false only in the case where P is true and Q is false. In our case, the proponent is confident that Q is false and, thus, P must be false so that the statement be true in the modus tollens. But not only that; he assumes a correlation between the case of the beggar and that of the debtor. He assumes that in an essential way they are similar, and that similar juristic qualifications should apply to them. In other words, the proponent makes an analogy which he clothes in the form of an entailment.”

Miller proceeds, however, to the “logical explanations” of al-Nasafī, where he not only equates al-Nasafī’s idiom of “in existence” and “in nonexistence” with “true” and “false,” but even presents al-Nasafī’s short cataloging of rules as “truth tables” (Larry Benjamin Miller (2020), Islamic Disputation Theory, p. 79-80).

13 NB: Reviewer B cautions that talāzum is more general than mere entailment, as it also includes presupposition.

14 Cf. Burhān al-Dīn al-Nasafī (2015), Al-Fuṣūl, in Necmettin Pehlivan and Hadi Ensar Ceylan, “Ādābu’l-Baḥs̱ Devrimine Doğru Son Evrim: Burhānuddīn en-Nesefī’nin el-Fuṣūl’ü,” Ankara Üniversitesi İlahiyat Fakültesi Dergisi 56(2), p. 1-75, at p. 44, where he notes the lāzim might be general in relation to the malzūm (e.g., animal in relation to human), or co-equal in relation to the malzūm (e.g., rationally articulate in relation to human).

15 This verse’s formula might be described as an enthymemic modus tollens, where the minor premise (they are not corrupted) and conclusion (there are no gods besides God) are unspoken but understood rhetorically.

16 On al-Fārābī and the biconditional, see Saloua Chatti (2019), Arabic Logic from al-Fārābī to Averroes: A Study of the Early Arabic Categorical, Modal, and Hypothetical Syllogistics, Studies in Universal Logic, Cham, Birkhäuser, p. 268-9; for Ibn Sīnā and the biconditional, see Riccardo Strobino (2018), “Ibn Sina’s Logic,” in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), URL = https://plato.stanford.edu/archives/fall2018/entries/ibn-sina-logic/, in two places; for detailed analyses of Ibn Sīnā’s conditionals see Kamran Karimullah (2014), Avicenna (d. 1037), Logical Theory and the Aristotelian Tradition, Ph.D. Dissertation, McGill University; and for hypotheticals more broadly in ancient and Arabic logic, see Saloua Chatti (2019), Arabic Logic, chap. 5 “The Hypothetical Logic.”

17 See Walter Edward Young (2016), “Mulāzama in Action,” 346, 352-3, passim.

18 See Walter Edward Young (2021), “The Formal Evolution of Islamic Juridical Dialectic: A Brief Glimpse,” in Shahid Rahman, Matthias Armgardt, & Hans Christian Nordtveit Kvernenes (eds.), New Developments in Legal Reasoning and Logic: From Ancient Law to Modern Legal Systems, Dordrecht/New York, Cham, Springer, section 4.3: “Postscript: A Brief Excursus on the Relation Between Taqdīr-Assumption and Mulāzama-Implication.”

19 On a related controversy (including al-Samarqandī’s input, from his Qisṭās) see Khaled El-Rouayheb (2009), “Impossible Antecedents and Their Consequences: Some Thirteenth-Century Arabic Discussions,” History and Philosophy of Logic 30(3), p. 209-225.

20 I suspect this indicates that this sort of unreal mulāzama exists “in the thing-itself” (fī nafs al-amr), along with mathematical models and the like; however, Reviewer A points out that this might entail the existence fī nafs al-amr of things whose nonexistence is necessary, while certain authors reject this, accepting the existence of nonexistent things fī nafs al-amr only in cases where their nonexistence is contingent (on mathematical models and nafs al-amr, see İhsan Fazlıoğlu (2014), “Between Reality and Mentality: Fifteenth Century Mathematics and Natural Philosophy Reconsidered,” Nazariyat Journal for the History of Islamic Philosophy and Sciences 1(1), p. 1-39; on nafs al-amr more broadly, see Hasan Spiker (2021), Things as They Are: Nafs al-Amr & the Metaphysical Foundations of Objective Truth, Classification of the Sciences Project, Tabah Papers Series no. 2, Abu Dhabi, Tabah Research. Also of interest, from at least a terminological perspective, is the interplay between “realization” (taḥaqquq) and “existence” (wujūd). The taḥaqquq of something (e.g., mulāzama) appears to be its acquiring of wujūd, although, again, just what kind of wujūd that may be is not immediately evident here.

21 That is, if it is not the case that existence of the malzūm entails existence of the lāzim and nonexistence of the lāzim entails nonexistence of the malzūm, then the malzūm will be realized without the lāzim; but it cannot be the case that the malzūm is realized without the lāzim; therefore, it is the case that the malzūm entails existence of the lāzim and nonexistence of the lāzim entails nonexistence of the malzūm (¬p→q; ¬q; p).

22 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, Albany, State University of New York Press, p. 376, Table 28.1.

23 “Other gods” being the malzūm for “corruption” in the Qurʾānic example. Thus, even though the existence of other gods is in reality impossible, it is nevertheless incorrect to assume non-corruption of heaven and earth upon hypothetically assuming the existence of other gods.

24 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 376, Table 28.1.

25 Thus, even though the nonexistence of God is in reality impossible, it is nevertheless incorrect to assume the existence of possible things upon hypothetically assuming the nonexistence of God.

26 Khaled El-Rouayheb (2009), “Impossible Antecedents.”

27 Thanks to Reviewer B for pointing out that al-Samarqandī’s formulae here do not parallel full equivalence rules, as I had originally stated. Whether al-Samarqandī has more complete expressions elsewhere—i.e., with both (p→q)→(q ¬p) and (q ¬p)→(p→q), and both (p→q)→(¬q→¬p) and (¬q→¬p)→(p→q)—is a question for further research.

28 Irving M. Copi, Carl Cohen, & K. D. McMahon (2016), Introduction to Logic, 14th ed., London, Routledge, p. 389-90; Galen A. Foresman, Peter S. Fosl, & Jamie C. Watson (2016), The Critical Thinking Toolkit, Malden/Chichester, Wiley Blackwell, p. 93.

29 In short, if I understand correctly: (1) if p exists q necessarily exists, (2) if p does not exist q does not necessarily not exist, (3) if q exists p does not necessarily exist, and (4) if q does not exist p necessarily does not exist. Therefore, it is always the case that either q exists (with [as in 1] or without [as in 3] the necessary existence of p) or p does not exist (without [as in 2] or with [as in 4] the necessary nonexistence of q). If it were not so, then q would be separated from p (the opposite of [1] and [4], and the very opposite of the mulāzama which had been assumed), or the existence of q would be indeterminate (the opposite of [2]), or the nonexistence of p would be indeterminate (the opposite of [3]).

30 Irving M. Copi, Carl Cohen, & K. D. McMahon (2016), Introduction to Logic, p. 389; Galen A. Foresman, Peter S. Fosl, & Jamie C. Watson (2016), The Critical Thinking Toolkit, p. 92-3.

31 See Shams al-Dīn Muḥammad al-Samarqandī (2014), Qisṭās al-Afkār fī Taḥqīq al-Asrār [= Kıstâsu'l-Efkâr : Düşüncenin Kıstası (Eleştirmeli Metin – Çeviri)], ed. and transl. (Ar.-Turk.) Necmettin Pehlivan, Istanbul, Türkiye Yazma Eserler Kurumu Başkanlığı, p. 252 ff. For ʿaks al-naqīḍ in action, see Quṭb al-Dīn al-Kīlānī (Forthcoming), Sharḥ al-Risāla al-Samarqandiyya, §§5.10, 13.3-4, 14.4, 22.9, with analyses of the same in Walter Edward Young (2016), “Mulāzama in Action.” For contraposition more broadly, as per al-Fārābī and Ibn Sīnā, see Asadollah Fallahi (2019), “Fārābī and Avicenna on Contraposition,” History and Philosophy of Logic 40(1), p. 22-41. Note that al-Samarqandī seems to critique Ibn Sīnā’s definition of ʿaks al-naqīḍ for excluding conditionals (Shams al-Dīn Muḥammad al-Samarqandī (2014), Qisṭās al-Afkār, p. 253).

32 The pure hypothetical is typically formulated today as (p→q), (q→r) (p→r).

33 That is: if it is rationally articulate, then it is a human; and if it is a human, then it is an animal; therefore, if it is rationally articulate, then it is an animal.

34 That is, it is fallacious to argue: If it is a horse, then it is an animal; and if it is a human, then it is an animal; therefore, if it is a horse, then it is a human.

35 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 396-397.

36 Reviewer A considers this an indication that talāzum should not be rendered as material conditionality. In short, if we were to understand → as a material conditional, and q as a necessarily true proposition, then (p→q) Λ (r→q) would be true no matter whether (r→¬p) is true or not.

37 Via the equivalence rule of transposition half-expressed in §10, it would be the case that (p→q) :: (¬q→¬p) and (r→q) :: (¬q→¬r). Thus, by transposition, ¬q becomes the malzūm for the contradictories ¬p and ¬r.

38 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 387, Table 29.1 (first column).

39 Note this as the solitary instance in the ʿAyn al-Naẓar of a term from the Arabic logic tradition’s idiom of truth and falsity. “True” (ṣādiq) occurs only this once, and neither “truth” (ṣidq), nor “falsity” (kidhb), nor “false” (kādhib) occur at all.

40 That is, either figure 1: (p q); ¬p; q or figure 2: (p q); ¬q; p of the modus tollendo ponens, or “denying a disjunct,” which are alone valid forms in the inclusive disjunctive syllogism (William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 387).

41 In fact, the basis for this disjunction is a versatile case (we will encounter it again in §38) of “compound consensus” (ijmāʿ murakkab). In brief: all four primary Sunnī schools of law maintain that there is no alms tax obliged for young girls’ jewelry, but for different reasons. For the Ḥanafīs, it is because no alms tax is obliged for minors; for the Mālikīs, Shāfiʿīs, and Ḥanbalīs, it is because no alms tax is obliged for jewelry. Thus with respect to the current case in §22, it can only be either that alms tax is obliged for women’s jewelry, or that it is obliged for children’s property—but not both (because jewelry and minority combine in the no-obligation consensus case), which fact marks this example as an exclusive, not inclusive disjunction—and which one it is cannot be known with certainty, due to the principle that even the best mujtahids may fail as well as succeed (and which have done which in this case is known, presumably, only to God). For a schematic of this case of compound consensus in a similar argumentative context, see Walter Edward Young (2016), “Mulāzama in Action,” p. 355. And on doctrines of ijtihādic infallibility and fallibility, see Aron Zysow (2013), The Economy of Certainty: An Introduction to the Typology of Islamic Legal Theory, Atlanta, Lockwood Press, p. 119-121.

42 It may also be noted that by De Morgan’s Law, (¬p ¬q) is equivalent to ¬(p q). In the terse presentation of the ʿAyn al-Naẓar, however, it is not clear whether this equivalence is being considered.

43 Questions to pursue include: (1) whether or not this excluded type is a corollary to the fallacy of affirming the consequent; (2) what bearing if any this has on whether or not al-Samarqandī distinguished between inclusive and exclusive disjunction; (3) whether or not this is connected to the distinction of purely hypothetical reasoning (like in the gods and corruption example).

44 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 389, Table 29.2.

45 For an example of this tripartite distinction between iftirāq and the two shumūls in dialectical action, see Shams al-Dīn Muḥammad al-Samarqandī (Forthcoming), Risāla fī Ādāb al-Baḥth, §§48-50; Shams al-Dīn Muḥammad al-Samarqandī (1353 [1934/5]), Ādāb al-Ḥakīm, p. 131-2; and Shams al-Dīn Muḥammad al-Samarqandī (2014), Risāla fī Ādāb al-Baḥth, p. 91-4; with Quṭb al-Dīn al-Kīlānī (Forthcoming), Sharḥ al-Risāla al-Samarqandiyya, §§48.1-50.5; all of which is discussed in detail in Walter Edward Young (2018), “Al-Samarqandī’s Third Masʾala: Juridical Dialectic Governed by the Ādāb al-Baḥth,” Oriens 46(1-2) [Special Issue: Rationalist Disciplines and Postclassical Islamic Legal Theories], p. 62-128.

46 Cf. instances of takhalluf in §§9, 54, and 56. In §§54-55, we will encounter al-takhalluf ʿadaman, which is that the dāʾir is realized upon nonexistence of the madār, overall (fī l-jumla).

47 Cf. the example of counter-indication (muʿāraḍa) in Quṭb al-Dīn al-Kīlānī (Forthcoming), Sharḥ al-Risāla al-Samarqandiyya, §§14.4 ff., wherein the two propositions have an implicative relationship in a modus tollens reductio: “If alms tax were obliged for the debtor, then it would be obliged for the poor person; but the lāzim [i.e., obligation for the poor person] is negated by way of consensus (ijmāʿ);” [therefore the malzūm (obligation for the debtor) is negated]. NB: if the entailment of this counter-indication holds true, then al-Kīlānī’s example is not a case of mode B1 tanāfin, but a case of mode A tanāfin: both components are negated. Both al-Samarqandī’s and al-Kīlānī’s use of these cases is merely illustrative, however, and need not reflect the authors’ doctrines—i.e., that al-Samarqandī holds the debtor is obliged because he is in a tanāfin relation with the poor person (whose obligation is officially negated), or that al-Kīlānī holds the debtor is not obliged because he is in a mulāzama relation with the poor person. A question worthy of pursuing is whether there is any significance to the fact that al-Kīlānī’s debtor example occurs in his commentary on the definition of counter-indication (muʿāraḍa) as opposed to the definition of contradicting (munāqaḍa), where in fact he uses the jewelry example (as al-Samarqandī next does for mode B2; see following note).

48 Cf. §22, above, and the example of contradicting (munāqaḍa) in Quṭb al-Dīn al-Kīlānī (Forthcoming), Sharḥ al-Risāla al-Samarqandiyya, §§13.3 ff. Again we might ask if there is any significance to the fact that al-Kīlānī uses the jewelry example here in his commentary on the definition of munāqaḍa as opposed to the definition of counter-indication (muʿāraḍa), where, as we have seen, he uses the debtor example (as al-Samarqandī did for mode B1; see previous note).

49 Recall that this stems from a compound consensus that no alms tax is obliged for young girls’ jewelry—for Ḥanafīs because there is no alms tax for minors, and for the other schools because there is no alms tax for jewelry. Thus it must be that either alms tax is obliged for jewelry or it is obliged for children’s property, but not both, and whichever it is is not known with certainty.

50 Cf. §21, above, where: “there necessarily follows that the negation of each one, specifically designated (ʿalā al-taʿyīn), is a malzūm for the realization of its counterpart.”

51 See William T. Parry & Edward A. Hacker (1991), Aristotelian Logic, p. 387, Table 29.1; p. 389, Table 29.2.

52 See Shams al-Dīn Muḥammad al-Samarqandī (Forthcoming), Risāla fī Ādāb al-Baḥth, §50 (wa-l-muḥāl jāza an yastalzima al-muḥāl); Walter Edward Young (2018), “Al-Samarqandī’s Third Masʾala,” p. 70, p. 75, p. 105, p. 108-11, passim; Shams al-Dīn Muḥammad al-Samarqandī (2014), Qisṭās al-Afkār, p. 389 (amr mumtaniʿ fa-jāza an yalzamahu al-muḥāl), p. 527 (wa-l-muḥāl jāza an yastalzima al-muḥāl), p. 557 (wa-l-muḥāl jāza an yastalzima al-naqīḍayn).

53 See Khaled El-Rouayheb (2009), “Impossible Antecedents.” In response to my query during a conference talk, Asad Q. Ahmed confirmed that this notion of “the absurd entails the absurd” (al-muḥāl yulzimu al-muḥāl) goes back at least to Ibn Sīnā (Conférence internationale “Fallacies in the Arabic, Byzantine, Hebrew and Latin Traditions”; Lille, 24-6 May 2021, organizers: Shahid Rahman & Leone Gazziero). Importantly, Riccardo Strobino (2018), “Ibn Sina’s Logic,” (“3.2.5 Impossible antecedents”) observes that: “Avicenna is keenly interested in conditionals with impossible antecedents (sophisticated discussions are to be found in his account of a- and e-conditionals and in connection with reductio arguments) but only in the sense in which an impossibility may genuinely be derived from another impossibility, as it were, out of the meaning of the terms involved, not in the sense in which an arbitrary consequent may trivially be inferred from an impossible antecedent.” Among other comparative inquiries, al-Samarqandī’s usage of the principle “it is possible that the absurd entail the absurd” (wa-l-muḥāl jāza an yakūna mustalziman li-l-muḥāl), here and elsewhere, should be compared with Ibn Sīnā’s, and the discussions of other post-Avicennan scholars.

54 See, for example, among many others, Imām al-Ḥaramayn al-Juwaynī (1981), Al-Burhān fī Uṣūl al-Fiqh, ed. ʿAbd al-ʿAẓīm al-Dīb, Kuwait, Dār al-Qalam, 2.835-55 (§§796-818); Abū Isḥāq Ibrāhīm al-Shīrāzī (1988), Sharḥ al-Lumaʿ, ed. ʿAbd al-Majīd Turkī, Beirut, Dār al-Gharb al-Islāmī, p. 2.857-60 (§995); Abū Ḥāmid Muḥammad al-Ghazālī (1413 [1993/4]), Al-Mustaṣfā min ʿIlm al-Uṣūl, 4 vols., ed. Ḥamza b. Zuhayr Ḥāfiẓ, Medina, Ḥ.b.Z. Ḥāfiẓ, 3.636-40; Fakhr al-Dīn Muḥammad b. ʿUmar al-Rāzī (1992), Al-Maḥṣūl fī ʿIlm Uṣūl al-Fiqh, ed. Jābir Fayyāḍ al-ʿAlwānī, 6 vols., Beirut, Muʾassasat al-Risāla, p. 5.207-216; ʿUthmān b. ʿUmar Ibn al-Ḥājib (2006), Mukhtaṣar Muntahā al-Suʾl wa-l-Amal fī ʿIlmay al-Uṣūl wa-l-Jadal, 2 vols., ed. Nadhīr Ḥamādū, Beirut, Dār Ibn Ḥazm, p. 1106-8; Sayf al-Dīn Abū al-Ḥasan ʿAlī b. Muḥammad al-Āmidī (2003), Al-Iḥkām fī Uṣūl al-Aḥkām, 4 vols. in 2, ed. ʿAbd al-Razzāq al-ʿAfīfī, Riyadh, Dār al-Ṣumayʿī, p. 3.374-8; Burhān al-Dīn al-Nasafī (2015), Al-Fuṣūl, p. 49-50; Abū ʿAbd Allāh Badr al-Dīn Muḥammad al-Zarkashī (1992), Al-Baḥr al-Muḥīṭ fī Uṣūl al-Fiqh, 6 Vols., ed. ʿAbd al-Qādir ʿAbd Allāh al-ʿĀnī, ʿUmar Sulaymān al-Ashqar, ʿAbd al-Sattār Abū Ghurra, et al. Kuwait, Wizārat al-Awqāf wa-l-Shuʾūn al-Islāmiyya, p. 5.243-7.

55 Undoubtedly part of the reason lies in the more nuanced treatment of multiple madārs we see with al-Nasafī and al-Samarqandī, an example of which we will encounter in the third faṣl of this third inquiry. A great deal more research is required, however, before a proper assessment of this apparent synthesis can be made.

56 See Walter Edward Young (2019), Concomitance to Causation,” p. 276-7, and sources cited therein.

57 A critical commentator (who may have been Ibn Taymiyya) on Burhān al-Dīn al-Nasafī’s Fuṣūl also makes this connection between E&N dawarān and co-equal entailment, referring to the E&N dāʾir as the “co-equal entailed thing” (al-lāzim al-musāwī). See Walter Edward Young (2019), Concomitance to Causation,” p. 224.

58 See Walter Edward Young (2019), Concomitance to Causation,” p. 221-2, 274-5.

59 These ideas are further developed in this current issue of Methodos, in the article “In Existence and in Nonexistence: Types, Tokens, and the Analysis of Dawarān as a Test for Causation.”

60 Such as we find in J.S. Mill’s “Four Methods of Experimental Inquiry.” Here and in his commentary on al-Nasafī’s Fuṣūl, al-Samarqandī in fact takes certain analyses further than Mill. See Walter Edward Young (2019), Concomitance to Causation,” p. 277-9.

61 Just as al-Samarqandī shows us (by transposition): if there is talāzum (no existential separation) between them, then there is madāriyya between them.

62 Elsewhere, al-Samarqandī dives deeper and produces a more complex set of rules for multiple madārs. See Walter Edward Young (2019), Concomitance to Causation,” p. 228-230.

63 See Walter Edward Young (2019), Concomitance to Causation,” p. 268-9; Walter Edward Young (Forthcoming A), Islamic Legal Theoretical and Dialectical Approaches to Fallacies of Correlation and Causation (7th-8th/13th-14th centuries),” [edited volume from the conference “Islamic Legal Theory: Intellectual History and Uṣūl al-Fiqh,” Istanbul, 2019], eds. R. Gleave and M. Bedir, [pre-print p. 8-9].

64 Ahmad Hasan (1986), Analogical Reasoning in Islamic Jurisprudence: a Study of the Juridical Principle of Qiyās, Islamabad, Islamic Research Institute, p. 334; Aron Zysow (2013), Economy of Certainty, p. 225; Walter Edward Young (Forthcoming A), Fallacies of Correlation and Causation,” [pre-print p. 15-16].

65 This is further supported by how the line breaks in MS British Library Or. 3730 (Ms. [أ] of the edition), at the end of line 1 fol. 76a, precisely where the omitted text would appear. That a similar line-break occurs in British Library Or. 3908 (Ms. [ب] of the edition) cannot be presently confirmed; at the time of writing I no longer have access to (or images of) that witness. Whether or not there is a similar break, however, the same text could be missing from both if the older (ب), copied in 1471 CE, served as exemplar for the newer (أ), copied in 1760 CE, or both had the same exemplar (note that both are of Yemeni provenance).

66 Note this explanation of the detachment (takhalluf) resonates with the formula for detachment in §29: “this [p] is not a malzūm for that [q] while this [p] might be realized and thus entail the negation of that [q] overall (fī l-jumla).”

67 Note that this rule is in the disjunctive ponendo tollens form, which, as mentioned before, is valid only in exclusive disjunctions.

68 This phrase supplying the full model for what appears partially omitted in §54.

69 In his Risāla fī Ādāb al-Baḥth, for example, he claims to have “invented” the three illustrative problem-questions with which the treatise concludes.

70 The latter has been suggested by Shahid Rahman. See the postscript to Walter Edward Young (2021), “Formal Evolution of Islamic Juridical Dialectic,” p. 110-111.

71 Note that Aristotle articulates contradiction in both ways. In Met. 4.4 he says: “it will not be possible to be and not to be the same thing,” and “the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be in fact;” but he later says in Met. 4.6 “since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing” (Aristotle (1954), Metaphysica, trans. W.D. Ross, The Works of Aristotle, vol. 8, Oxford, Oxford University Press). Moreover, he brings affirmation and negation into the picture in Met. 4.7 “there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate.” Some light is shed by Paula Gottlieb (2019), “Aristotle on Non-contradiction,” The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.), URL: https://plato.stanford.edu/archives/spr2019/entries/aristotle-noncontradiction/. Among other helpful things, she notes: “There are arguably three versions of the principle of non-contradiction to be found in Aristotle: an ontological, a doxastic and a semantic version.” Note that even the “doxastic” version uses be and not-be; only the “semantic” version uses true.

72 Riccardo Strobino (2018), “Ibn Sina’s Logic,” §3.2.3 notes that Ibn Sīnā treated three types of disjunction: “exclusive and exhaustive,” “exclusive non-exhaustive,” and “inclusive.” Later logicians called the latter two (in Strobino’s translation) “preventing the joint affirmation of the two disjuncts” (māniʿat al-jamʿ) and “preventing the joint negation of the two disjuncts” (māniʿat al-khuluww), respectively. These may also be translated more literally as “preventing the conjoining [of both disjuncts]” and “preventing the being devoid [of both disjuncts].” Either way, they parallel al-Samarqandī’s “mutual negation / exclusion in existence not in nonexistence” (E-not-N tanāfin) and “mutual negation / exclusion in nonexistence not in existence” (N-not-E tanāfin).

73 Reviewer A, in keeping with earlier opinions, suggests that the real answer is because al-Samarqandī’s talāzum and dawarān simply do not express propositional relations.

74 Again, Reviewer A, suggests that this is because al-Samarqandī’s talāzum and dawarān are not for propositional relations.

75 Abū ʿAlī al-Ḥusayn b. ʿAbd Allāh Ibn Sīnā (1985), Kitāb al-Najāt fī l-Ḥikma al-Manṭiqiyya wa-l-Ṭabīʿiyya wa-l-Ilāhiyya, ed. Mājid Fakhrī, Beirut, Dār al-Āfāq al-Jadīda, p. 85-86; cf. Asad Q. Ahmed’s transl. (which guided my own), in Abū ʿAlī al-Ḥusayn b. ʿAbd Allāh Ibn Sīnā (2011), Avicenna’s Deliverance: Logic; translation and notes by Asad Q. Ahmed; introduction by Tony Street, Karachi, Oxford University Press, p. 71, §§83.i-ii.

76 As we might expect, Reviewer A suggests that this is because qiyās istithnāʾī is for propositional relations while talāzum is not.

77 Al-Samarqandī’s universalizing program is even more evident in the illustrations of his Commentary (Sharḥ) on Burhān al-Dīn al-Nasafī’s Fuṣūl, wherein every juristic example is paired with one from the natural world or the domain of theological speculation.

78 Cf. for example al-Nasafī’s Fuṣūl, upon which al-Samarqandī wrote a commentary, and which is most likely the more immediate inspiration for the ʿAyn al-Naẓar. It opens with a discussion of these three logical relations (talāzum, tanāfin, dawarān), but then proceeds to a host of other legal theoretical and dialectical concerns.

79 For examples of the logic of entailment and opposition in dialectical objection and response, see Walter Edward Young (2016), “Mulāzama in Action.”

80 On denial with corroboration (manʿ maʿa mustanad), see Shams al-Dīn Muḥammad al-Samarqandī (Forthcoming), Risāla fī Ādāb al-Baḥth, §§16, 19; Shams al-Dīn Muḥammad al-Samarqandī (1353 [1934/5]), Ādāb al-Ḥakīm, p. 126; and Shams al-Dīn Muḥammad al-Samarqandī (2014), Risāla fī Ādāb al-Baḥth, p. 76, p. 77-8, with Quṭb al-Dīn al-Kīlānī (Forthcoming), Sharḥ al-Risāla al-Samarqandiyya, §§16.1-5; 19.1-13.

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Walter Edward Young, « On the Logical Machinery of Post-Classical Dialectic: The Kitāb ʿAyn al-Naẓar of Shams al-Dīn al-Samarqandī (d. 722/1322) »Methodos [En ligne], 22 | 2022, mis en ligne le 01 mai 2022, consulté le 06 juin 2023. URL : http://journals.openedition.org/methodos/9053 ; DOI : https://doi.org/10.4000/methodos.9053

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Walter Edward Young

McGill University, Institute of Islamic Studies

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