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Ibn Ḥazm on Heteronomous Imperatives. A Landmark in the History of the Logical Analysis of Norms
Abstract
Ibn Ḥazm of Córdoba’s (994–1064) defence of logic has lasting consequences for the logic of norms. His book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples is a demonstration of how Aristotelian logic may be applied in the religious sciences, especially law. Among other things, he thoroughly investigates deontic notions and their modal counterparts, assuring him a place among the fathers of the logic of norms. The basic units of Islamic deontic logic qualify the performance of actions as subject to either reward, or sanction, or neither; and they might therefore be called, indulging in terminological anachronism, heteronomous imperatives. With remarkable insight, Ibn Ḥazm pairs these with the natural modalities of necessity, possibility, and impossibility. Employing some features of Martin-Löf’s Constructive Type Theory (CTT) to shape the logic of heteronomous imperatives thus emerging from Ibn Ḥazm’s insights, the authors formulate a new approach to the logical analysis of deontic categories.KeywordsArabic logicHeteronomous imperativeIbn ḤazmDeontic logicIslamic jurisprudence
Qiyās, or “correlational inference” (often glossed as “analogy”), comprises a primary set of methodological tools recognized by a majority of premodern Sunnī jurists. Its elements, valid modes, and proper applications were the focus of continual argument and refinement. A particular area of debate was the methodology of determining or justifying the ʿilla: the legal cause (or occasioning factor, or ratio legis) giving rise to a ruling in God’s Law. This was most often discussed (and disputed) under the rubric of “the modes of causal justification” (masālik al-taʿlīl). Among these modes was the much debated test of dawarān (concomitance of presumed cause and effect). In brief, proponents of dawarān employed it to justify claims that a property (waṣf) occasioned the ruling (ḥukm) in an authoritative source-case (aṣl). In concert with other considerations, the demonstrated co-presence (ṭard) and co-absence (ʿaks) of property and ruling—that is, their concomitance “in existence” (wujūdan) and “in nonexistence” (ʿadaman)— was taken as an indication that the property was the ruling’s ʿilla. Delving further into dawarān and causation (ʿilliyya), the current study interprets “in existence” and “in nonexistence” not as a kind of metaphor for true and false (within the framework of a classical truth-functional formal semantics), but as an accurate terminology vis-à-vis the meaning of causality statements, fully compatible with dominant Islamicate views on causal agency. In brief, a deeper logical and linguistic analysis of the different existential modes of dawarān strongly suggests that we should distinguish property (or phenomenon) and ruling (or effect) as types (concepts or propositions linguistically expressed by a sentence) as opposed to tokens (instantiations of the type; the real, ontological events that verify the proposition). Our reading of dawarān as shaped by a finer-grained structure not only allows us to identify the efficient occasioning process as a function which takes some particular token of the ʿilla (arguably, the property or properties which provide the ruling’s material cause) and renders a token of the general ruling type, but it allows us to elucidate the role of taʿlīl (causal justification) in shaping an epistemological theory of argument to the best explanation: a sophisticated, premodern manifestation of abductive reasoning.
The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy.
Aron Zysow's 1984 PhD dissertation, "The Economy of Certainty," remains the most important, compelling, and intellectually ambitious treatment of Islamic legal theory (usul al-fiqh) in Western scholarship to date. It continues to be widely read and cited, and remains unsurpassed in its incisive analysis of the most fundamental assumptions of Islamic legal thought. Zysow argues that the great dividing line in Islamic legal thought is between those legal theories that require certainty in every detail of the law and those that will admit probability. The latter were historically dominant and include the leading legal schools that have survived to our own day. Zahirism and, for much of its history, Twelver Shi'ism, are examples of the former. The well-known dispute regarding the legitimacy of juridical analogy is only one feature of this fundamental epistemological division, since probability can enter the law in the process of authenticating prophetic traditions and in the interpretation of the revealed texts, as well as through analogy. The notion of consensus in Islamic legal theory functioned to reintroduce some measure of certainty into the law by identifying one of the competing probable solutions as correct. Consequently consensus has only a reduced role, if any, in those systems that reject probability. Another, more radical, means of regaining certainty was the doctrine that regarded the legal reasoning of all qualified jurists on matters of probability as infallible. The development of legal theories of both types, that of Zahirism no less than that of Hanafism, was to a large extent shaped by theology and, most significantly, by Mu'tazilism, and subsequently by Ash'arism and Maturidism. Zysow's important work is published here in full, for the first time, with updated references and some further reflections by the author.
This volume collects Davidson's seminal contributions to the philosophy of mind and the philosophy of action. Its overarching thesis is that the ordinary concept of causality we employ to render physical processes intelligible should also be employed in describing and explaining human action. In the first of three subsections into which the papers are thematically organized, Davidson uses causality to give novel analyses of acting for a reason, of intending, weakness of will, and freedom of will. The second section provides the formal and ontological framework for those analyses. In particular, the logical form and attending ontology of action sentences and causal statements is explored. To uphold the analyses, Davidson urges us to accept the existence of non‐recurrent particulars, events, along with that of persons and other objects. The final section employs this ontology of events to provide an anti‐reductionist answer to the mind/matter debate that Davidson labels ‘anomalous monism’. Events enter causal relations regardless of how we describe them but can, for the sake of different explanatory purposes, be subsumed under mutually irreducible descriptions, claims Davidson. Events qualify as mental if caused and rationalized by reasons, but can be so described only if we subsume them under considerations that are not amenable to codification into strict laws. We abandon those considerations, collectively labelled the ‘constitutive ideal of rationality’, if we want to explain the physical occurrence of those very same events; in which case we have to describe them as governed by strict laws. The impossibility of intertranslating the two idioms by means of psychophysical laws blocks any analytically reductive relation between them. The mental and the physical would thus disintegrate were it not for causality, which is operative in both realms through a shared ontology of events.
This volume collects the published essays of the late Professor Hourani on Islamic ethics in the earlier classical and formative periods of Islamic civilization. Ethics was from the start at the core of Islam, and the construction of philosophical theories to support normative ethics made those centuries among the most profound and intensely active in the history of ethical thought. The book opens with two general and contextual pieces and thereafter it is organized by schools of thought in a broadly chronological order. The essays centre around two related debates in Islamic philosophy: over the ontological status of value, and over the sources of our knowledge of value. The answers developed follow similar lines to the rational theology and philosophy of the West, and Professor Hourani brings out the frequent parallels. As a whole, the volume will introduce and establish the importance of the Islamic tradition of thought about ethics.
This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion.
One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning.
According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.
This monograph proposes a new (dialogical) way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general (including legal reasoning in Common and Civil Law) but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning studied in contemporary philosophy of science and argumentation theory.
After an overview of the emergence of qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor (qiyās al-'illa). The second part of the volume deliberates on the system of correlational inferences by indication and resemblance (qiyās al-dalāla, qiyās al-shabah). The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general.
In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of e-conversion, Darapti and Bocardo and e-subalternation, while showing how close to Aristotle’s text these proofs remain.
Before the rediscovery of Stoic logic during the 20th Century, the debate between the two French historians of philosophy Victor Brochard (1848-1907) and Octave Hamelin (1856-1907) triggered a renewed interpretation of Stoic syllogistics by focusing on the relations between logic and physics, and their philosophical implications.
This volume, the first dedicated and comprehensive companion to medieval logic, covers both the Latin and the Arabic traditions and shows that they were in fact sister traditions, which both arose against the background of a Hellenistic heritage and which influenced one another over the centuries. A series of chapters by both established and younger scholars covers the whole period including early and late developments, and offers new insights into this extremely rich period in the history of logic. The volume is divided into two parts, 'Periods and traditions' and 'Themes', allowing readers to engage with the subject from both historical and more systematic perspectives. It will be a must-read for students and scholars of medieval philosophy, the history of logic, and the history of ideas.
This volume, the first dedicated and comprehensive companion to medieval logic, covers both the Latin and the Arabic traditions and shows that they were in fact sister traditions, which both arose against the background of a Hellenistic heritage and which influenced one another over the centuries. A series of chapters by both established and younger scholars covers the whole period including early and late developments, and offers new insights into this extremely rich period in the history of logic. The volume is divided into two parts, 'Periods and traditions' and 'Themes', allowing readers to engage with the subject from both historical and more systematic perspectives. It will be a must-read for students and scholars of medieval philosophy, the history of logic, and the history of ideas.
One of the epistemological results emerging from this initial study is that the different forms of co-relational inference , known in the Islamic jurisprudence as qiyās , represent an innovative and sophisticated form of reasoning that not only provides new epistemological insights into legal reasoning in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical argumentation studied in contemporary philosophy of science. However, in the present paper we will only discuss the case of so-called co-relational inferences of the occasioning factor and only in the context of Islamic jurisprudence.
Sébastien Magnier provides a remarkable analysis of the notion of conditional right with the help of public announcement logic that he generalizes for the logical study of legal norms. Magnier’s main idea, motivated by the earlier exhaustive textual and systematic work of Matthias Armgardt and the subsequent studies carried out by Alexandre Thiercelin, involves Leibniz’s notion of certification, which plays a central role in the famous De conditionibus. Magnier proposes to render the notion of certification of A as there is public evidence for A. More generally, the meanings of “conditional right” and “conditional legal norm” are established by means of identifying a specific kind of dialogical interaction during a legal trial constituted by games of giving and asking for reasons. This yields a theory of meaning rooted in the practice itself of legal debates.
The main aim of this paper is to study the notion of conditional right by means of constructive type theory (CTT) which provides the means to develop a system of contentual inferences rather than of syntactic derivations. Moreover, in line with Armgardt, I will first study the general notion of dependence as triggered by hypotheticals and then the logical structure of dependence specific to conditional right. I will develop this idea in a dialogical framework where the distinction between play-object and strategy-object leads to the further distinction between two basic kinds of pieces of evidence and where meanings is constituted by the interaction of obligations and entitlements.
In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in the context of dialectical games. One consequence of our approach is a novel explanation of the doctrine of the existential import of the quantifiers in dialectical terms. After a brief survey of Lorenzen's dialogical logic, we offer a set of rules for dialectical games based on previous work by Castelnérac and Marion, to which we add here the rule for the universal quantifier, as interpreted in terms of its counterpart in dialogical logic. We then give textual evidence of the use of that rule in Plato's dialogues, thus showing that Aristotle only made explicit a rule already implicit in practice, while providing a new interpretation of ‘epagogic’ arguments. Finally, we show how a proper understanding of that rule involves further rules concerning counterexamples and delaying tactics, stressing again the parallels with dialogical logic.
This paper focuses on the role of presumptions and conjectures in Leibniz’s legal theory. Both presumptions and conjectures are closely connected to the question of the burden of proof for presumptions lead to a shift of the burden. Thus, these notions play an essential role in the practice of litigation: the odds to win a given case are stacked against the party that has to bear the burden of proof. The paper analyses three different texts which bear upon the topic and stem from different phases of Leibniz’s production: the Elementa Juris Naturalis (1671), the De legum interpretatione, rationibus, applicatione, systemate (1678/1679), and the Nouveaux Essais sur l’entendement humain (1704, published posthumously in 1765). The aim of the paper is to elucidate how Leibniz developed a subtle theory of legal presumptions and conjectures. Moreover, the paper attempts a first formal reconstruction of this theory.
In Prior Analytics 1.15 Aristotle undertakes to establish certain modal syllogisms of the form XQM. Although these syllogisms
are central to his modal system, the proofs he offers for them are problematic. The precise structure of these proofs is disputed,
and it is often thought that they are invalid. We propose an interpretation which resolves the main difficulties with them:
the proofs are valid given a small number of intrinsically plausible assumptions, although they are in tension with some claims
found elsewhere in Aristotle’s modal syllogistic. The proofs make use of a rule of propositional modal logic which we call
the possibility rule. We investigate how this rule interacts and coheres with the core elements of the modal syllogistic.
Let us rehearse what may be termed the standard account of the meaning of the monadic deontic operator ◯. Relative to each possible world, including our own, there is a non-empty class of possible worlds that are deontic alternatives to the given world. A sentence of the form ◯ A is adjudged true at a possible world just in case A itself holds true at each of the world’s deontic alternatives. The picture is of a non-empty class of worlds functioning collectively as a moral standard: What is true at all such worlds is what ought to be true. Let us call the logic of ◯ that arises from this account standard monadic deontic logic, or D*. On the basis of ordinary propositional logic, it is given by the rule of inference together with the axioms
and \begin{array}{*{20}{c}} {OK.} & {(\bigcirc A \wedge \bigcirc B) \to \bigcirc (A \wedge B).} \\ \end{array}
The existing literature treats of several investigations with a certain bearing on the question which is roughly indicated by the title “Imperatives and Logic.” Some of those investigations, however, are entirely outside the scope of the present work.
Mally sets himself the task of developing a “Logik des Willens” constituting a parallel to the usual logic, the “Logik des Denkens". In order to emphasize its independence, the author also calls this “Logik des Willens” “Deontik”, and he conceives it as being based on the “Wesensgesetze” of will in the same way as the usual logic is conceived as being based on the “Wesensgesetze” of thought. The author develops a formalistic deductive system on the basis of 5 axioms of demands (Grundsatze des Bollen), including the axiom that there is at least one fact which is unconditionally demanded, and through a lengthy series of theorems he arrives at the sentence that what is unconditionally demanded is identical with what is actually the case: “was sein soll, ist Tatsache”. Similarly, the author develops a system of axioms for “right” volition, including the axiom that right volition is non-contradictory.