This article models legal interpretation through argumentation and provides a logical analysis of interpretive arguments, their conflicts, and the resulting indeterminacies. Interpretive arguments are modelled as defeasible inferences, which can be challenged and defeated by counterarguments and be reinstated through further arguments. It is shown what claims are possibly (defensibly) or necessarily (justifiably) supported by the arguments constructible from a given interpretive basis, i.e., a set of interpretive canons coupled with reasons for (...) their application. It is finally established under what conditions such arguments provide single outcomes or rather support alternative interpretive conclusions, thus leading to propositions of law whose truth‐value is undetermined. (shrink)

Some philosophers have recently emphasized the similarities between lawmaking and the production of linguistic utterances in ordinary communication. Based on these similarities, they have defended a theory of legal interpretation that identifies the legal content of a lawmaking act with the communicative content of the authoritative “utterance”. While different versions of the theory differ with respect to which level of utterance content they regard as relevant, they agree that the theory’s scope is fully general in that it applies to all (...) legal systems. In this paper, we argue that this commitment of the theory is problematic. By examining the role of interpretative arguments in legal interpretation, we argue that there is a tension between this commitment and the doctrine of the rule of recognition. In light of this, we argue that Hartian positivism is only compatible with a weakened or “minimal” version of the theory. Insofar as both the communication theory and Hartian positivism provide true insights on how legal content is determined, this result gives us reason to accept only a minimal version of the theory. (shrink)

Le présent article vise à développer la notion d’« interprétation argumentative » introduite par Carel dans la Théorie des Blocs Sémantiques avec deux autres notions, celles de « décodage argumentatif » et de « Carte Argumentative du Lexique ». Il s’agira de montrer que l’interprétation argumentative est soumise à des contraintes alors que Carel semble donner plus de poids à la liberté qu’on a d’interpréter argumentativement un énoncé.

It is wrong to think that questions of interpretation are significant in informal logic only to the extent that they contribute to the assessment of an argument's conclusion. For one thing, logic is essentially about validity, about that in virtue of which conclusions do or do not follow from given premises, and not about the truth or falsity of conclusions by themselves. Secondly, the evaluation of a given argument requires first determining what the given argument is. Moreover, since arguments (...) are given in rational discourse in order to persuade-in order to arrive, by reason, at agreement-it is necessary to address the very arguments that arguers actually intend. (shrink)

How do we determine whether individuals accept the actual consistency of a political argument instead of just its rhetorical good looks? This article answers this question by proposing an interpretation of political argument within the constraints of political liberalism. It utilises modern developments in the philosophy of logic and language to reclaim ‘meaningless nonsense’ from use as a partisan war cry and to build up political argument as something more than a power struggle between competing conceptions of the good. Standard (...) solutions for ‘clarifying’ meaning through descriptive definition encounter difficulties with the biases of status quo idioms, as well as partisan translations and circularity. Collectively called linguistic gerrymandering, these difficulties threaten political liberalism’s underlying coherency. The proposed interpretation of political argument overcomes this with a new brand of conceptual analysis that can falsifiably determine whether rhetoric has hijacked political argument. (shrink)

This book shows how research in linguistic pragmatics, philosophy of language, and rhetoric can be connected through argumentation to analyze a recognizably common strategy used in political and everyday conversation, namely the distortion of another’s words in an argumentative exchange. Straw man argumentation refers to the modification of a position by misquoting, misreporting or wrenching the original speaker’s statements from their context in order to attack them more easily or more effectively. Through 63 examples taken from different contexts (including political (...) and forensic discourses and dialogs) and 20 legal cases, the book analyzes the explicit and implicit types of straw man, shows how to assess the correctness of a quote or a report, and illustrates the arguments that can be used for supporting an interpretation and defending against a distortion. The tools of argumentation theory, a discipline aimed at investigating the uses of arguments by combining insights from pragmatics, logic, and communication, are applied to provide an original account of interpretation and reporting, and to describe and illustrate tactics and procedures that can be used and implemented for practical purposes.. This book will appeal to scholars in the fields of political communication, communication in general, argumentation theory, rhetoric and pragmatics, as well as to people working in public speech, speech writing, and discourse analysis. (shrink)

This paper proposes an argumentation-based procedure for legal interpretation, by reinterpreting the traditional canons of textual interpretation in terms of argumentation schemes, which are then classified, formalized, and represented through argument visualization and evaluation tools. The problem of statutory interpretation is framed as one of weighing contested interpretations as pro and con arguments. The paper builds an interpretation procedure by formulating a set of argumentation schemes that can be used to comparatively evaluate the types of arguments used in (...) cases of contested statutory interpretation in law. A simplified version of the Carneades Argumentation System is applied in a case analysis showing how the procedure works. A logical model for statutory interpretation is finally presented, covering pro-tanto and all-things-considered interpretive conclusions. -/- . (shrink)

This chapter proposes a dialectical approach to legal interpretation, consisting of three dimensions: a formalization of the canons of interpretation in terms of argumentation schemes; a dialectical classification of interpretive schemes; and a logical and computational model for comparing the arguments pro and contra an interpretation. The traditional interpretive maxims or canons used in both common and civil law are translated into defeasible patterns of arguments, which can be evaluated through sets of corresponding critical questions. These (...) interpretive argumentation schemes are classified in general categories and a distinction is drawn between schemes supporting and rebutting an interpretation. This framework allows conceiving statutory interpretation as a dialectical procedure consisting in weighing arguments pro and contra an interpretation. This procedure is formalized and represented computationally through tools from formal argumentation systems. (shrink)

In this paper it is shown how certain defeasible argumentation schemes can be used to represent the logical structure of the most common types of argument used for statutory interpretation both in civil and common law. The method is based on an argumentation structure in which the conclusion, namely, the meaning attributed to a legal source, is modeled as a claim that needs that is be supported by pro and con defeasible arguments. The defeasible nature of each scheme is (...) shown by means of critical questions, which identify the default conditions for the accepting interpretative arguments and provide a method for evaluating a given argument as weak or strong. (shrink)

Statutory interpretation involves the reconstruction of the meaning of a legal statement when it cannot be considered as accepted or granted. This phenomenon needs to be considered not only from the legal and linguistic perspective, but also from the argumentative one - which focuses on the strategies for defending a controversial or doubtful viewpoint. This book draws upon linguistics, legal theory, computing, and dialectics to present an argumentation-based approach to statutory interpretation. By translating and summarizing the existing legal interpretative canons (...) into eleven patterns of natural arguments - called argumentation schemes - the authors offer a system of argumentation strategies for developing, defending, assessing, and attacking an interpretation. Illustrated through major cases from both common and civil law, this methodology is summarized in diagrams and maps for application to computer sciences. These visuals help make the structures, strategies, and vulnerabilities of legal reasoning accessible to both legal professionals and laypeople. (shrink)

The problem of establishing the best interpretation of a speech act is of fundamental importance in argumentation and communication in general. A party in a dialogue can interpret another’s or his own speech acts in the most convenient ways to achieve his dialogical goals. In defamation law this phenomenon becomes particularly important, as the dialogical effects of a communicative move may result in legal consequences. The purpose of this paper is to combine the instruments provided by argumentation theory with the (...) advances in pragmatics in order to propose an argumentative approach to meaning reconstruction. This theoretical proposal will be applied to and tested against defamation cases at common law. Interpretation is represented as based on a hierarchy of interpretative presumptions. On this view, the development of the logical form of an utterance is regarded as the result of an abductive pattern of reasoning in which various types of presumptions are confronted and the weakest ones are excluded. Conflicts of interpretations and equivocation become essentially interwoven with the dialectical problem of fulfilling the burden of defeating a presumption. The interpreter has a burden of explaining why a given presumption is subject to default, assuming that the speaker is reasonable and acting based on a set of shared expectations. (shrink)

The prospects for realistic interpretation of the nature of initial mathematical truths and objects are considered in the article. The arguments of realism, reasons impeding its recognition among philosophers of mathematics as well as the ways to eliminate these reasons are discussed. It is proven that the absence of acceptable ontological interpretation of mathematical realism is the main obstacle to its recognition. This paper explicates the introductory positions of this interpretation and presents a realistic interpretation of the arithmetical component (...) of mathematics. In summary, we should like to note that such constructions, as it is shown to us, ought to bring the direct use not only for the philosophical foundation of mathematics but for mathematics itself. In the justification of the author’s conclusions based on the works of famous mathematicians of the twentieth century, interpreting their findings in a broad historical and philosophical context. To illustrate his point, the author gives examples of arithmetic and geometry - both Euclidean and non-Euclidean. (shrink)

Testable predictions of quantum mechanics are invariant under time reversal. But the evolution of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This is a fact that challenges any realistic interpretation of the quantum state. On the other hand, this fact raises no difficulty if we interpret the quantum state as a mere calculation device, bookkeeping past real quantum events.

This paper is about the situation in which an author (writer or speaker) presents a deductively invalid argument, but the addressee aims at a charitable interpretation and has reason to assume that the author intends to present a valid argument. How can he go about interpreting the author’s reasoning as enthymematically valid? We suggest replacing the usual find-the-missing-premise approaches by an approach based on systematic efforts to ascribe a belief state to the author against the background of which the argument (...) has to be evaluated. The suggested procedure includes rules for recording whether the author in fact accepts or denies the premises and the conclusion, as well as tests for enthymematic validity and strategies for revising belief state ascriptions. Different degrees of interpretive charity can be exercised. This is one reason why the interpretation or reconstruction of an enthymematic argument typically does not result in a unique outcome. (shrink)

Arguments from fairness as described in Aristotle’s _Rhetoric_ are usually taken to aim at mitigating the strictness of the law or, in terms of procedure, to favour the defendant. This paper considers a more inclusive interpretation, that is, that arguments from fairness can work both ways. In the example given in the _Rhetoric,_ arguments from fairness are directed at a restrictive interpretation of the text. That may not be necessary however. Likewise, fairness may speak for the claimant. (...) Two examples may support this conclusion: a judicial speech by Hyperides, and the doctrine of issues appearing in Hellenistic school rhetoric. (shrink)

Analogously to Kuhn’s and Hanson’s understanding of observation as theory-impregnated, we try to test the hypothesis that observation and interpretation might also be value-impregnated. We use a written examination task for medical students who were asked to read and interpret a text where the authors provide arguments pro et contra euthanasia. Afterwards the students were asked to provide their own reflected opinion on the issue. We found that medical students who were against and indecisive provided interpretations of the text (...) which accorded with their own reflected opinions (P = 0.02), indicating that their interpretations were influenced by their own values. When including those who were pro euthanasia, the association was no longer significant. Although the present investigation was a small pilot-study, we obtained partial support for our hypothesis and have adjusted it to read as follows: observations and interpretations might be value-impregnated for respondents who have rather strong value-based attitudes. We think the adjusted hypothesis deserves to be further examined. (shrink)

The purpose of this paper is to improve on the logical and measure-theoretic foundations for the notion of probability in the law of evidence, which were given in my contributions Åqvist [ (1990) Logical analysis of epistemic modality: an explication of the Bolding–Ekelöf degrees of evidential strength. In: Klami HT (ed) Rätt och Sanning (Law and Truth. A symposium on legal proof-theory in Uppsala May 1989). Iustus Förlag, Uppsala, pp 43–54; (1992) Towards a logical theory of legal evidence: semantic analysis (...) of the Bolding–Ekelöf degrees of evidential strength. In: Martino AA (ed) Expert systems in law. Elsevier Science Publishers BV, Amsterdam, North-Holland, pp 67–86]. The present approach agrees with the one adopted in those contributions in taking its main task to be that of providing a semantic analysis, or explication, of the so called Bolding–Ekelöf degrees of evidential strength (“proof-strength”) as applied to the establishment of matters of fact in law-courts. However, it differs from the one advocated in our earlier work on the subject in explicitly appealing to what is known as “Pro-et-Contra Argumentation”, after the famous Norwegian philosopher Arne Naess. It tries to bring out the logical form of that interesting kind of reasoning, at least in the context of the law of evidence. The formal techniques used here will be seen to be largely inspired by the important work done by Patrick Suppes, notably Suppes [(1957) Introduction to logic. van Nostrand, Princeton and (1972) Finite equal-interval measurement structures. Theoria 38:45–63]. (shrink)

In this paper I critically discuss and, in the end, reject Morgan’s Canon, a popular principle in comparative psychology. According to this principle we should always prefer explanations of animal behavior in terms of lower psychological processes over explanations in terms of higher psychological processes, when alternative explanations are possible. The validity of the principle depends on two things, a clear understanding of what it means for psychological processes to be higher or lower relative to each other and a justification (...) of a general preference for explanations that refer to lower psychological abilities. However, I argue that we cannot spell out the idea of a psychological scale in a way that claim is satisfied. I start with the discussion of different interpretations of the notion of a psychological scale. In Sect. 3, I discuss different possible strategies to justify any of those interpretations and argue that all of them fail. Finally, in Sect. 4, I generalize the argument for all possible interpretations of Morgan’s Canon and propose an alternative strategy: We should base our interpretations of animal behavior on more general principles such as evidential support and explanatory power, as followed in other scientific domains. (shrink)

According to Schopenhauer’s compensation argument for pessimism, the non-existence of the world is preferable to its existence because no goods can ever compensate for the mere existence of evil. Standard interpretations take this argument to be based on Schopenhauer’s thesis that all goods are merely the negation of evils, from which they assume it follows that the apparent goods in life are in fact empty and without value. This article develops a non-standard variant of the standard interpretation, which accepts the (...) relevance of the negativity thesis but rejects that the argument assumes that life’s goods are all empty and valueless. Instead, it argues that whatever value negative goods might possess, they do not have the kind of value to compensate for positive evils. This involves additional development of the negativity thesis and a defence of it against objections from Byron Simmons (2021). (shrink)

This article addresses the relationship between understanding and believing from the cognitive perspective of information-processing. I promote, within the scope of the Critical Discourse Analysis agenda, the relevance of an account of belief-fixation sustained by a combination of argumentative and cognitive insights. To this end, I first argue that discursive strategies fulfilling legitimization purposes, such as evidentials, tap into the same cognitive mechanisms as arguments. I then proceed to examine the idea that the most effective arguments are the (...) ones that manage to obscure or make irrelevant counter-evidence and propose, from a cognitive pragmatic perspective, a formulation of rhetorical effectiveness as a constraint on information-selection taking place at the interpretation stage and decisively influencing the evaluation stage responsible for belief-fixation. (shrink)

We present an interdisciplinary approach to argumentation combining logical, probabilistic, and psychological perspectives. We investigate logical attack principles which relate attacks among claims with logical form. For example, we consider the principle that an argument that attacks another argument claiming A triggers the existence of an attack on an argument featuring the stronger claim A ∧ B. We formulate a number of such principles pertaining to conjunctive, disjunctive, negated, and implicational claims. Some of these attack principles seem to be prima (...) facie more plausible than others. To support this intuition, we suggest an interpretation of these principles in terms of coherent conditional probabilities. This interpretation is naturally generalized from qualitative to quantitative principles. Specifically, we use our probabilistic semantics to evaluate the rationality of principles which govern the strength of argumentative attacks. In order to complement our theoretical analysis with an empirical perspective, we present an experiment with students of the TU Vienna ( n = 139) which explores the psychological plausibility of selected attack principles. We also discuss how our qualitative attack principles relate to well-known types of logical argumentation frameworks. Finally, we briefly discuss how our approach relates to the computational argumentation literature. (shrink)

«De la Dénotation» est l’un des articles les plus importants de la tradition analytique, pourtant il n’existe pas d’interprétation canonique pour l’un de ses argument-clés. Certains croient que le passage en question démontre que les concepts dénotants en eux-mêmes sont contradictoires; d’autres que la théorie qui les sous-tend est incohérente. Les deux interprétations sont trop fortes et sont contredites par le texte du passage. Nous l’interprétons plutôt comme un ensemble de considérations qui conservent à l’ancienne théorie, bien qu’elle soit encombrante (...) et prolixe, la possibilité de concurrencer la nouvelle presentation sémantique de Russell. (shrink)

The subject of this study are the argumentation strategies applied by the Polish and German apex courts competent in criminal matters, namely the Supreme Court and the Federal Court of Justice, respectively. The investigation encompasses a total of 200 rulings issued by the criminal panels of these bodies. Particular focus was put on examining which arguments both courts apply to solve interpretation problems, and secondly, how these courts systematize the interpretation process. Methodologically, the examination utilizes, inter alia, the principles (...) of qualitative research, without neglecting the legal dogmatic perspective. A crucial theoretical foundation underlying this study is the distinction between formalistic and substantive legal cultures. The examination reveals that neither the Polish nor the German legal culture is purely formalistic or value-oriented. Nevertheless, the Supreme Court of Poland shows greater affinity for formalistic arguments, whereas the substantive interpretation methods are more widespread in the judicature of the German Federal Court of Justice. In particular, the Polish Court prefers the linguistic interpretation, whereas the German Court favours the purposive approach. (shrink)

We propose a formal theory built upon an abstract argumentation framework for handling argumentation dynamics. To that end, we analyze the acceptability dynamics of arguments through the proposal of two different kinds of sets of arguments which are somehow responsible for the acceptability/rejection of a given argument. We develop a study of the consequences of breaking the construction of such sets towards the acceptance of an analyzed argument. This brings about the proposal of a novel change operation which (...) allows to determine which arguments should be removed from the framework so that another particular argument becomes accepted. Finally, the proposed model is formalized in the light of the theory of belief revision by characterizing the corresponding operations through constructive definition and an axiomatic characterization, connecting them through the corresponding representation theorem. The theoretical proposal constitutes the fundamentals for a system implementation in many dynamic domains of application. In particular, we show its application for handling the dynamics of legal interpretation. In that sense, this proposal constitutes a fundamental approach and theoretical justification to handle the dynamics of legal arguments through changes of interpretative canons. We show a possible concretisation of our abstract theory for the legal domain by analysing a real legal case from the Argentinean jurisprudence. Such a system would be capable of suggesting alternative critical points in the current state of affairs of a legal case towards pursuing a specific goal for which the case is being investigated. (shrink)

In this comment I consider Jack Balkin’s general argument for his method of constitutional interpretation – the question of why interpret (the United States Constitution) in this way (as presented in his book Living Originalism). I contrast this question with the way in which the conclusion of this argument should be implemented with regard to specific clauses – the question of how to interpret (the United States Constitution). While the former question is concerned with the general form of the argument, (...) the latter is concerned with a substantiation of one premise in the argument. (shrink)

Hume’s argument concerning induction is the foundation stone of his philosophical system, and one of the most celebrated and influential arguments in the entire literature of western philosophy. It is therefore rather surprising that the enormous attention which has been devoted to it over the years has not resulted in any general consensus as to how it should be interpreted, or, in consequence, how Hume himself should be seen. At one extreme is the traditional view, which takes the argument (...) to be thoroughly sceptical, leading to the sweeping conclusion that all “probable reasoning” or “reasoning concerning matter of fact and existence” is utterly worthless, so that Hume is portrayed as a negative Pyrrhonian intent on undermining the credentials of all our would-be knowledge of the world. But at the other extreme a number of very prominent commentators, particularly in recent years, have put forward a strikingly contrasting view, that Hume’s intentions here are entirely non-sceptical, and that so far from advancing a negative thesis himself, he is merely intent on showing the implausible consequences of the “rationalist” position taken by some of his philosophical opponents. (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

In this paper, I examine Plantinga’s (1993, 2000, 2011) Evolutionary Argument Against Naturalism (EAAN). While there has been much discussion about Plantinga’s use of probabilities in the argument, I contend that insufficient attention has been paid to the question of how we are to interpret those probabilities. In this paper, I argue that views Plantinga defends elsewhere limit the range of interpretations available to him here. The upshot is that the EAAN is more limited in its applicability than Plantinga alleges.

In this essay, I first argue that the Gray’s Elegy Argument—the dense passage in Bertrand Russell’s ‘On Denoting’—can be interpreted as a single, coherent argument against the notion that a definite description corresponds to what I call a multifaceted object—an object having multiple facets or sides. I then look into some manuscripts Russell wrote in 1904 and in 1905. I show that he had envisaged the notion of a multifaceted object and used it for two different purposes before he discovered (...) various objections to it, which he turned into the Gray’s Elegy Argument. (shrink)

The chapter considers two semantic issues concerning will-sentences: Stalnaker’s Asymmetry and modal subordination in Karttunen-type discourses. The former points to a distinction between will and modal verbs, seeming to show that will does not license non-specific indefinites. The latter, conversely, suggests that will-sentences involve some kind of modality. To account for the data, the chapter proposes that will is semantically a tense, hence it doesn’t contribute a quantifier over modal alternatives; a modal feature, however, is introduced in the interpretation of (...) a will-sentence through a supervaluational strategy universally quantifying over possible futures. That this is not part of will’s lexical semantics is shown to have consequences that ultimately contribute to explain Stalnaker’s Asymmetry. Furthermore, that a modal quantification is present in the interpretation of a will-sentence is shown to imply the availability of modal subordination in Karttunen-type discourses. (shrink)

_ Source: _Volume 61, Issue 1, pp 43 - 59 Contemporary debate on Plato’s cosmogony often assumes that the ‘literal’ reading of the _Timaeus_ yields an account of creation, while the view that the cosmos always existed is non-literal. In antiquity, Taurus has been seen as a forerunner of the ‘non-literal’ interpretation. This paper shows, on the contrary, that Taurus’ argument for the sempiternity of the cosmos is a literalist one, relying on a strict linguistic analysis of _Timaeus_ 28b6-8.

This article intends to be a simple guide to understand how Hoppe built the Argumentation Ethics. In my early studies of libertarian ideas, and of Argumentation Ethics in particular, I could not find a unique text that would explain how Hoppe put the necessary bricks together to build the Ethics. As I was curious about this issue, I assumed others would also like to know it. To write this article, I reviewed the main literature on Argumentation Ethics, starting with Kinsella’s (...) Concise Guide [9]. Then, I interviewed Stephan Kinsella and Prof. Walter Block. Finally, I synthesized the main ideas from the literature and the interviews elaborating an interpretative model, presented in this article. (shrink)

The South China Sea territorial dispute has been a contentious issue in the international community. In the course of 3 years, China and the Philippines had undergone arbitral proceedings over the maritime rights and entitlements in the South China Sea. As the Permanent Court of Arbitration reached its decision, this paper aims to examine the interpretation process of the Arbitral Tribunal in the judgment of the South China Sea conflict between China and the Philippines. The primary objective of the study (...) is to reconstruct or explain how the Tribunal came up with its interpretation of the written arguments presented by the parties involved and to distinguish whether such reconstruction the Tribunal has successfully interpreted or made sense of the said arguments and submissions. Doing so would necessitate a pragmatic analysis– the relevance-theoretic account of human communication and cognition. Data analyzed include written submissions and arguments as well as the legal documents used during the arbitral process. Using content analysis, the data were evaluated through applying the tool of interpretation based on the criteria set by the three conditions of the relevance theory: logical condition, pragmatic condition, and condition of optimal relevance. This paper argues that in order for the addressee of an utterance, in this case the Arbitral Tribunal, to attain a successful interpretation, it should meet these three conditions. This study found that the reconstruction of the interpretation based on the three conditions showed that the Tribunal had attained a valid and correct interpretation of the Philippines’ and China’s arguments. Furthermore, the paper asserts that implied conclusion and the contextual assumptions can be a guiding principle for the cognitive comprehension or interpretation of legal texts. (shrink)

We present an interdisciplinary approach to study systematic relations between logical form and attacks between claims in an argumentative framework. We propose to generalize qualitative attack principles by quantitative ones. Specifically, we use coherent conditional probabilities to evaluate the rationality of principles which govern the strength of argumentative attacks. Finally, we present an experiment which explores the psychological plausibility of selected attack principles.

In this paper I shall argue that Proclus' criticism of Plotinus in De malorum subsistentia 31,5-21 is not entirely accurate, if we take into account Plotinus' theory of contraries as explained in Enn. I.8.6. For while Proclus thinks it impossible that anything could ever produce its contrary out of itself , Plotinus seems to propose that gradual ontological derivation from the first Principle will lessen the chain of being inevitably to the zero point of non-being . Non-being, however, is contrary (...) to the first Principle in a more radical way than the one Proclus thought of when he stated that absolute Good could never be the cause of Evil: according to Plotinus' interpretation, Good and Evil as well as being and non-being are contraries insofar they have no common substratum and do not share a common gšnoj. I shall try to plausibly explain this prima facie somewhat awkward notion of contrariety found in Plotinus by adducing analogies to numerical series, taking a recent paper by Dominic O'Meara as a starting point for the discussion. (shrink)