Doug Walton, who died in January 2020, was a prolific author whose work in informal logic and argumentation had a profound influence on Artificial Intelligence, including Artificial Intelligence and Law. He was also very interested in interdisciplinary work, and a frequent and generous collaborator. In this paper seven leading researchers in AI and Law, all past programme chairs of the International Conference on AI and Law who have worked with him, describe his influence on their work.

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 Aris... (shrink)

When in classical formal logic the notions of deduction, valid inference and logical consequence are defined, causal language plays no role. The founder of western logic, Aristotle, identified ‘non-cause’, or ‘positing as cause what is not a cause’, as a logical fallacy. I argue that a systematic re-examination of Aristotle's analysis of NCF, and the related language of logical causality, in the Sophistical Refutations, Topics, Analytics and Rhetoric, helps us to understand his conception of. It reveals that Aristotle's syllogismhood is (...) non-monotonic, and thus narrower than classical validity as consisting in, or coextensive with, necessary truth-preservation. It also supports the conclusion that a syllogism is a form of relevant consequence: the premisses must be causes of the conclusion in the sense that they are not only sufficient but also necessary for the conclusion to follow. Close analysis of NCF also suggests that syllogistic relevance is not a semantic matter, but a syntactic.. (shrink)

In Prior Analytics 1.27–30, Aristotle develops a method for finding deductions. He claims that, given a complete collection of facts in a science, this method allows us to identify all demonstrations and indemonstrable principles in that science. This claim has been questioned by commentators. I argue that the claim is justified by the theory of natural predication presented in Posterior Analytics 1.19–22. According to this theory, natural predication is a non-extensional relation between universals that provides the metaphysical basis for demonstrative (...) science. (shrink)

Formal dialectic has its roots in ancient dialectic. We can trace this influence in Charles Hamblin’s book on fallacies, in which he introduced his first formal dialectical systems. Earlier, Paul Lorenzen proposed systems of dialogical logic, which were in fact formal dialectical systems avant la lettre, with roles similar to those of the Greek Questioner and Answerer. In order to make a comparison between ancient dialectic and contemporary formal dialectic, I shall formalize part of the Aristotelian procedure for Academic debates. (...) The resulting system will be compared (1) with Van Eemeren and Grootendorst’s system of rules of Critical Discussion (the pragma-dialectical discussion procedure), which must, however, first itself be reconstructed as a formal dialectical system, and (2) with a Hamblin-type system, and (3) a Lorenzen-type system. When drawing comparisons, it will become clear that there is a line to be drawn from Aristotle to formal dialectic and pragma-dialectics, extending to contemporary computational models of argument. (shrink)

In this paper it is shown how plausible reasoning of the kind illustrated in the ancient Greek example of the weak and strong man can be analyzed and evaluated using a procedure in which the pro evidence is weighed against the con evidence using formal, computational argumentation tools. It is shown by means of this famous example how plausible reasoning is based on an audience’s recognition of situations of a type they are familiar with as normal and comprehensible in their (...) shared common knowledge. The paper extends previous work on this example by using three new multiagent argumentation schemes closely related to the scheme for argument from negative consequences. (shrink)

Sweet Analytics, ‘tis thou hast ravish'd me,Bene disserere est finis logices.Is to dispute well logic's chiefest end?Affords this art no greater miracle?(Christopher Marlow, Doctor Faustus, Act 1,...

I claim that, in the Topics, Aristotle advises dialectical questioners to intentionally argue fallaciously in order to escape from some dialectically awkward positions, and I work through the consequences of that claim. It will turn out that, although there are important exceptions, the techniques for finding arguments described in Topics I–VII are, by and large, locations that Aristotle thought of as appropriate for use in philosophical inquiry. The text that grounds this claim, however, raises a further problem: it highlights the (...) solitary nature of philosophical inquiry, which puts into question the philosophical relevance of Topics VIII. I find that the Topics provides inadequate grounds for thinking that Aristotle saw Topics VIII as describing standards or techniques of argument that were appropriate for philosophy, and so these texts cannot be used by contemporary commentators to shed light on Aristotle's philosophical practice. Finally, although Aristotle saw philosophy as a solitary activity, he th.. (shrink)

In the present article I attribute to the common topic in the Rhetoric a two-fold suggestive function and a guarantee function. These three functions are possible because this type of topic, while often quite abstract, nevertheless contains thought-steering, substantial terms, and formulates a generally empirical or normative endoxon. Assuming that according to Aristotle an enthymeme has at least two premises, it would appear that a common topic is the abstract principle behind the often implicit major premise. This means that the (...) topic may be regarded as the – generalizing – if-then statement in a modern argumentation scheme. Therefore it should be possible to see the enthymemes of Rhetoric 2.23 as a combination of a logical argument form (which can usually be reconstructed as modus ponens) and an argumentation scheme – even though we may not attribute this idea to Aristotle himself. (shrink)

Sweet Analytics, ‘tis thou hast ravish'd me,Bene disserere est finis logices.Is to dispute well logic's chiefest end?Affords this art no greater miracle?(Christopher Marlow, Doctor Faustus, Act 1,...

1. Something strange commenced to happen in the field of logic from the beginning of the seventeenth century. Oral disputation, rather than falling into oblivion as a relic of medieval darkness wit...

The presence of premises expressing comparison is a problem for the Aristotelian theory of the dialectical method, first because there is no general theory of comparison in the Organon and secondly because along with propositions on the opposition and inflexion of the terms, comparative statements seem to fall outside the explicit description which Aristotle gives of possible premises. The purpose of this paper is to offer a synthetic theory of comparisons according to Aristotle’s Topics, in an attempt both to supply (...) the aforementioned absence and to highlight the importance of the second problem. There are three main types of premises on the more, the less and the similar: some comparing the degree of possession of a predicate, others comparing the plausibility of a predication and finally, others expressing an analogy. Once expounded the very marked differences that occur between these three classes of propositions, the paper analyses the various kinds of argumentation based on comparative premises and offers a formalization of its logical laws. The complexity of this theory and the volume of topoi involved in the comparisons show the magnitude of a problem that has not been sufficiently studied. (shrink)

Saadya Gaon (882 – 942), one of the outstanding Rabbis in the period of the Geonim, rejected the legitimacy of legal inference, as part of his polemics with his contemporary Karaite scholars. The paper analyzes Saadya's stance regarding the logical basis of legal inference, and shows that Saadya's distinction between reason and revelation in the domain of legal inference is only in regard to the ‘illah– the factor that connects the case with its law. The rationality of the commandments, on (...) the other hand, is based according to Saadya upon the manfa‘ah– the utility of the commandments, and hence Saadya's religious doctrine turns out to be coherent and consistent. Maimonides (1138–1204), who was one of the most important figures in the Jewish scholarly world in the Middle Ages, adopted the Aristotelian concept of dialectics in order to facilitate his theory of Jewish legal argumentation. Unlike Saadya, Maimonides saw inferences in the realm of the law as legitimate. His position can be considered an inclination towards the Karaite ideology according to which reason must be the ruler in the realm of the law. Nevertheless, Maimonides' stance deviates from that of Karaites in a crucial point: according to Maimonides, only authorized institutions are qualified to use legal inference. Since the Talmud, according to Maimonides, represents the teachings of the rabbinical authorized institutions, its legal instructions must be followed. The article describes Maimonides' position regarding legal and Talmudic inferences, and shows that Maimonides' inclination towards the Karaite theory remains within the limits of the Rabbanite ideology. (shrink)

At Topics 8.11 161b19–33 Aristotle lists five criticisms () which may be leveled against a dialectical argument ‘in itself’ (). The five criticisms correspond in many respects to the familiar conditions Aristotle places on syllogism and refutation. However, begging the question —the violation of the condition that the conclusion of a syllogism be something different () from the premises—seems not to appear on the list of five criticisms. That this omission is only apparent becomes clear once it is seen that (...) the five criticisms are not independent but rather amount to five successive filters through which an argument may be passed before its non-genuineness is exposed. This result sheds light on Aristotle's curious insistence, in the face of the heterogeneity of his examples of BTQ in Topics 8.13, that every question-begging refutation contains a premise that is ‘the same’ as the conclusion. The fact that the five criticisms expose BTQ as a defect in syllogistic reasoni.. (shrink)

Aristotle’s classification of ideal number in Metaphysics M 6 has often been considered an unfair presentation of Plato’s actual views. I take another look at the passage and argue that Aristotle is a more careful critic than has been usually recognised. In particular, I argue that much of the scholarly discussion on the passage has failed to take account of Aristotle’s deeper concern, namely, the conditions necessary for numbers to be ordinal. I then set Aristotle’s critique within the broader context (...) of his concern to separate Form from Number, and thus to separate metaphysical questions from mathematical ones. The latter half of the article shows some of the consequences of mixing mathematics with metaphysics from a systematic and historical point of view. (shrink)

The presence of premises expressing comparison is a problem for the Aristotelian theory of the dialectical method, first because there is no general theory of comparison in the Organon and secondly because along with propositions on the opposition and inflexion of the terms, comparative statements seem to fall outside the explicit description which Aristotle gives of possible premises. The purpose of this paper is to offer a synthetic theory of comparisons according to Aristotle’s Topics , in an attempt both to (...) supply the aforementioned absence and to highlight the importance of the second problem. There are three main types of premises on the more, the less and the similar : some comparing the degree of possession of a predicate, others comparing the plausibility of a predication and finally, others expressing an analogy. Once expounded the very marked differences that occur between these three classes of propositions, the paper analyses the various kinds of argumentation based on comparative premises and offers a formalization of its logical laws. The complexity of this theory and the volume of topoi involved in the comparisons show the magnitude of a problem that has not been sufficiently studied. (shrink)

The present paper examines three parts of ancient school rhetoric: the issues, the topics, and the questions of style from the perspective of legal semiotics. It aims (1) to demonstrate the roles these have played and can play in the interpretation of legal discourses; and (2) to summarise what insights have been and can be gained from this classical tradition by contemporary legal research. It is argued that the promise of legal semiotics for rhetorical investigations is that it may help (...) to make sense of the functioning of the system of ancient rhetoric, and contribute to our understanding of how rhetorical tradition works, while the research of ancient rhetoric can explore a range of semiotic devices essential for lawyerly thinking, resulting in the knowledge of a richer framework of interpretation. (shrink)