Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

The overall goal of this paper is to show that computational modelling of argumentation theories is a useful tool to deepen them. Specifically, it provides a basic computational formalization of part of Pragma-dialectics’ model of a critical discussion, which serves as a basis for analyzing this influential theory of argumentation. Such analysis reveals some weaknesses and leaves some questions opened for Pragma-dialectics. Particularly, it shows that the model of a critical discussion is not independent of the model of reasoning/inference chosen, (...) because, while it performs differently with different models of reasoning, it does not work well with some of them. (shrink)

This paper attempts to systematically characterize critical reactions in argumentative discourse, such as objections, critical questions, rebuttals, refutations, counterarguments, and fallacy charges, in order to contribute to the dialogical approach to argumentation. We shall make use of four parameters to characterize distinct types of critical reaction. First, a critical reaction has a focus, for example on the standpoint, or on another part of an argument. Second, critical reactions appeal to some kind of norm, argumentative or other. Third, they each have (...) a particular illocutionary force, which may include that of giving strategic advice to the other. Fourth, a critical reaction occurs at a particular level of dialogue (the ground level or some meta-level). The concepts here developed shall be applied to discussions of critical reactions by Aristotle and by some contemporary authors. (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 explained that a dialogical approach to complex argumentation can be fruitful for solving two important problems concerning the analysis of the argumentation structure. First, such an approach makes it possible to clarify the distinction between coordinative and multiple argumentation structures, and to identify clues in the presentation for each of these structures. Second, a dialogical approach can provide a basis for dealing more adequately with refutations of counterarguments.

This volume gives a theoretical account of the problem of analyzing and evaluating argumentative discourse. After placing argumentation in a communicative perspective, and then discussing the fallacies that occur when certain rules of communication are violated, the authors offer an alternative to both the linguistically-inspired descriptive and logically-inspired normative approaches to argumentation. The authors characterize argumentation as a complex speech act in a critical discussion aimed at resolving a difference of opinion. The various stages of a critical discussion are outlined, (...) and the communicative and interactional aspects of the speech acts performed in resolving a simple or complex dispute are discussed. After dealing with crucial aspects of analysis and linking the evaluation of argumentative discourse to the analysis, the authors identify the fallacies that can occur at various stages of discussion. Their general aim is to elucidate their own pragma- dialectical perspective on the analysis and evaluation of argumentative discourse, bringing together pragmatic insight concerning speech acts and dialectical insight concerning critical discussion. (shrink)

In this book two of the leading figures in argumentation theory present a view of argumentation as a means of resolving differences of opinion by testing the acceptability of the disputed positions. Their model of a 'critical discussion' serves as a theoretical tool for analysing, evaluating and producing argumentative discourse. They develop a method for the reconstruction of argumentative discourse that takes into account all aspects that are relevant to a critical assessment. They also propose a practical code of behaviour (...) for discussants who want to resolve their differences in a reasonable way. This is a major contribution to the study of argumentation and will be of particular value to professionals and graduate students in speech communication, informal logic, rhetoric, critical thinking, linguistics, and philosophy. (shrink)

Argumentative discussion is successful only if, at the concluding stage, both parties can agree about the result of their enterprise. If they can not, the whole discussion threatens to start all over again. Dialectical ruling should prevent this from happening. The paper investigates whether dialectical rules may enforce a decision one way or the other; either by recognizing some arguments as conclusive or some criticisms as devastating. At the end the pragma-dialectical model appears more successful than even its protagonists have (...) claimed. (shrink)

In this paper, I present a dialogue game approach to the argumentation stage of a critical discussion. This formal perspective on the pragma-dialectical ideal model is meant to facilitate a contribution of pragma-dialectical theorising to the field of argumentation and computation. The dialogue game is based on the technical rules for a critical discussion that relate to the argumentation stage, and I will show how sequences of moves in the dialogue game relate to complex argumentation structures.