Topics (topoi), in a long tradition stemming from Aristotle's rhetoric and early writings on argumentation and logic, are the places where arguments can be found to make a case, and the warrants that can back a logical inference leading from premises to a conclusion. Argumentation schemes are tools of modern argumentation theory that have been developed to fulfil the latter function, but may also be useful to fulfill the former one as well. In this chapter we will outline the varied developments of the topoi in both the logical and rhetorical traditions, starting with Aristotle, the first to describe them. We will examine some leading accounts of them given in the Middle Ages, when they were studied in relation to logical consequences.

Aristotle's Topics contains accounts of many commonly used types of arguments he calls topics (topoi, or places). There are some 300–400 of these topics, depending on how you count them, according to Kienpointner (1997, p. 227). Many topics can also be found in Aristotle's Rhetoric. What these topics supposedly represent has been subject to many different interpretations over the centuries. Many have interpreted the topic as a device to help an arguer search around to find a useful argument she can use, for example, in a debate or in a court of law. Other have taken the topic to have a guaranteeing or warranting function that enables rational inferences to be drawn from a set of premises to a conclusion.

Argument from analogy is one of the fundamental forms of argumentation on which many other forms of argument – argument from precedent in law, for example – are based (Gordon, 1995; Weinreb, 2005). Our system of Anglo-American law is based on ratio decidendi, the principle that if a case has been decided by a court in a certain way, then a new case that is similar to it should be decided in the same way. Indeed, argument from analogy is the foundation of all case-based reasoning (CBR) in which the argumentation turns on a comparison of one case to another (Ashley and Rissland, 2003). CBR not only compares one case to another as similar, but also compares cases as more similar to others with respect to a given case, depending on the description of the problem posed in the given case. Thus argument from analogy is an extremely important and fundamental species of argumentation. So much has been written on it, in so many fields, including philosophy, cognitive science, artificial intelligence, linguistics, psychology, law, and computing, that we can barely scratch the surface here. Our more limited aim is to develop tools that can be used to identify the precise form of arguments from analogy, allowing us to better understand its close relationships with other important schemes, especially those representing argument from verbal classification and argument from precedent.

The schemes studied in this chapter typically represent arguments of a kind that are weak and subject to default. They work best as uses of plausible reasoning in situations of uncertainty and lack of knowledge. However, they are so fragile and prone to error that they have traditionally been treated in logic as fallacies under the headings argumentum ad populum and argumentum ad hominem. Even so, despite their inherent fragility and proneness to exploit prejudice, they can be reasonable arguments in many instances, and sometimes they may be the best kind of evidence we have to make a rational decision. First we address the kind of argument Aristotle called endoxic, meaning that it is based on an opinion accepted by the majority and/or by the wise (the experts). In logic, this form of argument is called appeal to popular opinion, but it might be less negative to label it argument from informed public opinion. Then we address ethotic argumentation, recognized by Aristotle as especially powerful. Ethos is the moral character of the speaker. It can be used to support an argument, but in the argumentum ad hominem, or personal attack on an arguer's character, it is used to discredit his argument. Many argumentation schemes fitting this general type have now been identified and studied, and much of the chapter is taken up with reviewing and discussing these schemes.

The connection between these two apparently different classes of argumentation schemes can be found in the analysis of the meaning of “plausibility.”

The goal of this chapter is to show how to formalize the schemes by expressing each scheme as a formal inference structure in a way comparable to forms of inference we all are already familiar with in deductive logic, and to some extent in inductive reasoning. Although deductive and inductive forms of argument can be included as argumentation schemes, the most difficult part of this project is the formalization of the defeasible schemes. The defeasible schemes listed in the compendium represent the most common forms of reasoning not only in everyday discourse, but also in special contexts of use like legal and scientific reasoning. The defeasible schemes presented in the compendium look to have a rough formal structure, but there is a wide variety of them, utilizing many different kinds of variables and constants. Before the schemes can be formalized, further clarifications need to be made (Verheij, 2003).

THE DEFEASIBLE MODUS PONENS FORM OF SCHEMES

In order to be useful in logic, artificial intelligence, and related scientific fields, schemes must be formalized, meaning that they have to be codified in some precise way so that the coder (whether machine or human) can recognize a particular argument as fitting a scheme and then use it to derive conclusions from the given set of premises based on that identification. Once an argument is recognized as fitting a scheme, an argument markup, utilizing an argument diagram, can reconstruct the argument in a given case using the scheme as a template or pattern on which to frame the reconstruction.

One of the most valuable uses of schemes is to enable an argument analyst to fill in implicit assumptions needed to make sense of a given argument she is trying to analyze. Arguments that have missing (unstated) premises or conclusions are traditionally called enthymemes in logic. One problem with enthymemes is that reasonable people can have differences of opinion on what the implicit assumptions are supposed to be. Filling in the missing parts of an enthymeme may depend on interpreting the natural language text in which the argument was put forward, to try to fairly judge what the speaker meant to say. The danger of attributing such missing assumptions to an arguer is that of unwittingly committing the straw man fallacy. This fallacy is committed when an arguer misrepresents her opponent's position to make it look more extreme or unreasonable than it really is, in order to attack it more easily. In some cases, more than one interpretation of a given argument is possible. Thus the problem is to find out what kind of evidence is needed to support or question the claim that some proposition really can be inserted into an apparently incomplete argument presented in a text of discourse, without unfairly distorting what the speaker meant to say. It will be shown in this chapter, by studying key examples, how argumentation schemes constitute an important part of this evidence.

The goal of this chapter generally is to explore the role of argumentation schemes in enthymeme reconstruction.

The theory of argumentation is a rich interdisciplinary area of research spanning philosophy, communication studies, linguistics, computer science, and psychology. In the past few years, formal models of argumentation have been steadily gaining importance in artificial intelligence, where they have found a wide range of applications in specifying semantics for logic programs, generating natural language text, supporting legal reasoning, and facilitating multi-agent dialogue and negotiation on the Internet. The most useful and widely used tool so far developed in argumentation theory is the set of argumentation schemes. Argumentation schemes are forms of argument (structures of inference) that represent structures of common types of arguments used in everyday discourse, as well as in special contexts like those of legal argumentation and scientific argumentation. They include the deductive and inductive forms of argument that we are already so familiar with in logic. However, they also represent forms of argument that are neither deductive nor inductive, but that fall into a third category, sometimes called defeasible, presumptive, or abductive. Such an argument may not be very strong by itself, but may be strong enough to provide evidence to warrant rational acceptance of its conclusion, given that its premises are acceptable (Toulmin, 1958). Such an argument can rightly carry weight, or be a plausible basis for acceptance, on a balance of considerations in an investigation or discussion that is moving forward, as new evidence is being collected.

In this chapter, a new model of causation is formulated that views causal argumentation as defeasible. The new model structures many of the most common cases of causal argumentation as dialectical, meaning that the case is viewed in the context of an investigation or discussion in which two parties take part in a collaborative process of rational argumentation. The model is shown to apply very well, particularly during the initial stages of an investigation, where information is incomplete but preliminary hypotheses are formed. But it will also be argued that causal arguments need to be evaluated differently in different contexts. In scientific argumentation, there is an investigative process in which tentative hypotheses are formulated about a cause at an early stage, and then tested and refined at later stages. In legal argumentation, the method of evaluation typically is a trial or some other form of dispute resolution in which a causal claim made by one side is opposed to one made by the other side. For example, it could be a case in tort law concerning whether a toxic substance caused cancer in a population. In a criminal case, it could be a trial concerning the cause of an accident. In such cases, there are differing opposed views on what the cause of something is, and it is to such cases that the defeasible model applies best.

In this chapter we develop a pragmatic theory of refutation in which a refutation is defined as a sequence of dialogue moves in which an argument is used by one party to attack and defeat an opposed argument put forward previously by the other party. A fundamental distinction is drawn between refutation and rebuttal. A rebuttal is an argument that is opposed to another argument. It stands against the argument it is opposed to. But it does not necessarily refute that argument. Refutation is something more powerful. A refutation knocks down the original argument. It not only is opposed to the original argument, but also has enough strength itself as an argument that it overpowers the original argument and knocks it down (defeats it). This distinction is not a very firm or precise one in everyday conversational usage. An attempted refutation is, after all, a refutation in conversational English, even if it is not strong enough to knock down the argument it is opposed to. But still, as we hope to show, there is something to this distinction. Refutation is stronger than rebuttal. A refutation is something like a strong rebuttal, or a rebuttal that has active force in successfully attacking the argument it is aimed at.

A parallel distinction that has been very influential in recent work in artificial intelligence can be drawn between attacking and defeating an argument (Dung, 1995; Prakken, 1997).