Since argument is so central to critical thinking, Part III, comprising seven chapters, has been set aside to focus on contemporary theories of, approaches to, and construction of argument.

In Chapter 8, Anthony Blair sets out two different referents of ‘argument’ and discusses the connection between the study of arguments and the study of critical thinking. In Chapter 9, David Hitchcock develops a careful analysis of the concept of an argument as, in the case of a simple argument, a set of reasons for or against a claim. Chapter 10, by pioneers and experts in the development of argument mapping software, Martin Davies, Ashley Barnett and Tim van Gelder, offer instructions for using some of the current computer assisted argument mapping (a.k.a. tree-diagramming) programs for the purpose of interpreting and displaying arguments. Chapter 11 is an introduction to argument schemes, which are widely referenced in the contemporary argumentation literature, by their most renowned theoretician, Douglas Walton. Chapter 12 outlines the theoretical framework that lies behind constructing arguments by rhetoric and communications scholar, Beth Innocenti. In Chapter 13, Blair lays out the different steps involved in judging arguments—identifying, interpreting, displaying, evaluating and responding to them—and sets out a variety of ways arguments may be assessed. Christopher Tindale’s Chapter 14 expands on one method of evaluating arguments, namely assessing them for fallacies, at the same time providing an account of how fallacies have come to be understood in today’s argumentation literature.