David Hitchcock
1. Introduction[1],[2]
The concept of an argument for which I propose an analysis is the reason-giving sense in which one speaks, for example, about Daniel Kahneman’s argument (2011, pp. 334-335) that the tendency of most people to be risk averse about gains but risk-seeking about losses is irrational. This sense of the word ‘argument’ should be sharply distinguished from the disputational sense in which one speaks about two people having an argument, discussed in Chapter 8. That these are two different senses is clear from the fact that languages other than English use two different words for the two senses. For example, in French, ‘to argue’ in the sense of quarrelling is ‘disputer’, whereas ‘to argue’ in the sense of giving reasons for or against is ‘argumenter’.
We could give a rough lexical definition of the word ‘argument’ in this sense by quoting the definition by the Hellenistic Stoics of an argument as “a system composed of premisses[3] and a conclusion” (systêma ek lêmmatôn kai epiphoras, Diogenes Laertius 1925/ca. 210-240, 7.45). Aside from its idiosyncratic failure to recognize one-premiss arguments, this definition is an acceptable starting point for a conceptual analysis. That analysis would need to answer a number of questions raised by the lexical definition. What is a premiss? What is a conclusion? What sorts of entities can function as a premiss? What sorts can function as a conclusion? How do premisses and a conclusion form a unified system? Does such a system have an intrinsic function or purpose, or on the contrary can it be used for various purposes? What about complex arguments?
We should recognize that arguments are not necessarily the content or product of argumentation—that is, of communications in which arguments are exchanged. One can consider an argument for a certain position or policy even if nobody has ever used that argument. One can imagine crazy arguments that no sane person would ever put forward. One can apply the term ‘argument’ to unified stretches of solo reasoning where some conclusion is reached on the basis of reasons, as when one considers mentally various aspects of a situation and then describes “the argument that finally convinced me”. Indeed, it seems consistent with our ordinary use of the term ‘argument’ in its reason-giving sense to say that there are arguments that nobody has ever thought of and nobody ever will. The most we can demand is that an argument must be thinkable and expressible. Arguments as a class thus have no common function or purpose. They are not necessarily used to justify or establish something. Nor are they necessarily used to persuade anybody.
Thus, critical thinking textbooks that define ‘argument’ as “rational persuasion—an attempt to influence another or others using reasons” are actually describing one use of arguments, not the concept itself.
2. Simple arguments
Begin by considering simple arguments, in the sense of single-inference systems that consist