1.1.2. Inference and arguments

The norms studied in logic can concern many different features of reasoning, and we will consider several of these. The most important one and the one that will receive most of our attention is inference, the action of drawing a conclusion from certain premises or assumptions.

Fig. 1.1.2-1. The action of inference.

Inferences are to be found in science when generalizations are based on data or when a hypothesis is offered to explain some phenomenon. They are also to be found when theorems are proved in mathematics. But the most common case of inference calls less attention to itself. Much of the process of understanding what we hear or read can be seen to involve inference because, when we interpret spoken or written language, our interpretation can usually be formulated as a statement, and we base this statement on statements in the text we interpret.

The terminology we will use to speak of inference deserves some comment. The terms premise and assumption both to refer to the starting points of inference—whether these be observational data, mathematical axioms, or the statements making up something heard or read. The term premise is most appropriate when the claim or claims from which we draw a conclusion are ones that we accept. The term assumption need not carry this suggestion, and we may speak of something being assumed merely for the sake of argument. In general, we will be far more interested in judging the quality of the transition from the starting point of an inference to its conclusion than in judging the soundness of its starting point, so the distinction between premises and assumptions will not have a crucial role for us. For the most part, we will use the two terms interchangeably, as alternative expressions for the same idea.

(If it should seem strange to consider conclusions inferred from claims that are not accepted, imagine going over a body of data to check for inconsistencies either within the data or with information from other sources. In this sort of case, you may well draw conclusions from data that you do not accept and, indeed, do this as a way of showing that the data is unacceptable—by showing, for example, that it leads to draw contradictory conclusions.)

It is convenient to have a term for a conclusion taken together with the premises or assumptions on which it is based. We will follow tradition and label such a combination of premises and conclusion an argument. A particularly graphic way of writing an argument is to list the premises (in any order) with the conclusion following and separated off by a horizontal line (as shown in Figure 1.1.2-1). The sample argument shown here is a version of a widely used traditional example and has often served as a paradigm of the sort of reasoning studied by deductive logic.

When we need to represent an argument horizontally, we will use / (virgule or slash) to divide the premises from the conclusion, so the argument above might also be written as All humans are mortal, Socrates is human / Socrates is mortal.

Notice that the information expressed in the conclusion of this argument is the result of an interaction between the two premises. In its broadest sense, the traditional term syllogism (whose etymology might be rendered as ‘reckoning together’) applies in the first instance to inference that is based on such interaction, and the argument above is a traditional example of a syllogism. Another traditional term, immediate inference, applied to arguments with a single premise. The term immediate is not used here in a temporal sense but instead to capture the idea of a conclusion that is inferred from a premise directly and thus without the mediation of any further premises.