1.1.2. Inference

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.

This conclusion could be one of the premises, but more often it is different from all of them and draws on several.

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 the statements 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 we draw a conclusion from a claim or claims that we accept. The term assumption need not carry the suggestion of acceptance (or even acceptability), 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. The two terms will serve mainly as alternative expressions for the same idea.

(If it seems strange to consider drawing conclusions 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 contradictory conclusions.)