Some judgments, then, namely inferences, are derived. What about those from which they are derived or inferred? They also may be inferred from others, but sooner or later, of course, we must come to judgments which are not inferred from others. How are they obtained? Well, they are immediate judgments either of perception or of intuition. That is to say, they are the outcome either of sense-perception or of that kind of intellectual intuition by which we apprehend so-called self-evident truths. It is sometimes rather difficult to say whether a given judgment is immediate or inferred. With advance in the power of analysis and discrimination it may be seen readily that many judgments which are commonly considered to be perpetual or self-evident are really inferences, at least in part. Still, the difficulties are not, as a rule, insurmountable. But what is of special interest at pres ent is that logic is mainly concerned with inferred judgments, and with others only in so far as they furnish a basis for inference. The nature and reliability of immediate judgments as such con stitute problems which belong partly to psychology and partly to the theory of knowledge. Logic is the study of inferences, not of all kinds of beliefs.
Having explained the term inference, we must next consider what is meant by valid inference in the definition of logic from which we started. It means, of course, the same as accurate, correct, sound. But it must not be treated as synonymous with true. An inference is valid when it is justified by the evidence given in support of it. It is true if it expresses the facts as they are. Now careful reasoners generally aim at inferences which shall be both correct and true. But an inference may be either without the other. For example, speculators sometimes make inferences which turn out to be true although they were not really valid, that is, were not justified by the available evidence. On the other hand, propositions are sometimes refuted by a mode of reasoning commonly known as "reduction to absurdity," that is, by showing that a valid inference drawn from it is untrue. Now logic is the study of valid inference, not true inference. This is not because logic is not interested in truth, for its own function is to explain the true conditions of valid inference. It is simply a case of that division of labour which necessity has forced upon all the sciences. The study of the conditions of valid inference means the study of the general relations between inferences and premises. This is a sufficiently important task by itself. The study of the conditions of true inference would mean, in addition, an investigation into the truth of all possible premises—an ob viously impossible task.
ence only makes explicit what is latent in implication. Now the judgments which imply the inference or conclusion are usually called the evidence or the premises. Sometimes the evidence con sists of formulated propositions ; sometimes it consists of facts of observation. This distinction is not a hard and fast one, because, on the one hand, "facts" only become evidence when they give rise to judgments, which can always be expressed in propositions; and, on the other hand, all judgments are in the last resort based on facts. But the distinction is a convenient one in some ways.
There are cases in which the question of objective fact, in the usual sense of the term, does not arise.
For example, every State has its laws, which are in a sense the arbitrary (though not capricious) decisions or enactments of the legislature, and so are, in many ways, different in different states. The judges who have to administer these laws have to treat them as authoritative and final for the time being. They only have to understand them and their full implications, and to apply them to relevant cases. It is not their business to check the truth of these laws in the way in which it is the business of a man of science to check the truth of what are currently accepted as laws of nature. So that there are cases in which inference or reasoning is mainly concerned with the meaning and implication of certain propositions or premises, and not with the facts (if any) from which they derive. Such inference or reasoning may be called formal, or deductive, in the rather wide and loose sense of these terms that has become traditional. On the other hand, inference or reasoning which sets out from facts of observation without relying in a special degree on propositions accepted either on authority, or even provisionally for the sake of argument, may be called inductive, material or empirical, again in the loose traditional sense of these terms. As the term "deductive" is needed for another purpose, the former type of inference will be described here as formal; and the latter type will be called inductive, which is the least unsatisfactory of the traditional terms. It should be noted at once, however, that whereas formal reasoning can often be carried far without the intervention of inductive reasoning (or simply "induction"), induction can rarely go far without the auxiliary use of formal inference at certain stages, such as the verification of tentative hypotheses, for in stance. Again, inductive reasoning constitutes what is widely known as scientific method. As a mere matter of convenience inductive inference will be dealt with under the heading of SCIEN TIFIC METHOD, while this article will deal mainly with formal inference, and with one or two other special types of inference.