Sec. 2.  Inferences, in the Logical sense, are divided into two great classes, the Immediate and the Mediate, according to the character of the evidence offered in proof of them.  Strictly, to speak of inferences, in the sense of conclusions, as immediate or mediate, is an abuse of language, derived from times before the distinction between inference as process and inference as result was generally felt.  No doubt we ought rather to speak of Immediate and Mediate Evidence; but it is of little use to attempt to alter the traditional expressions of the science.

An Immediate Inference, then, is one that depends for its proof upon only one other proposition, which has the same, or more extensive, terms (or matter).  Thus that one means to national prosperity is popular education is an immediate inference, if the evidence for it is no more than the admission that popular education is a means to national prosperity: Similarly, it is an immediate inference that Some authors are vain, if it be granted that All authors are vain.

An Immediate Inference may seem to be little else than a verbal transformation; some Logicians dispute its claims to be called an inference at all, on the ground that it is identical with the pretended evidence.  If we attend to the meaning, say they, an immediate inference does not really express any new judgment; the fact expressed by it is either the same as its evidence, or is even less significant.  If from No men are gods we prove that No gods are men, this is nugatory; if we prove from it that Some men are not gods, this is to emasculate the sense, to waste valuable information, to lose the commanding sweep of our universal proposition.

Still, in Logic, it is often found that an immediate inference expresses our knowledge in a more convenient form than that of the evidentiary proposition, as will appear in the chapter on Syllogisms and elsewhere.  And by transforming an universal into a particular proposition, as No men are gods, therefore, Some men are not gods,—­we get a statement which, though weaker, is far more easily proved; since a single instance suffices.  Moreover, by drawing all possible immediate inferences from a given proposition, we see it in all its aspects, and learn all that is implied in it.

A Mediate Inference, on the other hand, depends for its evidence upon a plurality of other propositions (two or more) which are connected together on logical principles.  If we argue—­

      No men are gods;
      Alexander the Great is a man;
    .’.  Alexander the Great is not a god: 

this is a Mediate Inference.  The evidence consists of two propositions connected by the term ‘man,’ which is common to both (a Middle Term), mediating between ‘gods’ and ‘Alexander.’  Mediate Inferences comprise Syllogisms with their developments, and Inductions; and to discuss them further at present would be to anticipate future chapters.  We must now deal with the principles or conditions on which Immediate Inferences are valid:  commonly called the “Laws of Thought.”