| Instead of, | Write, |
| All men will die. | Every A is B. |
| All men are rational beings. | Every A is C. |
| Therefore some rational beings will die. | Therefore some Cs are Bs. |
The second of these is the same proposition, logically considered, as the first; the consequence in both is virtually contained in, and rightly inferred from, the premises. Whether the premises be true or false, is not a question of logic, but of morals, philosophy, history, or any other knowledge to which their subject-matter belongs: the question of logic is, does the conclusion certainly follow if the premises be true?
Every act of reasoning must mainly consist in comparing together different things, and either finding out, or recalling from previous knowledge, the points in which they resemble or differ from each other. That particular part of reasoning which is called inference, consists in the comparison of several and different things with one and the same other thing; and ascertaining the resemblances, or differences, of the several things, by means of the points in which they resemble, or differ from, the thing with which all are compared.
There must then be some propositions already obtained before any inference can be drawn. All propositions are either assertions or denials, and are thus divided into affirmative and negative. Thus, A is B, and A is not B, are the two forms to which all propositions may be reduced. These are, for our present purpose, the most simple forms; though it will frequently happen that much circumlocution is needed to reduce propositions to them. Thus, suppose the following assertion, ‘If he should come to-morrow, he will probably stay till Monday’; how is this to be reduced to the form A is B? There is evidently something spoken of, something said of it, and an affirmative connexion between them. Something, if it happen, that is, the happening of something, makes the happening of another something probable; or is one of the things which render the happening of the second thing probable.
| A | is | B |
| The happening of his arrival to-morrow | is | an event from which it may be inferred as probable that he will stay till Monday. |
The forms of language will allow the manner of asserting to be varied in a great number of ways; but the reduction to the preceding form is always possible. Thus, ‘so he said’ is an affirmation, reducible as follows:
| What you have just said (or whatever else ‘so’ refers to) | is | the thing which he said. |
By changing ‘is’ into ‘is not,’ we make a negative proposition; but care must always be taken to ascertain whether a proposition which appears negative is really so. The principal danger is that of confounding a proposition which is negative with another which is affirmative of something requiring a negative to describe it. Thus ‘he resembles the man who was not in the room,’ is affirmative, and must not be confounded with ‘he does not resemble the man who was in the room.’ Again, ‘if he should come to-morrow, it is probable he will not stay till Monday,’ does not mean the simple denial of the preceding proposition, but the affirmation of the directly opposite proposition. It is,
| A | is | B |
| The happening of his arrival to-morrow, | is | an event from which it may be inferred to be improbable that he will stay till Monday, |
whereas the following,