(1) “He goes by this train to-day.” “He goes by that train to-morrow.” This conjunction, as simply stated, gives no inference from the truth or falsehood of either statement to the truth or falsehood of the other.
Contrary Opposition, exclusive
(2) “He goes by this train,” and “He goes by that train,” with a meaning equivalent to “No, he goes by that.” If it is true that in the sense suggested by the context he goes by this train, then it is not true that he goes by the other, and if it is true, in the sense explained, that he goes by the other, then he does not go by this. Each excludes the other, but both may be excluded by a third alternative. If it is not true that he goes by this {133} train—nothing follows. There may be any number of trains he might go by, or he might give up going; i.e. your Universe of discourse, your implicit meaning is not expressly limited. If it is not true to say, “No, he goes by that”—taking the whole meaning together, and not separating its parts, for this combination is essential to the “contrary”—nothing follows as to the truth of the other statement. He may not be going at all, or may be going by some third train, or by road.
Combined Contrary and Contradictory Negation
But if you limit your Universe, or general subject, then you can combine the value of contrary and contradictory negation. Then you say,
(3) “He goes either by this train or by that.” Then you can infer not only from “He goes by this train,” that “He does not go by that,” but from “He does not go by this train” to “He does go by that.”
The alternative between “A is B” and “A is not-B” remains exhaustive, but not-B has been given a positive value, because we have limited the possibilities by definite knowledge. The processes of accurate thinking and observation aim almost entirely at giving a positive value C to not-B, and a positive value B to not-C, under a disjunction, because it is then that you define exactly where and within what conditions C which is not B passes into B which is not C. Take the disjunction, “Sound is either musical or noise.” If the successive vibrations are of a uniform period it is musical sound; if they are of irregular periods it is noise. This is a disjunction which assumes the form,
A is either B or C. That is to say, If it is B it is not C. If it is not B it is C.
{134} Therefore I think that all “determination is negation”—of course, however, not bare negation, but significant negation; the essence of it consists in correcting and confirming our judgment of the nature of a positive phenomenon by showing that just when its condition ceases, just then something else begins, and when you have exhausted the whole operation of the system of conditions in question, so that from any one phase of their effects you can read off what it is not but the others are, then you have almost all the knowledge we can get. The “Just-not” is the important point, and this is only given by a positive negation within a definite system. You want to explain or define the case in which A becomes B. You want observation of not-B; but almost the whole world is formally or barely not-B, so that you are lost in chaos. What you must do is to find the point within A, where A1 which is B passes into A2 which is C, and that will give you the just-not-B which is the valuable negative instance.
Negative judgment expressing fact