_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.
5. You will find it said that a Negative Judgment cannot express fact; _e.g._ that a Judgment of Perception cannot be negative. This is worth reflecting upon; I hope that what has been said makes clear how far it is true. The bare form of Negation is not adequate to fact; it contains mere emptiness or ignorance; we nowhere in our perception come upon a mere “not-something.” No doubt negation is in this way more subjective than affirmation. But then as it fills up in meaning, the denial becomes more and more on a level with the affirmation, till at last in systematic knowledge both become double-edged--every affirmative denies, and every negative affirms. When a man who is both a { 135} musician and a physicist says, “this compound tone A is a discord Y,” he knows exactly how much of a discord, what ratio of vibration makes it so much of a discord, how much it would have to change to become a concord (X which is not Y), and what change in the vibration ratio from a1 to a2 would be needed to make it a concord. To such knowledge as this, the accurate negation is just as expressive as the affirmation, and it does not matter whether he says “A is Y,” or “A is by so much not X.” It becomes, as Venn says, all but impossible to distinguish the affirmation from the negation. No doubt affirmative terms come in at this stage, though the meaning is negative. Observe in this connection how we sometimes use the nearest word we can think of, knowing that the negative gives the positive indirectly--“He was, I won’t say insolent,” meaning _just not_ or “_all but_” insolent; or again, “That was not right,” rather than saying bluntly “wrong.”