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.” _Operation of the denied idea_ 6. Every significant negation “A is not B” can be analysed as “A is X which excludes B.” Of course X may not be a distinct C; _e.g._ we may be able to see that A is not red, but we may not be able to make out for certain what colour it is; then the colour X is “an unknown colour which excludes red.” How does the rejected idea operate in Judgment? I suppose it operates by suggesting a Judgment which as you make it destroys some of its own characteristics. It is really an expression of the confirmatory negative instance or “just-not.” _Just_ when two parallel straight lines swing so that they can meet, _just_ then the two interior angles begin to be less than two right angles, which tells us that the {136} straight lines are ceasing to be parallel. Just in as much as two straight lines begin to enclose a space we become aware that one or other of them is not straight, so that A in turning from Y to X turns _pari passu_ from A1 to A2, and we are therefore justified in saying that A, when it is Y, cannot be X. This lecture may pave the way for Induction, by giving some idea of the importance of the negative instance which Bacon preached so assiduously.