3. In the first place, we use it because it indicates exclusion, and without it we cannot distinguish between mere differents on the one hand and contraries on the other. If you ask me, “Are you going to Victoria, London Chatham and Dover station?” and I answer, “I am going to Victoria, London Brighton and South Coast,” that will not be satisfactory to you, unless you happen to know beforehand that these stations are so arranged that if you are at one you are not at the other. They might be a single station used by different companies, and called indifferently by the name of either. To make it clear that the suggestion and the answer are incompatible, I must say, “I am _not_ going to Victoria, London Chatham and Dover,” and I may add or not add, “I _am_ going to Victoria, London Brighton and South Coast.” That tells you that the one predicate excludes the other, and that is the first reason why we use the generalised form of exclusion, _i.e._ negation. But in the second place, it can give us more, and something absolutely necessary to our knowledge, and that is not {131} merely exclusion, but exhaustion. In literal form negation is absolutely exhaustive, that is to say, contradictory. The Judgment “A is not B” forms an exhaustive alternative to the Judgment “A is B,” so that no third case beyond these two is possible, and therefore you can argue from the falsehood of either to the truth of the other. Now this form is potentially of immense value for knowledge, and all disjunction consists in applying it; but as it stands in the abstract it is worthless, because it is an empty form. “A is red or not-red.” If either of these is false the other is true. But what do you gain by this? You are not entitled to put any positive meaning upon not-red; if you do so you slide into mere contrary negation, and the inference from falsehood becomes a fallacy. Make an argument, “The soul is red or not-red.” “It is not-red ∴ it is some other colour than red.” The argument is futile. We have construed “not-red” as a positive contrary, and that being so, the disjunction is no longer exhaustive. We had no right to say that the soul is either red or some other colour; the law of Excluded Middle does not warrant that.