Here, then, is the clue to the analysis of _all Abstract Judgments_, Like Perceptive Judgment, they affirm something of Reality, but they do this indirectly and not directly. {123} Underlying them there is the implied Categorical Judgment, “Reality has a character, such that, supposing so and so, the consequence will be so and so.” And if this implied assertion is true, then the Hypothetical Judgment is true, although its terms may be not only unreal, but impossible. “If a microscopic object-lens with a focal length of 1/100 in. were used, its magnifying power with an A eye-piece would be so many diameters.” This is a mere matter of calculation, and is unquestionably true, depending upon the effects of refraction upon the optical image. But I do not suppose that such an object-lens could be made, or used. Does such a Judgment, although true, express a _fact_? No, I should say not, although common usage varies. I remember a _Pall Mall_ leading article which said, “It is an absolute fact, that, if Mr. Gladstone had not done something--the Government would have committed--some iniquity or other.” Is this what we call a fact? We observe that the content actually mentioned was never real at all. The implied connection with reality is “There existed in reality a condition of things (unspecified) in which _if_ Mr. Gladstone, etc., etc.” Are mathematical truths facts, and in what sense? Abstract truth need not, and perhaps cannot express fact, but implies fact indirectly. _Disjunctive Judgment_ (5) The Disjunctive Judgment “A is either B or C,” is again not a judgment of doubt but a mode of Knowledge, It may be taken as numerical; then it gives rise to the statement of Chances. But in its perfect form it is appropriate to the exposition of a content as a system, and it may be taken as returning to the Categorical Judgment, and combining it with the Hypothetical, because its {124} content is naturally taken as an individual, being necessarily concrete. The peculiar point of the Disjunctive is that it makes negation positively significant. “This signal light shows either red or green.” Here we have the categorical element, “This signal light shows some colour,” and on the top of this the two Hypothetical Judgments, “If it shows red it does not show green,” “If it does not show red it does show green.” You cannot make it up out of the two Hypothetical Judgments alone; they do not give you the assertion that “it shows some colour.” [1] [1] The example in the text, chosen for its simplicity, may be objected to as involving perceptive concreteness by the pronoun “this.” You can have a disjunction, it may be said, dealing with “the triangle” as such; and why should this be more “Categorical” than the assertion that the triangle has its angles = three right angles? Still, it might be replied, the development of a single nature into a number of precise and necessary alternatives, always gives it an implication of self-completeness.