(3) We have another form of compound judgment when we affirm that one or other of two given judgments is true. This form of judgment, “P or Q,” is usually called disjunctive, though alternative would be a better name. It has been already pointed out that Not both P and Q is the more distinctively disjunctive form.
It may be denied that P or Q is a compound judgment on the same grounds as those on which this is denied of If P then Q. Since, however, the points at issue are practically the same as before, the discussion need not be repeated.
The denial of “P or Q” yields “Neither P nor Q.” This may be called a remotive judgment if a distinctive name is wanted for it.
It should be added that not all forms of proposition which would ordinarily be described as hypothetical or disjunctive are really the expressions of compound judgments as above described. Thus the forms If any S is P it is Q (If a triangle is isosceles the angles at its base are equal). Every S is either P or Q (Every blood vessel is either a vein or an artery), do not—like the forms If P is true Q is true (If there is a righteous God the wicked will not escape their just punishment), Either P or Q is true (Either free will is a fact or the sense of obligation is an illusion)—express any relation between two independent judgments or propositions. This point will be developed [subsequently] in a distinction that will be drawn between the true hypothetical (If P is true Q is true) and the conditional (If any S is P it is Q).
56. The Modality of Judgments.—Very different accounts of the modality of judgments or propositions are given by different writers, and the problems to which distinctions of modality give 85 rise are as a rule not easy of solution. At the same time such distinctions are of a fundamental character, and they are apt to present themselves in a disguised form, thus obscuring many questions that at first sight appear to have no connexion with modality at all. It is a drawback to have to deal with so difficult a problem nearly at the commencement of our treatment of judgments, and the space at our disposal will not admit of our dealing with it in great detail. Moreover, it can hardly be hoped that the solution offered will be accepted by all readers. Still a brief consideration of modal distinctions at this stage will help to make some subsequent discussions easier.
The main point at issue is whether distinctions of modality are subjective or objective. In attempting to decide this question it will be convenient to deal separately with simple judgments and compound judgments.
57. Modality in relation to Simple Judgments.—The Aristotelian doctrine of modals, which was also the scholastic doctrine, gave a fourfold division into (a) necessary, (b) contingent, (c) possible, and (d) impossible, according as a proposition expresses (a) that which is necessary and unchangeable, and which cannot therefore be otherwise; or (b) that which happens to be at any given time, but might have been otherwise; or (c) that which is not at any given time, but may be at some other time; or (d) that which cannot be. The point of view here taken is objective, not subjective; that is to say, the distinctions indicated depend upon material considerations, and do not relate to the varying degrees of belief with which different propositions are accepted.[82]
[82] The consideration of modality as above conceived has sometimes been regarded as extra-logical on the ground that necessity, contingency, possibility, and impossibility depend upon matters of fact with which the logician as such has no concern. But it also depends upon matters of fact whether any given predicate can rightly be predicated affirmatively or negatively, universally or particularly, of any given subject. Distinctions of quality and quantity can nevertheless be formally expressed, and if distinctions of modality can also be formally expressed, there is no initial reason why they should not be recognised by the logician, even though he is not competent to determine the validity of any given modal. In so far, however, as the modality of a proposition is something that does not admit of formal expression, so that propositions of the same form may have a different modality, then the argument that the doctrine of modals is extra-logical is more worthy of consideration.
86 Kant’s doctrine of modality is distinguished from the scholastic doctrine in that the point of view taken is subjective, not objective, according to one of the senses in which Kant uses these terms. Kant divides judgments according to modality into (a) apodeictic judgments—S must be P, (b) assertoric judgments—S is P, and (c) problematic judgments—S may be P ; and the distinctions between these three classes have come to be interpreted as depending upon the character of the belief with which the judgments are accepted.
The distinction between these two doctrines is fundamental; for, as Sigwart puts it,[83] the statement that a judgment is possible or necessary is not the same as the statement that it is possible or necessary for a predicate to belong to a subject. The former (which is the Kantian doctrine) refers to the subjective possibility or necessity of judgment; the latter (which is the Aristotelian doctrine) refers to the objective possibility or necessity of what is stated in the judgment.