present and future being treated as simply existing, by
what logicians used to call suppositio naturalis. We mean then
by “all existing” every similar individual whatever, whenever,
and wherever existing. Hence Sigwart is right in saying that
“All bodies are extended” means “Whatever is a body is
extended,” but wrong in identifying this form with “If anything
is a body it is extended.” “Whatever” is not “if anything.”
For the same reason it is erroneous to confuse “all existing”
with a general idea. Nor does the use of abstract ideas and
terms make any difference. When Bosanquet says that in
“Heat is a mode of motion” there is no reference to individual
objects, but “a pure hypothetical form which absolutely
neglects the existence of objects,” he falls far short of expressing
the nature of this scientific judgment, for in his Theory of Heat
Clerk Maxwell describes it as “believing heat as it exists in a
hot body to be in the form of kinetic energy.” As Bacon would
say, it is a belief that all individual bodies qua hot are individually
but similarly moving in their particles. When, again, Bradley
and Bosanquet speak of the universal as if it always meant one
ideal content referred to reality, they forget that in universal
judgments of existence, such as “All men existing are mortal,”
we believe that every individually existing man dies his own
death individually, though similarly to other men; and that we
are thinking neither of ideas nor of reality; but of all existent
individual men being individually but similarly determined. A
universal is indeed one whole; but it is one whole of many
similars, which are not the same with one another. This is
indeed the very essence of distribution, that a universal is
predicable, not singly or collectively, but severally and similarly of
each and every individual of a kind, or total of similar individuals.
So also the essence of a universal judgment is that every individual
of the kind is severally but similarly determined.
Finally, a universal judgment is often existential; but whether
it is so or not it remains categorical, so long as it introduces no
hypothetical antecedent about the existence of the thing signified
by the subject. It is true that even in universal judgments of
existence there is often a hypothetical element; for example,
“All men are mortal” contains a doubt whether every man
whatever, whenever and wherever existing, must die. But this
is only a doubt whether all the things signified by the subject are
similarly determined as signified by the predicate, and not a
doubt whether there are such things at all. Hence the hypothetical
element is not a hypothetical antecedent “If anything
is a man,” but an uncertain conclusion that “All existing men
are mortal.” In other words, a categorical universal is often
problematic, but a problematic is not the same as a hypothetical
judgment.
4. The Judgment and the Proposition.—Judgment in general is the mental act of believing that something is (or is not) determined. A proposition is the consequent verbal expression of such a belief, and consists in asserting that the thing as signified by the subject is (or is not) determined as signified by the predicate. But the expression is not necessary. Sensation irresistibly produces a judgment of existence without needing language. Children think long before they speak; and indeed, as mere vocal sounds are not speech, and as the apprehension that a word signifies a thing is a judgment, judgment is originally not an effect, but a cause of significant language. At any rate, even when we have learnt to speak, we do not express all we think, as we may see not only from the fewness of words known to a child, but also from our own adult consciousness. The principle of thought is to judge enough to conclude. The principle of language is to speak only so far as to understand and be understood. Hence speech is only a curtailed expression of thought. Sometimes we express a whole judgment by one word, e.g. “Fire!” or by a phrase, e.g. “What a fire!” and only usually by a proposition. But even the normal proposition in the syllogistic form tertii adjacentis, with subject, predicate and copula, is seldom a complete expression of the judgment. The consequence is that the proposition, being different from a judgment arising after a judgment, and remaining an imperfect copy of judgment, is only a superficial evidence of its real nature. Fortunately, we have more profound evidences, and at least three evidences in all: the linguistic expression of belief in the proposition; the consciousness of what we mentally believe; and the analysis of reasoning, which shows what we must believe, and have believed, as data for inference. In these ways we find that a judgment is both different from, and more than, a proposition. But recent logicians, although they perceive the difference, nevertheless tend to make the proposition the measure of the judgment. This makes them omit sensory judgments, and count only those which require ideas, and even general ideas expressed in general terms. Sigwart, for example, gives as instances of our most elementary judgments, “This is Socrates,” “This is snow”—beliefs in things existing beyond ourselves which require considerable inferences from many previous judgments of sense and memory. Worse still, logicians seem unable to keep the judgment apart from the proposition. Herbart says that the judgment “A is B” does not contain the usually added thought that A is, because there is no statement of A’s existence; as if the statement mattered to the thought. So Sigwart, in order to reduce universals to hypotheticals, while admitting that existence is usually thought, argues that it is not stated in the universal judgment; so also Bosanquet. But in the judgment the point is not what we state, but what we think; and so long as the existence of A is added in thought, the judgment in question must contain the thought that A exists as well as that A is B, and therefore is a judgment that something is determined both as existing and in a particular manner. The statement only affects the proposition; and whenever we believe the existence of the thing, the belief in existence is part of the judgment thought, whether it is part of the proposition stated or not.
Here Sir William Hamilton did a real service to logic in pointing out that “Logic postulates to be allowed to state explicitly in language all that is implicitly contained in the thought.” Not that men should or can carry this logical postulate out in ordinary life; but it is necessary in the logical analysis of judgments, and yet logicians neglect it. This is why they confuse the categorical and the universal with the hypothetical. Taking the carelessly expressed propositions of ordinary life, they do not perceive that similar judgments are often differently expressed, e.g. “I, being a man, am mortal,” and “If I am a man, I am mortal”; and conversely, that different judgments are often similarly expressed. In ordinary life we may say, “All men are mortal,” “All centaurs are figments,” “All square circles are impossibilities,” “All candidates arriving five minutes late are fined” (the last proposition being an example of the identification of categorical with hypothetical in Keynes’s Formal Logic). But of these universal propositions the first imperfectly expresses a categorical belief in existing things, the second in thinkable things, and the third in nameable things, while the fourth is a slipshod categorical expression of the hypothetical belief, “If any candidates arrive late they are fined.” The four judgments are different, and therefore logically the propositions fully expressing them are also different. The judgment, then, is the measure of the proposition, not the proposition the measure of the judgment. On the other hand, we may go too far in the opposite direction, as Hamilton did in proposing the universal quantification of the predicate. If the quantity of the predicate were always thought, it ought logically to be always stated. But we only sometimes think it. Usually we leave the predicate indefinite, because, as long as the thing in question is (or is not) determined, it does not matter about other things, and it is vain for us to try to think all things at once. It is remarkable that in Barbara, and therefore in many scientific deductions, to think the quantity of the predicate is not to the point either in the premises or in the conclusion; so that to quantify the propositions, as Hamilton proposes, would be to express more than a rational man thinks and judges. In judgments, and therefore in propositions, indefinite predicates are the rule, quantified predicates the exception. Consequently, A E I O are the normal propositions with indefinite predicates; whereas propositions with quantified predicates are only occasional forms, which we should use whenever we require to think the quantity of the predicate, e.g. (1) in conversion, when we must think that all men are some animals, in order to judge that some animals are men; (2) in syllogisms of the 3rd figure, when the predicate of the minor premise must be particularly quantified in thought in order to become the particularly quantified subject of the conclusion; (3) in identical propositions including definitions, where we must think both that 1 + 1 are 2 and 2 are 1 + 1. But the normal judgment, and therefore the normal proposition, do not require the quantity of the predicate. It follows also that the normal judgment is not an equation. The symbol of equality (=) is not the same as the copula (is); it means “is equal to,” where “equal to” is part of the predicate, leaving “is” as the copula.
