Judgment, since it expresses the present union of two thoughts now before the mind, must always appear as the present tense of a verb, usually of the verb to be: Is or IS NOT is commonly regarded as the only distinctive expression of the logical Copula. Thus the Propositions, the sun shines; pluit; cogito, ergo sum; he came yesterday; John will arrive; if reduced to their logical form as Judgments, must be thus expressed: the sun is shining; the rain is falling; I am thinking, therefore I am existing; he is the person who came yesterday; John is he who will arrive. In each of these cases, all that precedes the Copula, is or am, is the Subject, and all that follows the Copula is the Predicate.* The substantive verb, when used as a Copula, * Hence we perceive how unfounded is the objection which has been made to the science of Formal Logic, on the ground that it does not expound the whole theory of reasoning, because it furnishes no explanation of an inference so obvious as this: : A is greater than B; therefore, B is less than A. But here the Predicate is not B or A, but "greater than B" and "less than A"; the meaning of these two expressions, therefore, belongs to the Matter of Thought, with which, as a logician, I have nothing more to do than with the meaning of A or B taken alone. That these two expressions have a correlative meaning, is a fact which belongs to the science of language rather than to that of Thought. Instead of regarding one of them as an inference from the other, it would be more correct to say that the two are equivalent statements of the same fact; they express one relation between two Concepts. That two lines converge from A to B is only another way of saying that the same two lines diverge from B to A; there is but one thing to be said, though there are two modes of saying it. In like manner, we may say, but we do not argue, that Socrates is the husband of Xantippe ; therefore, no one is omnipotent but God. In such cases, the second proposition is an interpretation of the preceding one, not an inference from it. We learn from a dictionary, not from a treatise on Logic, what different phrases are equivalent statements of one and the same Thought. never means exists; but the idea of existence, when it is intended to be conveyed, forms the Predicate. He is, in the sense of he exists, is logically interpreted, he is existing. Fuit Ilium; Troy is that which has been, is that which exists no longer. Logicians generally maintain that the Copula is precisely equivalent to the mathematical sign of equality. In many cases, this is undoubtedly true. If the Predicate is simply a definition of the Subject, or if the Proposition in any manner expresses the entire equivalence of its two Terms, it can then be expressed in the manner of an equation. Thus, Saltpetre nitrate of Potash; Alexander the son of Philip. But the two Terms of a Judgment are not always convertible or equivalent. What is thought and expressed is always a relation between the two Terms, but is not always a relation of equivalence or identity. Sometimes, as in a negative Judgment, it is a relation of disagreement; sometimes the Predicate expresses merely one attribute of the Subject, and then the relation is that of a whole to its part, since only a portion of the Subject's Intension is affirmed of the Subject. When we say, the apple is red, we do not mean apple red, but only that a red color is one out of many attributes of the apple, is a part of its Intension. In this case, the Copula signifies rather possession, to have, than equality, to be. The form of the Judgment as thought is, the apple has a red color as one of its many attributes. = It is evident, then, that there are two classes of Judgments, properly distinguished by Dr. Thomson as Substitutive and Attributive. In Substitutive Judgments, the sign of equality may be used as the Copula; the Predicate is properly identified with the Subject, or made convertible with it, and therefore every attribute of the one may also be affirmed of the other. If AB, then every x of A is also x of B; all that is true of "Alexander" is also true of "the son of Philip." But if the Judgment is only Attributive, the sign of equality cannot be used; the two Terms are not convertible, and consequently it cannot be inferred that they possess the same attributes. Sweetness or sourness is a quality of the apple, but not of the red color which belongs to the apple. The distinction here explained is a valid and important one in respect to Judgments considered simply as such, or as mere phenomena of Thought, irrespective of any use to be subsequently made of them in reasoning or other mental processes. In Attributive Judgments, the Predicate is actually thought only connotatively, as a Mark or attribute of the Subject, and not denotatively, as the name of a class of things. And hence Mr. Mill is led to maintain, that such Judgments never express truths of classification, and, therefore, that the generally received doctrine of Predication, that it consists in placing something in a class or excluding something from a class, is entirely unfounded. "When I say that snow is white," he argues, "I may and ought to be thinking of snow as a class; but I am certainly not thinking of white objects as a class; I am thinking of no white object whatever except snow, but only of that, and of the sensation of white which it gives me." All this is granted. At the moment of forming the Judgment, white is not consciously before the mind as the name of a class of things. We then think of it only connotatively, - only as a Mark. But it is still true that we originally learned the meaning of the word white not only as a Mark connoting a quality, but also as a Concept denoting a class of things, namely, white objects; otherwise, it would not be, what it certainly is, a Common Name of snow, milk, chalk, and many other things. And though this its denotative meaning its Extension is not consciously before the mind when it is used as a Mark or as a Predicate, it is still there potentially, and must be brought out or expressed -- when we attempt to found an inference upon this Judgment, or to employ it as one of the premises in a syllogism. To borrow Mr. Mill's own instance, if I am in doubt whether Chimborazo is snow-covered, I may reason thus: All mountains of a certain altitude, and whose summits are perpetually white, are snow-covered. But Chimborazo's lofty summit is always white, that is, it is one of this class of mountains. Therefore, Chimborazo is snow-covered. As already observed (p. 64), "the distinction between Concepts and Marks is not absolute, but relative; they may be used interchangeably." That a Concept or Common Name is sometimes used only as a Mark, or with no conscious reference at the moment to its denotation, is surely no proof that it is always so used, or even that the denotative meaning, or Extension, is not potentially present in this very case, so. that it may be revived, if need be, and an inference founded upon it. Because words are sometimes used symbolically, or without spreading out in Thought all their signification, it does not follow that they are always so used, or that such use of them may not be checked, and kept from falling into error, by occasionally bringing up into consciousness what they always potentially signify in Thought. It follows, then, that although a Judgment, as actually thought, may not be a truth of classification, and therefore that the Copula may not be equivalent to the mathematical sign of equality, yet it may always be reduced to the form of such a truth, and then this mathematical sign fully expresses its proper form; and in reasoning, such a reduction is generally necessary. Though it is not true that apple red, it is true that apples =some red objects; or, as it is more commonly expressed by Conversion, some red objects are apples. 1. THE PREDICABLES AND THE CATEGORIES. In his analysis of Judgments, Aristotle was led to consider how many kinds of Predicates there are, when viewed relatively to their Subjects;-in other words, to determine the Second Intentions of Predicates considered in relation to Subjects. Thus was formed his celebrated doctrine of the Predicables, a doctrine which was considerably modified, but not improved, by his followers, Porphyry and the Schoolmen. According to Aristotle, every Judgment affirms or denies one of four relations of a Predicate to its Subject. It expresses either, -1. the Genus, i. e. the class under which it is included, as when we say, man is an animal; or, 2. the Definition, which, as we have seen, is the Genus and the Specific Difference taken together, and may be reduced to an enumeration of all the essential Marks of the Subject, as, a Carnivor is a flesh-eating Mammal; or, 3. a Property, that is, some peculiar attribute of the Subject, belonging to it universally, belonging to nothing else, and yet not regarded as essential to it, for we could conceive of the thing without it, as polarity is a Property (proprium) of the magnet, and risibility of man; or, 4. an Accident, which is an attribute that happens to belong to the Subject, but, as unessential, is separable from it, as man is learned. Two of these Predicables, namely, the Definition and the Property, are convertible with the Subject, or may change places with it; and of these two, the former expresses the whole Essence (all the essential qualities), while the latter, strictly speaking, is no part of the Essence; for we can conceive of man as not having the attribute of risibility, but we cannot conceive of him as deprived of rationality. So, the magnet can be conceived of without polarity, as its magnetic or attractive power was known long before its property of pointing to the north was dis |