Our subordination of the distinction between affirmative and negative quality to the common assertive character proper to all propositions does not in any way affect its genuineness. This genuineness of the qualitative distinction has, however, been disputed. Some logicians have attempted to state all propositions in affirmative form, insisting that 'S is-not P,' the typical form of the negative proposition, is logically equivalent to 'S is not-P.' The attempt, however, ignores the primary significance of negation in the act of judgment. We often require to negate simply, to give to a statement a bare, blank denial, without any positive implication in the background. If we say that a thing is not white, we merely mean that the term 'white' is not applicable to it. We just contradict quite barely the statement that the thing in question is white. We destroy the predication 'white' without making the slightest mental effort to replace it by another. Genuine logical denial can, in fact, do nothing more than deny: it fulfils itself in negating. We conclude, then, that 'S is not-P,' the meaning of which we have discussed in connexion with our treatment of negative terms, is not synonymous with 'S is-not P,' and that the two can be equated only by weakening the natural distinction between the affirmative and the negative. 3. The Copula. The Copula may be briefly defined as the identity-principle* as operative within a categorical judgment. This principle is the reason itself as inspired by a logical ideal. Present in subject and predicate alike, it claims both, in their interrelatedness, as specifications of its own meaning. It is in virtue of the unity and continuity of the logical interest that our meaning developes all of a piece. Oneness and identity of logical interest means oneness and identity of the judgment, or the system of judgments, through which that interest expresses itself. We have here to do with the very nature of the logical interest itself, the fundamental and authoritative factor in all logical inquiry, and we cannot get behind it. What makes an identity of an affirmation (or a denial) is that a reasoned interest specifies, and to that extent fulfils, itself in the assertion of it. The general form in which such an interest fulfils itself is in specifying the meaning of a subject through a predicate. The copula is, strictly speaking, the judgment-activity itself in process of self-fulfilment in the form of a judgment: this active logical interest is, in fact, constitutive of the identity-in-difference which pervades and characterizes the Judgment. * The copula should not be confused with the copula-mark. The copula-mark takes two typical forms: 'is' when the assertion is affirmative in character, 'isnot' when the assertion is negative. 'Is' may conveniently be called the synthetic, 'is-not' the dialytic copula-mark. The Copula, then, is omnipresent in the Judgment. It cannot be identified with any part or aspect of it, for in that case whatever lay outside could have no part or lot in the judgment. An element that had no share in that which unifies a proposition could not be an element of that proposition. This point is important, and we proceed to amplify and to emphasize it. The copula is frequently called a coupling-link between the subject and the predicate. This metaphor is misleading if it be interpreted as meaning that the terms of a judgment can be given independently of the relation between them. This is, in the nature of things, impossible. For the words or concepts, set down independently of the relation between them, are not 'terms in the judgment,' but terms out of the judgment. The act of synthesis or dialysis which defines the relation between S and P first brings S and P into the judgment. They are not there prior to the relating act. But a coupling-link cannot be considered as first constituting railwaycarriages into railway-carriages. These remain the same before and after the coupling. It is true that the car first becomes part of a train by being thus coupled with another; and if this is insisted on, the coupling metaphor might serve the purpose, though still rather lamely. The essential point to recognize, however, is that the term of a proposition exists only in the proposition itself as organically one with it, so that the Copula, as relating activity, cannot be identified with any single partial element in the Judgment-with a relation, for instance, that is outside the terms. It must be the activity which brings terms and relation, content and form, not togetherfor this implies a previous separate existence in mutual isolationbut into-birth-together. We may illustrate this important point by what is really much more than a mere analogy. It is sometimes stated that a poet works upon a certain content, moulding it into poetic form; and we are left with the impression that what is intrinsically poetic is the form. But the truth is that the poet works upon a certain subject-matter, which, as such, is certainly not the content of his poem. In bringing poetic unity into this subject-matter, he brings into birth, in intimate unison, content and form together. With the content comes the form, and with the form the content. The content is the subject-matter poetically formed; the form is the form of the content. The poetic end is not to superinduce form upon content, but to transform subject-matter into a formed content.* So with the Categorical Judgment. The matter of the judgment, that about which we judge, exists prior to the judgment. But the act of judgment consists not in superinducing a relation upon given terms, but in transforming the given matter, through the selective and unifying agency of a dominating interest, into terms-in-relation * Cf. Professor A. C. Bradley, 'Poetry for Poetry's Sake.' (the relation of subject to predicate), or into that formed content which we call a proposition. The systematic intimacy of subject and predicate within a proposition is customarily indicated through the use of copula-marks of the expressions 'is' and 'is-not.' The function of the word 'is' in the judgment 'S is P' is not that of serving as a coupling-link between subject and predicate, but that of indicating the identityrelation between the two. It tells us that the term 'P' which it precedes and introduces must be used as predicate-i.e., as the predicate of the subject-term S.* The foregoing discussion will serve to meet Dr. Sigwart's objection against a 'negative copula.' A copula, he argues, has by its very nature a synthetic function. Hence a copula that divides is a selfcontradictory absurdity. There is no such thing,' he writes, 'as a negative, but only a negated copula.'† If the function of the copula were 'synthetic' in that sense of the word in which it is opposed to 'dialytic,' this argument would be pertinent enough. But, as we interpret the copula, its function is to operate as the identity which the assertion expresses, whether that assertion take the form of a synthesis or that of a dialysis. Concepts do not cease to be related to each other because the relation between them happens to be an opposition or a severance. We show our dependence upon society most energetically, it has been said, when we assert our independence against it. The ascetic who renounces the world has been made an ascetic by the very evil which he shuns. The young lecturer who lectures in direct opposition to the tenets he has imbibed from his late University teachers thereby proclaims the potent effect which the lectures have produced upon his mind. The assertion of a relation between‡ S and P which the copulamark expresses is independent of the nature of that relation. Hence, if by 'negative' copula we mean the dialytic relation between S and P, the expression is perfectly reasonable. The 'negated copula,' on the other hand, as we understand the term 'copula,' is a logical fiction. It means nothing. It indicates an operation that cannot be carried out. We cannot deny an assertion without ourselves asserting. For denial is, as we have seen, a form of assertion. Hence the negated copula is itself a copula a self-contradictory conclusion which we could never have reached had not the original conception itself been self-contradictory and therefore meaningless. * Cf. Dr. Christoph Sigwart, 'Logic,' vol. i., ch. ii., § 17, English translation by Helen Dendy (Mrs. Bosanquet), p. 94. † Ibid., ch. iv., § 20, Eng. tr., p. 122. The word 'between' must not be understood in the coupling-link sense. What the copula-mark expresses is the S and P relation, a relation which cannot be understood as distinct from the terms related. CHAPTER XIII. IV. (iii.) THE MEANING OF POSSIBILITY. Real Possibility. THE ultimate source of the idea of possibility is to be found in the 'I can' of the free agent-the 'I can' itself implying the 'I ought.' As personalities, we have ideals which we ought to cherish, duties which we ought to perform, spiritual imperatives which we ought to obey; and, as personalities, it is also possible for us to fulfil the essential obligations of our free-born nature. It is as an agent capable of free choice that a man is justified in saying 'I can be patient (or sincere),' 'I can obey my conscience (or my reason).' Similarly, the ultimate source of the idea of necessity is to be found in the 'I cannot' of the free agent, in the compulsion which limits his freedom. 'I must' because 'I cannot help it.' It is true that we frequently use the phrase 'I must' in a more positive sense. But such usage is misleading. It is misleading to say 'I must' when what we really mean to say is 'I ought to,' or, more decisively, 'I ought to, and I will.' 'I must obey my conscience,' we say, whereas what we really mean to say is, 'I ought to obey my conscience.' So, when Regulus insists that he must return to Carthage, his true meaning is given in the words, 'I ought to return to Carthage, and I will.' , There are, however, many derivative uses of the words can and 'must.' Thus, restricting our attention to the former word and its uses, we may allow that there are many aspects under which even that which is not free admits of being treated as free; and consequently a corresponding set of senses in which the word 'possible' can be used. We may conceive the universe, for instance, as containing the whole ground of everything which the future will bring forth; and we should then say : 'The universe can be what in the fullness of time it will be.' So, again, we may appropriately say, 'Water can freeze and evaporate, for we here mentally isolate the idea of water, and, abstracting it from the conditions of actual existence, consider its changes of composition as though they emanated from itself alone, as the changeless, persistent ground of all these various transformations. Thus it comes to pass that we say 'Water can freeze and evaporate,' much as we should say 'A cat can mew and purr.' Again, the word 'can' may suitably be used to denote the power of further determination that a general idea possesses. Thus we say 'A triangle can be obtuse-angled; it can also be right-angled;' or, again, 'A horse can be black; it can also be grey;' and so forth. The Scheme of Opposition* proper to these relations of intrinsic necessity or possibility may be set down as follows : Assertion of Intrinsic Necessity: S must be P. (E.g., 'A proposition must be an identity-in-difference'; i.e., the nature of a proposition is such that it must be an identity-in-difference.) Contradictory: S need not be P. (E.g., A proposition need not be affirmative.') Contrary: Scannot be P. (E.g., 'A proposition cannot be self-contradictory.') Subalternate (Contradictory of Contrary): S can be P. Where the necessity-or possibility-is explicitly teleological, bearing on the relation between means and end, the Scheme of Opposition needs a certain readjustment, giving what we may call the Teleological Scheme : Assertion of Teleological Necessity: If X is accepted as end, Contradictory: If X is accepted as end, then S need not be P. Example of Teleological Opposition. Assertion of Teleological necessity: If a man's aim is to keep well, he must take regular exercise. Contradictory: If a man's aim is to keep well, he need not take regular exercise (i.e., the failure to take regular exercise will not be fatal to the attaining of his end). Contrary: If a man's aim is to keep well, he must not take regular exercise. Subalternate: If a man's aim is to keep well, he mayş take regular exercise. (I.e., taking regular exercise will not be fatal to the attainment of his end.) The various uses of 'possibility' we have so far discussed have pointed to a positive capacity in the subject considered, whether that subject be a personal agent, a spatial object, a proposition, means to an end, or what not. Thus, when I say 'This acorn can * This section presupposes an acquaintance with ch. xix. † Note that 'must' is here not exclusive of 'can.' The necessary is also the possible. ‡ Here, again. 'must' is not exclusive of 'may.' § The 'may' is here permissive, and by no means implies limitation of knowledge (vide infra). |