We conclude, then, that the logical order of the propositional forms is: 1. Categorical; 3. Hypothetical; and we propose to adopt this order in the following discussions on the nature of Proposition and Inference. But before we proceed to the detailed discussion of the Categorical Proposition, it is essential that we should emphasize a distinction of fundamental importance arising out of the relation in which a question stands to the reality in reference to which the answer is sought. The logical interest that inspires a question may be either occasional or systematic. It may be conventionally restricted within the limits of some definite topic, or it may aim at an answer that shall respect systematic connexion of facts apart from any such conventional restriction. In the former case the answer has a 'formal' value; in the latter case it has a 'real' value. Where it has only a formal value, the judgment or proposition in which it is expressed may be designated as 'formal'; where it has a real value, as 'real.' Thus, if I inquire 'Is my friend in a good temper this morning?' my question may express the merely occasional interest of ascertaining whether our meeting is likely to be pleasant or not. On the other hand, if I should chance to be a doctor, I may be scientifically interested in the effects on his nervous organization of some special condition such as neuralgia or a sleepless night. In the former case the question refers to formal reality, and expects a formal answer; in the latter both question and answer have a real or systematic character.* The distinction between a formal and a real logical interest may be aptly illustrated by the difference in meaning acquired by the Singular Proposition (the proposition which has for its subject a singular term) according as it is considered in the light of the one interest or of the other. In the service of our unorganized everyday experience as well as in the service of Science the singular proposition plays an important part. In all our talk about individuals, be they persons, things or events, as well as in scientific observations and verifications, our direct, explicit reference is to the individual fact. In the case of Science, however, the sense-individuality of observed fact derives all its significance from the scientist's belief in natural law. A fact, for natural Science is a fact under law, and a species, instance, or example of a common nature. The reverence for fact which is so * The reality of Nature, as interpreted by Science, is not the reality of Spiritual Experience. The same question might express a spiritual interest-e.g., in my friend's power to be cheerful in difficult circumstances. The logical discussion of this more personal point of view belongs, however, to a Philosophical Logic. characteristic of the scientific attitude is ultimately rooted in reverence for this common nature. This attitude towards the facts of observation gives to the singular proposition as understood by Science-i.e., to the 'real' singular proposition-a peculiar import. The reference to individual fact is not to the individual qua individual, but to the individual as symbolic of a universal or common nature. In the case of the formal singular proposition, though this reference to a common nature must always be impliedthe isolated individual being at bottom unthinkable it is not implied in the same systematic sense. The fact is not conceived as a fact under law, but as having an individual importance relative to a certain topic. If I say 'This chair has only three legs,' my topic is the possible uses of a chair, and my meaning is that, whatever chair I may choose to sit on, I must avoid the chair in question. It is convenient to distinguish from formal and real propositions alike the strictly verbal proposition. The Verbal Proposition states the meaning of a word or verbal sign qua word. Man means rational animal' and 'Man is a verbal symbol which stands for "rational animal"' illustrate the two forms in which a verbal proposition may be expressed. In either case the meaning we define is that of the word as such, and not that of the object signified by the word. Thus, the proposition which states a definition is not usually verbal, since what we wish to define is, as a rule, not the meaning of the word qua purposive combination of letters or sounds, but the meaning of that significate of which the word is but the verbal sign. The proposition 'Man is a rational animal' is a definition of the common nature conventionally symbolized by the sign 'Man,' and not a definition of the sign itself. It is therefore material (formal or real), and not verbal. CHAPTER XII. IV. (ii.) ANALYSIS OF THE CATEGORICAL PROPOSITION. 1. Subject and Predicate in the Categorical Proposition. We have defined-or, rather, distinguished-the Categorical Proposition as one which states something about something else, as a proposition, therefore, including a subject as well as a predicate term.* * Whether these two terms stand for existents or not, and if so, in what sense. are further questions which concern what is called the Theory of the Existential Import of propositions. Prof. Keynes, in particular, has given an elaborate discussion of this problem in his 'Studies and Exercises in Formal Logic,' 4th edition, Part ii., ch. viii. But on this point see p. 189. There are certain embryonic forms of the Categorical Judgmentviz., the Exclamatory and the Impersonal Judgments in which the Subject-Predicate relation, though present, is still not obviously expressed. By Exclamatory Judgments we mean such ejaculations as 'Fire!' 'Man overboard!' where' Fire!' is equivalent to 'There is a fire,' or 'A fire has broken out'; Man overboard !' to 'There is a man overboard,' or 'A man has fallen overboard.' Impersonal Judgments are, from this point of view, abbreviations of a more perplexing kind. They are sometimes instanced as categorical propositions without a subject, but there seems to be no adequate reason for this view. In such cases as 'It is too bad,' 'It isn't fair,' the 'it' is quite properly regarded as an indeterminate subject-concept, which through its very indeterminateness truly represents some unnameable and unlabellable subject-thing, some total impression in its natural vagueness and indeterminacy. Such propositions as 'It snows,' 'It is foggy' hardly seem to be true impersonals. Grammatically, indeed, they have an indefinite 'provisional' subject (cf. Fr. Il-y-a); but as soon as they are reduced to the form of logical propositions-'Snow is falling,' Fog is prevailing'-we see that the subject-terms are really definite. By the 'subject' of a categorical proposition we mean, of course, the 'logical subject.' The question which term is subject and which predicate must be decided, not by grammatical structure or by the respective positions of the words, but by the meaning of the sentence. At the same time, the subject is usually the less emphatic, the predicate that which is asserted-usually and naturally the more emphatic term. Hence in ordinary conversation we have the help of the speaker's voice and intonation; and in written work, where the right stress can be given through our knowledge of the meaning of the whole context in which the proposition occurs, we may frequently be helped out by emphasis. Thus, in reading the ancient proverb 'In the multitude of counsellors there is safety,'* we feel that the emphatic part of the proposition is 'in the multitude of counsellors.' 'Safety' is not what we are asserting about 'in the multitude of counsellors,' but 'in the multitude of counsellors' is what we are asserting about 'safety.' But if the sentence occurs quite alone, and we have not the requisite data for unambiguously specifying the logical subject, we are reduced to stating the various alternatives which the logical subject may assume. Take, for instance, the isolated sentence: The Novum Organum of Bacon was not intended to supersede the Organon of Aristotle.' * Proverbs xxiv. 6. Here the meaning may be 1. The Novum Organum of Bacon was not intended to supersede I.e. (The work of Bacon which was intended to supersede (his Novum Organum)-Predicate. 2. The Novum Organum of Bacon was not intended to supersede I.e. (The Novum Organum that was intended to supersede (Bacon's work of that name)-Predicate. 3. The Novum Organum of Bacon was not intended to supersede the Organon of Aristotle. I.e. (The statement that the Novum Organum of Bacon was intended to supersede the Organon of Aristotle) Subject is-not (true)-Predicate. 4. The Novum Organum of Bacon was not intended to supersede the Organon of Aristotle. I.e. (The superseding of Aristotle's Organon by Bacon's is-not (a result that was intended by Bacon) - Predicate. 5. The Novum Organum of Bacon was not intended to supersede the Organon of Aristotle. I.e. (The relation which Bacon intended his Novum Organum (the relation of superseding) -Predicate. 6. The Novum Organum of Bacon was not intended to super- I.e. (The work of Aristotle which Bacon intended that his (the Organon)-Predicate. 7. The Novum Organum of Bacon was not intended to supersede the Organon of Aristotle. I.e. (The Organon which Bacon intended to supersede by his own Novum Organum)-Subject is-not (the work of Aristotle) - Predicate. The main conclusion to which we are driven by the foregoing analysis is that a proposition depends as much on context for its true meaning as do the terms which are its elements. Everywhere we find the part incomplete and pointing beyond itself. Now, it is of fundamental importance that we should not interpret this reference of part to whole in abstraction from the limiting or defining reference to purpose or interest; for, apart from this defining reference, we cannot hope to fulfil the logical requirement of relevance. A logical whole is objective reality as defined and, as it were, individualized through the selective agency of some specific interest. What Logic here demands as a requirement of right thinking is recognized in Art as a canon of right feeling. If, for instance, in looking at a picture we are to feel æsthetically, we must be able to feel the full appeal of the picture within the frame of the picture itself. As Professor Stout has somewhere said, * 'Whatever content enters into the work of art must be so connected with the whole as never to divert attention from the whole: picture or poem must be apprehended as a world in itself, the whole interest being gratified within it; hence to think of the real landscape whilst looking at its picture is to slip away from the artistic unity of the picture, and the enjoyment is no longer æsthetic.' So it is with a logical whole, the object that can satisfy a given logical interest. Its natural framework is defined by the limitations of the interest. What in respect of that interest is extra-marginal is logically irrelevant: it cannot enter into the whole within which the definite interest finds its definite satisfaction. It follows that, when we say of a proposition that its true, or logically ultimate, meaning is given to it by its logical context, we understand by 'logical context' that limited topic or 'universe of discourse' within which the interest which inspires the statement in question lives and moves and has its being. The relation in which the subject of a proposition stands to the relevant universe of discourse may, perhaps, be made clearer by the help of an illustration. Let the subject (or 'universe') of discourse (2) be the wanderings of Odysseus, and the proposition in question Ulysses (S) bends the bow that no other could bend.' Here the true and logically ultimate subject of the sentence is S as interpreted in the light of Σ. It is not ∑ itself, but S as qualified by E. We are speaking of Ulysses, the hero of a hundred adventures already detailed, but now in Ithaca once again, and just about to reassert himself as lord of his own house and country. The true and ultimate subject of the proposition is therefore 'Ulysses '-Ulysses as we have come to know him through the story of his past adventures, not the bare 'Ulysses' severed from all reference to a past which alone gives to the present action, the bending of the bow, its critical significance. As for the predication 'bends the bow that no other could bend,' its relation to the subject 'Ulysses' may be defined by * I quote from notes, but the statement substantially reproduces Professor Stout's point. |