Lecture Vii the Categorical and Hypothetical Characters in

JUDGMENT

Some criticism on the ordinary scheme

1. We will first consider why we want to examine the types of Judgment, and then what arrangement of them best fulfils our want.

Read Mill, ch. iv. (Bk. I.), on Propositions; Venn, Empirical Logic, ch. ix., x. Cf. Knowledge and Reality pp. 57-8; and Venn, p. 264. Ordinary statement, Jevons, p. 60, ff.; cf. p. 163.

Why we need an arrangement

(a) If we attended purely to the propositions in common use, we should get an unmanageable variety of forms, though the reality of thought would be fairly represented. We cannot quite do this; we must try to select the forms which for some reason are the most fundamental and constant.

On the other hand, it is possible to think simply of what is convenient in logical combination; and then for working with syllogistic Logic we get the well-known scheme of four propositions, each with Subject and Predicate; and for working with symbolic Logic we get the existential scheme in which Subject and Predicate disappear, and “All S. are P.” turns into “There exists no S. which is not P.”; or we get Jevons’ Equational Logic, in which “All A is B” stands as A = AB. Now every Judgment has a great many aspects, {113} being really a very complex systematic act of mind, and a logical method can be founded on any of these aspects which is sufficiently constant to stand for the Judgment. You can take “All men are mortal” to mean “There are no not-mortal men,” or “Men = some mortals,” or two or three more meanings. The two former are artificial or formal corollaries from the natural Judgment, representing it for some purposes but omitting a great part of its natural meaning. They tell you nothing about a relation of causality between the content of man and the property mortal, and they destroy all implication of existence in the Subject man.

What we want is neither to follow mere everyday language, nor be guided by mere convenience of logical combination. We want to look at the Judgment on its merits with reference to its power of expressing the principal kinds of our experience, which in fact are constructed in the medium of Judgment. The great kingdoms of intellectual experience are Perception, History, and Science, and of these three, Science, including Philosophy, is the form towards which all knowledge presses on, and its judgment must therefore be considered as the most complete type.

The common scheme

(b) With this purpose in mind, let us look at the traditional scheme, omitting the negative Judgments of which we have not yet spoken. We may dismiss the Indefinite Judgment “Men are mortal” as imperfect by not being “quantified,” and we have left, as Categorical Judgments, the Particular Affirmative “Some men are mortal,” the Universal Affirmative “All men are mortal,” and the Singular Affirmative “Socrates is mortal.” The Singular Affirmative, however, is not treated of any further under the old scheme, {114} because in it the Subject is taken in its full extent, and therefore the Singular Affirmative Judgment is ranked with the Universal Affirmative. So as Categorical Judgments we have left the Particular Affirmative and the Universal Affirmative.

Outside the account of the Categorical Judgment we find the Hypothetical and Disjunctive Judgments touched on as a sort of Appendix, standing as “Conditional.” The historical reason of this is, that they were not recognised by Aristotle, and have never been incorporated in the diagram of judgments employed in traditional Logic. Then on the ordinary scheme we have--

Categorical. Conditional.

Particular Universal Hypothetical Disjunctive Judgments. Judgments, Judgments. including Singular Judgments.

The defects of this scheme from our point of view are—

(i.) Our Impersonal and Demonstrative Judgments are omitted. They might be classed under the particular, which also has an undefined element in the subject.

(ii.) The Singular Judgment (of which the chief instance is the judgment with proper name) is rightly classed as Universal, but yet is wrongly absorbed in the abstract universal, from which it ought to be distinguished.

(iii.) In the treatment of the Universal Judgment there are two defects—

(1) The Collective Judgment, resulting from enumeration, {115} direct or indirect, is not distinguished from the Generic Judgment, resting on a connection of content or presumption of causality. “All the papers have been looked over” should be distinguished from “All triangles have their three angles equal to two right angles.”

“The” as here used indeed practically = “these,” so that, by our analysis, such a judgment has no claim to rank as a universal judgment It is difficult to find a plainly collective judgment which has not some affinity to judgment with demonstrative pronoun or proper name. A judgment in which “All M.P.’s” stands as subject, has affinity with the latter.

(2) The nature of the Universal Judgment is not examined with a view to the distinction between Categorical and Hypothetical. The common Logic does not go behind the grammatical form, which on this point is not decisive.

(iv.) The Hypothetical Judgment is said to consist of two categorical propositions, or to be “complex” But of course it is a simple judgment, prima facie expressing a relation of reason and consequent. Its parts are not Judgments, for they are not such as to stand alone.

Bain, p. 85; Jevons, p. 160.

(v.) The Disjunctive Judgment is often (e.g. by Mill and Bain) said to be equivalent to two Hypothetical Judgments. The strange thing is that both of these writers take the wrong two. If we allow conversion of a Hypothetical Judgment two are enough, but of course they must be the two which cannot be got from each other by conversion, viz. the two beginning, “If A is B ...” and “If A is not B ...” respectively. If we do not admit conversion we must have all four. Let the disjunction be, “This signal light is either red or green.” In order to know this we must know not {116} only that, “If it is red it is not green” (with its equivalent, “If it is green it is not red”), but that, “If it is not red it is green” (with its equivalent, “If it is not green it is red”). The former by itself leaves open the possibility that it may be not red or green, but blue or yellow; the latter by itself the possibility that when it is red it may also at the same time be green. The former secures that the two terms exclude each other; the latter, that, taken together, they exclude all other predicates.

Mill, ch. iv.; Bain, p. 86.

In any case, the disjunctive is more than any combination of Hypotheticals, and really tends to be Categorical, and ought not to be claimed as Conditional.

Which are Categorical?

2. We will now look at these Judgments in order, consider their real meaning, and also ascertain the limits of the Categorical Judgment, viz. that which affirms the existence of its Subject, or in other words, asserts a fact.

The Particular Judgment

(i) The Particular Judgment of common Logic, “Some S. is P.,” has different meanings according as it is understood naturally, or tied down to be a result of enumeration.

In any case it is an imperfect, unscientific Judgment, in which the mind cannot rest, because it has an undefined limitation imposed upon the Subject.

Its natural meaning

(a) For the natural meaning, take the example, “Some engines can drag a train at a mile a minute for a long distance.” This does not mean a certain number of engines, though of course they are a certain number. It {117} means certain engines of a particular make, not specified in the Judgment. The Judgment is Categorical, because the undefined reservation implies a reference to something unanalysed, but merely touched or presented in experience. If it was a mere idea it would have to be clear; and if the full description or definition were inserted, the Judgment would cease to affirm the existence of the engines in question. And the Judgment itself challenges this completion.

To be accurate, the Judgment would demand the insertion of precise details about train, distance, and other matters. But this illustrates the point of the text, because the assignment of such details would naturally extend to the Subject, and then the “Some” would be displaced.

A narrower meaning

(b) A more artificial meaning is to take the Judgment as not formed by imperfect description, but by imperfect enumeration (understanding it almost wholly in denotation). “Some Conservatives are in favour of women’s suffrage.” This means or may mean that we have counted a certain number, large or small, who are so, and we may or may not know about the others. Thus understood, the Judgment challenges complete enumeration; it contains of course the elements of a fraction--half, most, nine-tenths of, and so on.

This again is Categorical; not merely because it implies counting, but because it implies counting units separately given to experience.

The Particular Judgment does not include our Impersonal and Demonstrative Judgments; they are not classed in the common text-books. But as referring to perception they too are categorical and assert facts, whether they have ideas to help out the perceptive reference or not. And there is no reason against including them under the Particular Judgment. The assertion, “This engine can drag a train a mile a minute,” is much the same kind of Judgment as, “Some engines can, etc.” Either of these would be false {118} if no such engines existed. These Judgments are of the essence of perception. They have the connection of content and the undefined complex of presentation struggling together in them. They assert fact.

Singular Judgment

(2) The Singular Judgment of the common Logic is pretty much our Judgment with a proper name, which I call Individual, and which, as we saw, is in part rightly called universal--because the Subject extends beyond perception, and the Predicate follows the Subject. But it is a concrete or individual Universal, not an abstract Universal, and therefore asserts the existence of its Subject. The reason why it is taken to assert the reality of its Subject must be, I suppose, that it can assert this, its Subject being a name for an existence that has limited reality within the temporal series, and cannot assert anything else, not having any general fixed content or connotation which could imply a general connection of Subject and Predicate. The general connection of content which is so fatal to the asserting of fact does not exist in this case. We see this in Mill’s instance. “The summit of Chimborazo is white,” When the Subject is a unique name with precise connotation, “The centre of gravity of the material universe is variable,” then we are passing into the abstract Universal, and I think we may take such a Judgment perhaps as one of the best examples of a conjunction of categorical and hypothetical meaning, i.e. of a connection of content ascribed to a Subject affirmed to exist. But usually one meaning or the other is uppermost.

These Judgments, called Singular or Individual, correspond to the region of history or narrative. The realities {119} with which they deal have their definite position in a single system of time and space, and this is often made emphatic by the use of tenses. But these change with the date relative to the speaker, so that a Judgment with real tense must once have been false, or must become false by lapse of time. Thus the Judgment of fact may be not absolutely true. Nothing is genuinely true which a change of date can make false. The permanently true time-relations between Subject and Predicate are determined by their content, and the copula is not a tense, but a mere sign of affirmation. The Singular as Categorical is sharply distinguished from the Abstract Universal, with which common Logic classes it.

Universal Judgment

(3) Down to this point the judgment states a fact. When we come to the ordinary universal affirmative, we see at once that it may express very different meanings. In its natural meaning it strongly implies that its Subject has a particular existence within the series of time and space, but hardly asserts it.

Import of Propositions

Mill, for example, says “the objects are no longer individually designated, they are pointed out only by their attributes;” “most of them not known individually at all.” That means that the explicit Subject is not made of individuals. The natural meaning is disputed; I incline to think with Venn, that the Subject is naturally taken more in Denotation (not solely, which is unmeaning), and the Predicate more in connotation. But clearly in literal form the Subject is simply a significant idea, and its existence in things or events is not affirmed though it may be strongly implied. Hamilton {120} says quite calmly--“‘Rainy weather is wet weather’ is a Categorical Proposition; ‘If it rains it will be wet’ is Hypothetical.” Between the two I can see no distinction of meaning at all. If indeed we take the Universal Affirmative in the pure sense of aggregate formed by enumeration, and therefore finite, it may be said that we assert the existence of the individuals composing it; but this is a very unreal view of the meaning of the Judgment (though suggested by its customary form), and even then it would be hard to prove that we continue to think of the Subject as individuals. This reference to a finite aggregate makes the Collective Judgment or Judgment of Allness. It cannot really exist in the case of a class like man, of unknown extension, and is confined, at its widest, to such cases as “All present Members of Parliament have to take a line on the Irish question.” This might be Categorical, but need not be so.

Lectures, vol, iii. p. 327.

Contrast Jevons, Elementary Logic, p. 163.

Otherwise, the Universal Affirmative of common Logic is literally Hypothetical, though in some cases it may strongly imply the assertion of reality. Dr. Venn has discussed this question. He says the implication of existence is much stronger with a single-word Subject than with a many-worded Subject; i.e. perhaps with a natural than with an artificial conception. But in any case, the expressed bond with perception is lost, and in pure form the Subject is a mere abstract idea, so that the relations of content entirely predominate over the implication of existence.

Empirical Logic, pp. 258-9.

Thus the Universal Affirmative in its full meaning fairly {121} represents the sciences of classification, combining a subordinate meaning of Allness or numerical totality with a primary meaning of connotation of attributes or presumed causality. When we say “All the Buttercup family have an inferior corolla,” of course we mean that there is a reason for this. Often we omit the term all, as in “Heat is a mode of motion.” In doing this we wipe out the last trace of a reference to individual objects, and we pass to the pure hypothetical form which absolutely neglects the existence of objects.

“Hypothetical” Judgment

(4) The simplest type of this Judgment is, if A is B it is C. This Judgment corresponds to abstract science, but it is only making explicit what was implied in the Universal Affirmative. That expressed a presumption of causality, this expresses a clear Reason and Consequent or scientific necessity. The point of this form is (i.) that it drops all reference to individual objects, (ii.) that it challenges you to explain how the Subject-content is tied to the Predicate-content. “Water boils at 212°,” is a statement we should generally pass in so-called Categorical form, because it does not challenge any great accuracy of connection. But “If water boils, it is at a temperature of 212°,” puts us upon asking, “Is the condition adequate?” and we see at once that we must at least say, “If water boils under pressure of one atmosphere, it is at a temperature of 212°,” or else the judgment is untrue. Of course we may apply the form rightly or wrongly, as you may fill up your census paper rightly or wrongly. We can only say that it calls upon you to put in an adequate condition. Therefore I rather object to the form “If A is, B is,” because it adds very little to the so-called Categorical shape.

{122} We have now to ask how the Hypothetical Judgment connects its content with reality, i.e. how it is a Judgment at all? And the same explanation must apply to so-called Categorical Judgments, which can be thrown into this form without change of meaning.

The point from which the explanation starts is taking hypothesis as supposition. This is much more true, I think, than connecting it with doubt. In Dr. Venn’s Empirical Logic the connection of Hypothetical Judgment and doubt to my mind disfigures the whole treatment of the Scientific Judgment. Supposition is distinct from affirmation--that is true--but just because it is distinct from affirmation, it cannot indicate doubt. It probably arose out of doubt, but as a method of science it does not imply doubt, but only the accurate limitation of attention. What doubt is there when we judge “If equals be added to equals, the wholes are equal”? We are attending to one particular thread of the nexus.

Hypothetical Judgment, then, is Judgment that starts from a supposition. Every supposition is made upon a certain basis of Reality. Take as an extreme case, “If you ask permission of A.B., he will refuse it.” This is a supposition and its result, on the basis of the known character of A.B. And the full judgment is “A.B. is of such a character, that, supposing you ask him for permission, etc.” The Hypothetical Judgment may be true, as an assertion about A.B.’s character, though you may never ask.

Here, then, is the clue to the analysis of all Abstract Judgments, Like Perceptive Judgment, they affirm something of Reality, but they do this indirectly and not directly. {123} Underlying them there is the implied Categorical Judgment, “Reality has a character, such that, supposing so and so, the consequence will be so and so.” And if this implied assertion is true, then the Hypothetical Judgment is true, although its terms may be not only unreal, but impossible. “If a microscopic object-lens with a focal length of 1/100 in. were used, its magnifying power with an A eye-piece would be so many diameters.” This is a mere matter of calculation, and is unquestionably true, depending upon the effects of refraction upon the optical image. But I do not suppose that such an object-lens could be made, or used. Does such a Judgment, although true, express a fact? No, I should say not, although common usage varies. I remember a Pall Mall leading article which said, “It is an absolute fact, that, if Mr. Gladstone had not done something--the Government would have committed--some iniquity or other.” Is this what we call a fact? We observe that the content actually mentioned was never real at all. The implied connection with reality is “There existed in reality a condition of things (unspecified) in which if Mr. Gladstone, etc., etc.” Are mathematical truths facts, and in what sense? Abstract truth need not, and perhaps cannot express fact, but implies fact indirectly.

Disjunctive Judgment

(5) The Disjunctive Judgment “A is either B or C,” is again not a judgment of doubt but a mode of Knowledge, It may be taken as numerical; then it gives rise to the statement of Chances. But in its perfect form it is appropriate to the exposition of a content as a system, and it may be taken as returning to the Categorical Judgment, and combining it with the Hypothetical, because its {124} content is naturally taken as an individual, being necessarily concrete.

The peculiar point of the Disjunctive is that it makes negation positively significant.

“This signal light shows either red or green.” Here we have the categorical element, “This signal light shows some colour,” and on the top of this the two Hypothetical Judgments, “If it shows red it does not show green,” “If it does not show red it does show green.” You cannot make it up out of the two Hypothetical Judgments alone; they do not give you the assertion that “it shows some colour.”

The example in the text, chosen for its simplicity, may be objected to as involving perceptive concreteness by the pronoun “this.” You can have a disjunction, it may be said, dealing with “the triangle” as such; and why should this be more “Categorical” than the assertion that the triangle has its angles = three right angles? Still, it might be replied, the development of a single nature into a number of precise and necessary alternatives, always gives it an implication of self-completeness.

Does this state a fact? I think it implies a fact much more distinctly than the hypothetical does, but of course it is a question whether an alternative can be called a fact. It seems a precise expression of some kinds of reality, but it is not a solid single momentary fact. It is very appropriate to the objects of philosophy as the higher concrete science, which are conceived as systems of facts bearing definite relations to each other; e.g. “Society is a structure of individual characters, having positions which are not interchangeable.” Taken all as a mass, they are conjunctively connected, but taken in distinguishable relations they are disjunctively related. A human being as such has some position and no other, and this is ultimately determined by {125} the nature of the social whole to which he belongs. He is if this, nothing else, and if nothing else, then this. A more artificial example, which illustrates the degree in which actual abstract knowledge and purpose can be embodied by man in machinery, is the interlocking system of points and signals at a great railway station. I suppose that the essence of such a system lies in arrangements for necessarily closing every track to all but one at a time of any tracks which cross it or converge into it. The track X receives trains from A, B, C, D; if the entrance for those from A is open, B, C, and D are ipso facto closed; if A, B, and C are closed, D is open, and so on. This is a disjunction consciously and purposely incorporated in material fact, and differs from a Disjunctive Judgment only in so far as existence necessarily differs from discursive thought.

The disjunction seems to complete the system of judgments, including all the others in itself, and it is wrong in principle to distinguish, e.g. between a hypothetical and categorical disjunction, or to consider how a disjunction can be denied. For disjunction in itself implies a kind of individuality which is beyond mere fact and mere abstract truth, though allied to both; and all intelligible negation is under, not of, a disjunction. Negation of a disjunction would mean throwing aside the whole of some definite group of thoughts as fallacious, and going back to begin again with a judgment of the simplest kind. It amounts to saying, “None of your distinctions touch the point; you must begin afresh.”

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