[1] InMind, no. 62.
Words are needed when we have to attend to the general plan of any system, as in thinking about organisms with reference to their type, or about political relations—about anything, that is, which is not of such a nature that the members of the idea can be symbolised in pictorial form. It would be difficult, for example, to comprehend the respiration of plants under a symbolic picture-idea drawn {81} from the respiration of the higher animals. The relations which constitute a common element between the two processes do not include the movements, feelings, and visible changes in the circulatory fluid from which our image of animal respiration is chiefly drawn; and we could hardly frame a pictorial idea that would duly insist on the chemical and organic conditions on which the common element of the process depends. In a case of this kind the word is the symbol which enables us to hold together in a coherent system, though not in a single image, the relations which make up the content of our thought.
“Words” may be of many different kinds—spoken, written, indicated by deaf and dumb signs; all of these are derived from the word as it is in speech, although writing and printing become practically independent of sound, and we read, like the deaf and dumb alphabet, directly by the eye. Then there may be any kind of conventional signals either for letters, words, or sentences, and any kind of cipher ormemoria technicaeither for private or for general use—in these the “conventional” nature of language reaches its climax, and the relation to a natural growth of speech has disappeared. And finally there are all forms of picture-writing, which need not, so far as its intrinsic nature goes, have any connection with speech at all, and which seems to form a direct transition between picture-thinking and thinking through the written sign.
All these must be considered under the head of language, as a fixed system or signs for meanings, before we can ultimately pronounce that we think without words.
Every Judgment, however, can be expressed in words, {82} though not every Judgment need be so expressed or can readily be so.
Proposition and sentence.
2. A Judgment expressed in words is a Proposition, which is one kind of sentence. A command question or wish is a sentence but not a proposition. A detached relative clause [1] is not even a complete sentence. The meaning of the imperative and the question seems to include some act ofwill; the meaning of a proposition is always given out simply for fact or truth. We need not consider any sentence that has no meaning at all.
[1] See above, Lect. IV.
Difference between Proposition and Judgment
3. Almost all English logicians speak of the Proposition and not of the Judgment. [1] This does not matter, so long as we are agreed about what they mean. They must mean the propositionas understood, and this is what we call the judgment.
[1] So Mill, Venn, Jevons, Bain (see his note, p. 80).
In order to make this distinction clear, let us consider the proposition as it reaches us from without, that is to say, either as spoken or as written. The words, the parts of such a proposition, as we hear or read them, are separate and successive either in time alone, or in time and space. Further, the mere sounds or signs can be mastered apart from the meaning. You can repeat them or copy them without understanding them in the least, ase.g.in the case of a proposition in an unknown language. So far, the proposition has not become a judgment, and I do not suppose that any logician would admit that it deserved the name even of a proposition. But if not, then we must not confuse the attributes which it has before it becomes a proposition with those which it has after.
{83} Further, in understanding a proposition, or in construing a sentence into a proposition (if the sentence only becomes a proposition when understood), there are many degrees. I read upon a postcard, “A meeting will be held on Saturday next by the Women’s Liberal Association, to discuss the taxation of ground-rents.” The meaning of such a sentence takes time to grasp, and if the words are read aloud to us, must of necessity be apprehended by degrees. We understand very quickly that a meeting is to be held next Saturday. This understanding is already a judgment. It is something quite different from merely repeating the words which we read. It consists in realising them as meanings, and bringing these meanings together into a connected idea, and affirming this idea to belong to our real world. The meanings are not separate, outside one another, as the words are when we first hear or read them. They enter into each other, modify each other, and become parts of an ideal whole. This gradual apprehension of a sentence recalls to one the boyish amusement of melting down bits of lead in a ladle. At first the pieces all lie about, rigid and out of contact; but as they begin to be fused a fluid system is formed in which they give up their rigidity and independence, and enter into the closest possible contact, so that their movements and position determine each other. But still some parts, like words not yet grasped, remain hard and separate, and it is only when the melting is complete that this isolation is destroyed, and there are no longer detached fragments, but a fluid body such that all its parts are in the closest connection with one another.
Thus then in understanding a sentence we have a judgment {84} from the first. The rest of the process of understanding consists in completing the content of this judgment by fusing with it the meanings of the words not yet apprehended; and in the completeness with which this is effected there will always be great differences of degree between different minds, and also between the same mind at different times. Some of us attach a complete and distinct meaning to the words “Women’s Liberal Association”; some of us do not know, or have forgotten, exactly what it is, and what are its aims and history. All of us have some conception of the purpose described as “taxation of ground rents,” but the phrase conveys a perfectly definite scheme hardly to one in a thousand readers. Nevertheless, in so far as we have some symbolic idea which refers to this place or context in the world of objects, the content of this idea enters into and modifies the total meaning which in apprehending the sentence before us we affirm of reality. The heard or written proposition (or sentence, if it is not a proposition till understood) serves as an instrument by which we build up in our intellectual world a sort of plan or scheme of connected meanings, and also, not subsequently but concurrently with this work of building, affirm the whole content thus being put together to be true of reality. Then we have what I call a Judgment. It is not that the words are necessarily forgotten; they, or at least the principal significant terms, are probably still in the mind as guides and symbols; but yet a constructive work has been done; a complex experience has been called up and analysed, and its parts fitted together in a certain definite order by the operation of universal ideas or meanings, each of which is a system playing {85} into other systems; and the whole thus realised has been added as an extension to the significance of the continuous judgment which forms our waking consciousness. The inconvenience of the term “proposition” is that it tends to confuse the heard or written sentence in its separate words with the proposition as apprehended and intellectually affirmed. And these two things have quite different characteristics.
Parts of Speech
4. Thus we must be very careful how we apply the conception of “parts of speech.” The grammatical analysis which classifies words as substantives, adjectives, adverbs, verbs, and the like, is not to be taken as telling us what words are by themselves, but just the opposite, viz. what they do when employed in a significant sentence. They are studied separately for convenience in attending to them, as we may study the wheels and pistons of an engine; but the work which gives them their names can only be done when they are together. This truth is often expressed by saying that “the sentence is the unit of language,”i.e.a word taken by itself cannot have a complete meaning—unless it is a verb, or used with verbal force, for a verb is an unanalysed sentence. If any one uses a substantive or adverb by itself, we think that he has not finished his sentence, and no meaning is conveyed to our minds. We ask him, “Well, what about it?” The same is true, as we saw, of a relative clause. If we read in a newspaper such a clause as this, “The epidemic of influenza, which has appeared in England for three successive seasons,” followed by a full stop, we should infer, without hesitation, that some words had dropped out by accident. Of course such a {86} combination of words would make us think something, but the meaning which we might ascribe to it would be conjectural; we should necessarily complete the thought for ourselves by some affirmation—some relation to reality—while recognising that no such relation was given in the clause as we read it. Nothing less than a sentence, or, omitting the wish and the command, nothing less than a proposition, conveys a meaning in which the mind can acquiesce as not requiring to be supplemented conjecturally. There are traces in language that indicate the sentence to have been historically prior to the word. I question whether the word could be certainly distinguished within the sentence in early languages that have not been reduced to writing. The tendency of reflective analysis, as in grammar and dictionaries, is to give it a more and more, artificial isolation. The Greeks did not separate their words in writing, and they wrote down the change in a terminal consonant produced by the initial letter of the next word, just as if it was within a compound word. Nor had they really any current term co-extensive with our “word.” Where we should say “the word ‘horse’” they most commonly use the neuter article “the” followed by the word in question as if in quotation-marks (”the ‘horse’“). In defining noun and verb, Aristotle has no simple class name like ”word“ to employ as a common element of the definition, but uses the curious description ”a portion of discourse, of which no part has a meaning by itself.“
Of course, single words often stand as signs for propositions. It is interesting to note the pregnant meaning of a single word in the mouth of a child. Thus “stool” was {87} used to mean “(1) Where is my stool? (2) My stool is broken; (3) Lift me on to the stool; (4) Here is a stool.” [1] There is in this an interesting conflict of form and meaning, owing to the child of European race having at command only “parts of speech.” In a less analytical language he might have at command a sound corresponding to a sentence rather than to a “noun substantive.”
[1] Preyer, quoted inHöffding, Psych., 176.
The verb of inflected languages, [1] such as Greek or Latin, in which the “nominative case” need not be supplied even by a pronoun, is the type for us of a sentence not yet broken up.
[1] In German and English, though the verb is inflected, custom forbids it to stand without the pronoun.
The bearing of this truth on Logic is to make us treat it in two parts and not in three. We do not treat of Name, Proposition, Syllogism, or of Concept, Judgment, Inference, but only of the two latter parts. The name or concept has no reality in living language or living thought, except when referred to its place in a proposition or judgment. We ought not to think of propositions as built up by putting words or names together, but of words or names as distinguished though not separable elements in propositions. Aristotle takes the simple and straightforward view. “A term is the element into which a proposition is broken up, such as subject and predicate.” [1] Of course different languages separate the parts of the proposition very differently, {88} and uneducated people hardly separate them at all. Formal Logic breaks down the grammatical meaning of “name,” so far as to treat as a “logical name” any complex words that can stand as Subject or Predicate in a Proposition (e.g.a relative clause).
[1]Anal. prior., 24b, 16. The opposite view seems to be expressed in the beginning of the περὶ Ἑρμενείας [= peri Hermeneias,de Interpretatione], that the separate word corresponds to the separate idea. I have attempted to explain this as an illusion, p. 73, above.
Denotation and Connotation
5. The doctrine of the meaning of names has suffered from their relation to propositions not being borne in mind. Mill’s discussion [1] is very sensible, but, as always, very careless of strict system. More especially it seems a pity to state the question as if it concerned a division of names into Connotative and Non-connotative; because in this way we from the first let go of the idea that the meaning of a name has necessarily two aspects, [2] and we almost bind ourselves to make out that there are some non-connotative names. It is better to consider this latter subject on its merits. Mill says that an ordinary significant name such as “man” “signifies the subjects directly, the attributes indirectly; itdenotesthe subjects, and implies or involves or indicates, or, as we shall say henceforth,connotes, the attributes.” In short, the denotation of a name consists of the thingsto whichit _ap_plies, the connotation consists of the properties which it _im_plies. The denotation is made up of individuals and the connotation of attributes. Denotation is also called Extension, especially if we are speaking of Concepts rather than of names. Connotation is then called Intension. In the German writers it is more usual to say that the Extension or Area (Umfang) consists not of the individuals, but of the species that are contained in {89} the meaning of a general name. They oppose it to Content (Inhalt) corresponding to our “Connotation.” Thus the “Area” of “rose” would not be the individual roses in the world, but rather all the species of rose in the world (Rosa Canina, Rosa Rubiginosa, etc.). This raises a difficulty as to the denotation of a specific name, but perhaps represents the actual process of thought, in the case of a generic name, better than that which Mill adopts. The difference is not important.
[1]Logic, Bk. I. c. ii. § 5. Cf. Venn, 174 and 183, and Bain, 48.
[2] See Bradley, p. 155.
Well, then, according to Mill, when we say, “The Marshal Niel is a yellow rose,” we refer directly to a group of real or possible objects, and we mean that all these individual objects are yellow roses. The attributes are only mentioned by the way, or implied. So Dr. Venn says that the denotation is real, and the connotation is notional.
But there is another side to this question. The objects may bewhat you meanbut the attributes seem to bethe meaning, for how can you (especially on Mill’s theory of the proposition) refer to any objects except through these attributes, unless indeed you can point to them with your finger? And so again it seems, especially if we consider Mill’s account of predication, as if the Connotation were the primary meaning and the Denotation the secondary meaning. The Connotation determines the Denotation; and if we “define” the meaning of the name it is the Connotation that we state. And so Mill tells us two or three pages further on, that whenever the names given to objects have properly any meaning, the meaning resides not in what they denote, but in what they connote. In short, {90} the denotation of a general name is simply the meaning of its plural, or of its singular, in that sense in which it implies a plural, while the connotation is the meaningper se, not considered in its instances.
It is clear then that every name has these two kinds of meaning—first, a content, and then instances, whether possible or actual, of the content; and the two are obviously inseparable, although they are distinguishable. Ultimately, indeed, the denotation itself is an attribute, and so part of the connotation. It is one of the attributes of man to be a unit in the plurality men,i.e.to be “a man.” It may be said that some names have no plural. If so, these would be non-denotative rather than non-connotative, but in fact this is not true. The content of a significant name can always, unless hindered by a special convention (see below on proper names), beprima facieregarded, in respect of its actual embodiment, as a unit against other possible units. Granting that there may be an object, which according to our knowledge can only be real as an isolated case, the very consideration of it as such a case is enough to distinguish its existence, whether real or possible, from its content. Thus, as a real or possible existence, the object isipso factoconsidered in the light of a particular, and as capable of entering into a plurality. But its nature or content, the meaning of its name, cannot enter into a plurality. Twomeanings, two connotations, are alternative and irreconcilable. Denotation and connotation are thus simply the particular, or particulars, which embody or are thought of as embodying a content, and the single or universal content itself.
{91}Have Proper Names Connotation?
6. Therefore I think that Mill is wrong, when he goes on, “The only names of objects which connote nothing are Proper Names, and these have, strictly speaking, no signification.” [1] If the name has no signification, for what reason, or by what means, is it attached to a person or a place? You may say that it is only a conventional mark. But a mark which has power to select from all objects in the world, and bring to our minds, a particular absent object, is surely a significant mark. Granted that it is conventional, yet by what mechanism, and for what purpose, does the convention operate?
[1] Cf. Venn, 183 ff, and Bradley, 156.
Mill’s point, however, is quite clear. To be told the name of a person or object does not inform us of his or its attributes. Directly, it only warns us by what sign the same person or object will be recognisable in language again. [1] If a name is changed, the new name tells us nothing different from the old, [2] whereas if an object that was called vegetable is now called animal, our conception of it is radically transformed. A name expresses the continued identity of an object, and this implies only a historical continuity of attributes and relations, and no constant attribute whatever.
[1] We cannot make it a distinctive mark of proper names that they recur in different and quite disconnected meanings, because the words which are used as general names have this same property. Nor can we say that a proper name is not used in the same sense of more than one object. Family names and national names make this plainly untrue. Through these, and names typically employed, there is a clear gradation from proper to general names.
[2] The case of marriage may be urged. But a lady’s change of name does not by itself indicate marriage. It is a mere fact, which may have various explanations. The change of title (from “Miss” to “Mrs.”) is more significant, but it is not a change of name.
{92} Thus apropername is a contradiction in terms. [1] A name should have a meaning. But a meaning cannot be proper—that is, particular. The name-word is therefore like a demonstrative pronoun, if this were attached, by a special convention, to one identifiable object only. It acquires meaning, but its meaning is an ever-growing contradiction with its usage. The meaning is necessarily general, the usage isex hypothesiparticular.
[1] So, from the complementary point of view, is ageneralname. A name, it may be urged,ismeant to designate a particular thing or things. And this a name with a true “meaning” cannot do.
This convention of usage, which prevents a proper name from becoming general,i.e.from being cut loose and used simply for its meaning, is always on the point of breaking down. [1] Christian names usually indicate sex; family names, though now with little certainty, descent and relationship. There are germs of a general meaning within the several usages of names; while a Solon, a Croesus, a Christian, a Mahometan, have become purely general names cut loose from all unique reference. Still in a proper name, as such, we have no right to build on any general meaning. Recognition is its only purpose; and the law permits, it has been said, that a man should have one name for Mondays, Wednesdays, and Fridays, and another for Tuesdays, Thursdays, and Saturdays. The essence of a name is a reference to unique identity; it employs meaning only to establish identity.
[1] See note on last page.
What kinds of things have proper names given, then? Always thingsindividuallyknown to the people who give {93} the name, and interesting to them for some reason beyond generic or specific qualities. Pet animals have names, when other animals of the same kind have not. The peasants throughout England use names, it is said, for all the fields, although strangers are not usually acquainted with them.
A Proper Name, then, has a connotation, but not a fixed general connotation. It is attached to a unique individual, and connotes whatever may be involved in his identity, or is instrumental in bringing it before the mind.
When we think of history, the importance of proper names becomes very great. This is the characteristic logical difference between history and science. “England” and “France” are proper names, names of individual existences in contact with our world of perception, not scientific abstractions. Even the words, “1892 A.D.,” are partly of the nature of a proper name. They say nothing merely general or abstract about this year; they assign the year a name by counting forwards from a unique point in the series of years, itself designated by the name of a historical personage. Everything that is simply distinguished by its place in the series of events in space and time is in some degree a proper name. Thus we could not identify the French Revolution by mere scientific definition. It is known by its proper name, as a unique event, in a particular place and time. When thus identified it may have all kinds of general ideas attached to it. It would be hard to show that “Our earth,” “Our solar system” are not proper names, in virtue of their uniqueness.
{94}Inverse ratio of Connotation and Denotation
7. It has sometimes been said that Connotation is in inverse ratio [1] to Denotation. Mill explains the fact upon which any such idea rests. [2] If we arrange things in classes, such that the one class includes the other—e.g. Species“Buttercup,”Genus“Ranunculus,”Order“Ranunculaceae,”—of course the genus will contain many species besides the one mentioned, and the order many genera besides the one mentioned. The object of the arrangement is that they should do so, and thus bring out the graduated natural affinities which prevail in the world. Thus the denotation of the genus-name is larger than that [3] of the species, and the denotation of the order-name is larger than that of the genus-name.
[1] See Venn, p. 174, for reference to Hamilton. Venn points out the fallacy.
[2]Logic, Bk. I. ch. vii. § 5.
[3] Or “than the species,” if we take the denotation as made up of species.
But further, in such an arrangement the genus can contain only the attributes which are common to all the species, and the order can contain only the attributes which are common to all the genera; so the genus-name implies fewer attributes (less connotation) than any one species-name under it, and the order-name implies fewer attributes (less connotation) than any one genus-name under it.
That is the fact which suggests the conception of Denotation andConnotation as varying inversely.
But in any case it would not be right to speak thus mathematically of an inverse ratio, because there is no meaning in a numerical comparison of attributes and {95} individuals, and the addition of one attribute will exclude sometimes more and sometimes fewer individuals. [1]
[1] See Jevons, p. 40.
And there are more important objections to the whole idea of a corresponding gradation in these two kinds of meaning. The idea of abstraction thus implied is altogether wrong. The meaning of a genus-name does notomitthe properties in which the species differ. If it did, it would omit nearly all properties. What happens is that the genus-idea represents the general plan on which the species are built, but provides for each of the parts that constitute the whole, varying in the specific cases within certain limits. Thus in the Ranunculaceae some species have no petals. But we do not omit the character “petals” from the genus-idea. We state the general plan so far as this element is concerned as “Petals five or more; rarely none.” This is read by a botanist to mean that in some groups the petals tend to be aborted, and sometimes are actually missing. In a symbolic representation of the genus-idea such a property may stand as A, and its various specific forms as A1, A2, A3, etc. There is nothing to prevent these specific phases approaching and sometimes reaching zero. No doubt if the classification is pursued in the direction of “universals” containing fewer and fewer properties, it is possible to arrive at concepts which appear to have a larger denotation and a smaller connotation than those “below” them. “Ranunculaceae,” “Dicotyledons,” “Plants,” “Organisms.”
But this is only because we choose to form our system by that process of abstraction which consists in leaving out properties.E.g.comparing Frenchmen with men in general, {96} we assume that “Frenchman” indicates (a) all the qualities of humanity as such, and (b) the qualities of French humanity in addition to these. But is this so in fact? Humanity, considered as a wider, and therefore as a deeper, idea, may have more content, as well as more area, than Frenchmanity. We do not really, in thinking of humanity, omit from our schematic thought all references to qualities of Greek, Jew, English, and German, and their bearing and interaction upon one another. It is only that we have been drilled to assume a certain neatness in the pyramidal arrangement by which we vainly try to reduce the meaning of a great idea to something that has no system and no inter-relation of parts, but approaches as near as possible in fixity to the character of a definite image, though far removed from such a character in the impossibility of bringing it before the mind.
So we can only say, “the greater the denotation the less the connotation,” and “vice versâ”, in as far as we arrange ideas by progressive abstraction in the sense of progressive omission. But it is not the only way of regarding them. Things may develop new inter-relations as their number increases. Has the community, as Mr. Bradley asks, less meaning than the individual person? But we must not consider the community, would be the answer; we must simply consider the relation of an idea of one individual to any idea that applies to many individuals. This is simply to rule out those relations that arise within progressively larger wholes. We can do so, if we think the exclusion necessary in the interests of logical purity, but it is only by doing so that we can maintain the traditional view of connotation and denotation. It is worth while to think out the {97} matter for ourselves in relation to such familiar ideas as those of man and animal. It is plain that the idea of “animal” cannot omit all reference to intelligence, but must in some way allow for the different phases of this property which run throughout the animal kingdom, and only find a climax in man. And it is plain also, that even if intelligence were wholly omitted, this would not leave behind, as in a simple stratification, properties in which the whole animal kingdom was the same. Man’s animality is modified throughout in a way corresponding to his rationality, so that no general idea could be framed including him and other animals, simply by collecting properties which are the same and omitting those which are different. The idea of “man” really becomes richer when considered in the light of a comparison [1] with the rest of the animal world. Our great systems of natural classification, representing affinities graduated by descent, are what give the view which we have criticised a certain objective importance. But they do not establish it as an exclusive logical doctrine.
[1] If we insist on throwing the whole of this comparison, in explicit shape, into the complete idea of man, then the progress to the idea “animal” can add nothing; even so, however, it loses nothing, but simply becomes the same set of relations, looked at, so to speak, from the other end.
{98}
Parts of the Judgment
1. The result of taking the Judgment as one with the Proposition has been to assume that its parts were the same as those of the Proposition; [1] and moreover the same as those of the Proposition in a very artificial form, viz. as analysed into three separable elements, “Subject,” “Predicate,” “Copula,” commonly represented in the examples of the text-books by Substantive, Adjective or Substantive, and the Verb “is.”
[1] This assumption involves (see Lecture V.) a confusion between the Proposition as thoroughly understood, and the Proposition as a series of partially significant sounds or signs. For obvious reasons, this confusion is very readily made.
For the operation of Formal Logic it is almost necessary to have these parts, because it is requisite to transpose the terms (as in Conversion) without changing their meaning, [1] and to get rid oftenses, which do not belong to Scientific Judgment, and are very troublesome in Formal Inference.
[1] If the “predicate” is a Substantive, this presents no difficulty; and if it is an Adjective, it can be done by a little straining of grammar, or the insertion of “thing” or “things.” With a verb it is more clumsy.
Thus in Formal Logic we prefer the shape of sentence “Gold is lustrous” to “Gold glitters,” and “The bridge is {99} cracked” to “There is a crack in the bridge.” And practically all propositions can be thrown into this shape, which is convenient for comparing them. The educational value of elementary formal logic consists chiefly, I am convinced, in the exercise of paraphrasing poetical or rhetorical assertions into this typical shape, with the least possible sacrifice of meaning. The commonest mistakes in the work of beginners, within my experience as a teacher, consist in failures to interpret rightly the sentence given for analysis.
But this type is not really ultimate. The judgment can be conveyed without a grammatical subject, and without the verb “is”—indeed without any grammatical verb at all. On the whole this agrees with Mill’s view in the chapter “Of Propositions.” [1] He points out (§ 1) that we really need nothing but the Subject and Predicate, and that the copula is a mere sign of their connectionasSubject and Predicate. He does not, however, discuss the case in which the grammatical Subject is absent.
[1] Mill’sLogic, Bk. I. ch. iv.
Copula
2. In analysing the Judgment as an act of thought we may begin by dismissing the separate Copula. It has no separate existence in thought corresponding to its separate place in the typical proposition of Formal Logic. It has come to be considered separately, because the abstract verb “is” is used in our languages as a sign of the complete enunciation. But there is not in the Judgment any separate significant idea—any third idea—coming in between the Subject and Predicate of Judgment. We should try to think of the Copula not as a link, separable and always {100} intrinsically the same, [1] connecting two distinct things. We should think of it rather as the grip with which the parts of a single complex whole cohere with one another, differing according to the nature of the whole and the inter-dependence of its parts. Benno Erdmann [2] has strikingly expressed this point of view by saying, that in the Judgment, “The dead ride fast,” the Subject is “the dead,” the Predicate “fast riding,”and the Copula “the fast riding of the dead.” In other words, the Copula is simply the Judgment considered exclusively as a cohesion between parts of a complex idea, the individual connection between which can only be indicated by supplying the idea of those parts themselves.
[1] In a comic Logic, with pictures, meant to stimulate dull minds at a University, I have seen the Copula represented as the coupling-link between two railway carriages. This is an excellent type of the way in which we shouldnotthink of it.
[2]Logik, p. 189.
Are Subject and Predicate necessary?
3. The explicit Predicate is more necessary than the explicit Subject.
We have spoken of Judgments expressed by one word, “Fire!” “Thieves!” etc., and also of impersonal Propositions, “It is raining,” “It is thawing.” These two classes of Judgments show hardly any explicit Subject at all. But we could not assert anything without a Predicate—that would be to assert without asserting anything in particular.
As these Judgments have, roughly speaking, a Predicate and no Subject, I do not think it convenient to call them, with Dr. Venn, existential judgments. It is true that they refer to reality, but theirpeculiarityis in not referring to a distinct subject. And when used for definite and complex assertions they become very artificial,e.g.“There is a {101} British Constitution by which our liberties are guaranteed.” Instead of organising the content of the Judgment, such a form of assertion simply tosses the whole of it into the Predicate in a single mass.
The question is only one of words; but it appears to me more convenient to reserve the term Existential judgments for those highly artificial assertions which actually employ the Predicate “exist” or “existence,”e.g.“Matter exists.” These are at the opposite end of the scale from those last-mentioned, and are the nearest approach to Judgment with Subject and no Predicate. That is to say, their Predicate is the generalised abstract form of predication [1] without any special content—the kind and degree of existence asserted being understood from the context.
[1] Expressed in Greek by the word corresponding to “is,” used with an accent, which does not belong to it in its ordinary use. He is good = ἄγαθός ἐστι [= agathos esti]; He exists = ἔστι [= esti Tr.].
Except, however, in the case of these peculiarly abstract and reflective assertions, it must be laid down that a predicated content is necessary to judgment, while anexplicitsubject of predication is unnecessary.
Two Ideas of Things
4. If it is possible, in some cases, to throw the whole content of judgment into the predicate, this rather disposes us to criticise the notion that there must be two distinct matters, objects, ideas, or contents, in every judgment. The notion in question has two forms.
It is thought that the Judgment consists in putting twoideastogether, [1] or, {102} That the Judgment consists in comparing two or more things. [2]
[1] For this conception, see Hamilton’sLectures on Logic, i. 227, and for a criticism on it. Mill’sLogic, Bk. I. ch. v.,init, Dr. Venn seems to incline to Hamilton’s view, but I do not feel sure that he intends to discuss the question in the form in which it is referred to in the text. See hisEmpirical Logic, pp. 210 and 211.
[2] See Jevons, pp. 61-2; and Mill, Bk. I. ch. iii.,init.; and ch. iv.,init.
Two Ideas
(a) The notion of “two ideas” has two principal difficulties.
Notion of mental transition pure and simple
(i.) In its simplest shape the notion of “two ideas” involves the great blunder which I explained in Lecture IV. It suggests that the parts of Judgment are separate and successive psychical states, and that the Judgment consists in a change from the one to the other. Herbert Spencer, as I understand him, considers every relation to be apprehended as a mental change or passage from one idea to another. This view would degrade logical connection into mere psychical transition. I do not say that there is no psychical transition in Judgment. I do say that psychical transition is not enough to make a Judgment. The parts of Judgment, as we saw in the last lecture, do not succeed one another separately like the parts of a sentence. The relation between Subject and Predicate is not a relation between mental states, but is itself the content of a single though continuous mental state. Mill has rightly touched on this point. “When I say that fire causes heat, do I mean that my idea of fire causes my idea of heat?” [1] and so on. The fact is that “Fire-causing-heat” is itself the single content or meaning represented in my symbolic idea; it is not a succession of psychical states in my mind, or a passage from the idea of fire to the idea of causing heat.
[1]Logic, Bk. I. ch. V. § I.
{103}Absence of assertion
(ii.) But further, understanding now that the Judgment is composed of a single ideal content, and is not a transition from one mental state to another, there is still a difficulty in the conception that its component elements are nothing but ideas. If the Subject in Judgment is no more than an ideal content, how, by what means, does the Judgment claim to be true of Reality? “The Subject cannot belong to the content or fall within it, for in that case it would be the idea attributed to itself.” [1] If the Subject were only a part of an ideal content it would not claim to be true of Reality, and where itappearsto be only an ideal content there is much dispute in what sense the Judgment does claim to be true of Reality. “Violations of a law of nature are impossible.” “The three angles of a triangle are equal to two right angles.” “All trespassers will be prosecuted.” In these Judgments we should find it hard to make out that the Subjects are real things corresponding to our ideas. And yet, if they are not, how can the Judgment attach itself to Reality? This is the difficult question of the distinction between the categorical and the hypothetical Judgment, and we shall have to return to it. In the meantime, we must adhere to our judgment of perception as the true underlying type. The Subject is here not an idea, but is the given reality,thisorthat, and the Judgment is not a conjunction of two ideas, but is present reality qualified by an idea. We say, “It is very hot,” meaning that heat, the general quality embodied for us in an ideal content, is true of—forms one tissue with—the surroundings which here and now press upon our attention. Or again, “This is red,” {104}i.e.the content of the idea red is what my attention selects and emphasises within the mass of detail presented to it in its own unique focus which the pronoun “this” simply points out as though with the finger. We shall find such a structure underlying all the more artificial forms of Judgment.
[1]Bradley’s Principles of Logic, p. 14.
Two Things
(b) Thus it would seem that Jevons and Mill are much nearer the real point when they say that the proposition has to do with two Things, or with a Thing and a group of Things. But we must notice in passing that Mill, [1] after fighting hard against calling them Ideas, takes our breath away by saying that they are states of consciousness. There is, of course, a difficulty, which I will not try to deal with now, in the fact that however much wereferto things, we have nothing towork with intellectuallybut our ideas of them, and in some types of Judgment the reference to real things is difficult to trace. Mill further emphasises this by showing, that what we assert in ordinarygeneralJudgment is co-existence of attributes. [2] “Now when we say, Man is mortal, we mean that wherever these various mental and physical phenomena (the attributes of man) are all found, then we have assurance that the other physical and mental phenomenon called death, will not fail to take place.” That is, no doubt, a very indirect way of referring to the real things which we call men. Moreover, he treats all conclusions in geometry and mechanics as hypothetical. [3] All this we shall have to return to, in order to reconcile it with our doctrine; which is apparently coincident with {105} Mill’s view in the place first alluded to, that the subject in Judgment is always reality.
[1]Logic, Bk. I. ch. V. § 5. [2]Ibid., § 4.
[3]Ibid., Bk. II. ch. vi. §§ 3, 4.
But our point at present is only the duality ascribed to the Judgment by saying that it essentially deals withtwothings or groups of things. Jevons even says [1] that every Judgment is a comparison of two things—though these “things” are really, it would seem, groups of things. [2] We thus have it impressed upon our minds that there is one “thing” corresponding to the Subject-word (or clause) of the Propositional sentence, and another “thing” corresponding to the Predicate-word (or clause), and that these are somehow separate, like two railway carriages, till we bring them together by the coupling-link of the copula. This is a very inconvenient way of looking at the matter. It is not true that all Judgment is comparison, in the proper and usual sense of the word. It is not true that Judgment involves two things; two or more things may be mentioned in a Judgment, but they cannot correspond respectively to the Subject and Predicate. It is a real Comparison if you say, “A.B. is taller than C.D.,” but C.D. is here not a term in the Judgment. The one person, A.B., is qualified by the ideal content “taller than C.D.,” and the idea of A.B. so qualified is referred to, or discriminated within, perceptive reality. Comparison is a rather complex process, and consists in a cross-reference by which each of two objects is judged according to a standard furnished by the other; but this complex process is not necessary to all Judgment, and cannot be expressed with complete convenience in a single Judgment. And in {106} any case the two objects that enter into the comparison do not correspond to two essential parts of Judgment.
[1]Elementary Lessons in Logic, p. 61. [2]Ibid. p. 62.
It is far more simple and true to say that Judgment is always the analysisandsynthesis of elements in some one thing or ideal content. “Gold is yellow” has not within it, as Jevons says it has, [1] any direct comparison of gold with other yellow substances. It simply drags to light the property “yellow” as distinct within the complex of attributes belonging to gold, while at the same time insisting that this property—this meaning of an idea—belongs to, is of one piece with, perceived reality in so far as gold is given in such reality. The Judgment exhibits the content in its parts. It breaks it up, and pronounces it to be all of one tissue, by one and the same indivisible act. We should practically have a much fairer chance of seeing clearly what Judgment is if we began by considering it as not two things or two terms — but as one thing or one term drawn out into elements by discriminating selection. Even if the paradox that every “Thing” is a Judgment neglects some necessary distinctions, I am convinced that we shall understand Judgment much more clearly if we do our best to approach it from this point of view. Whenever we look or listen, andnoticefeatures and qualities in the perceptions that arrest the eye and ear, we are rapidly and continuously judging. “The fire is crackling,” “The daylight is waning,” “That bookshelf is not full,” “The window-curtain is twisted.” In none of these cases is there any separation other than an intellectual distinction between the predicated content and the perceived reality. The Judgment is simply a distinct {107} insistence on a quality within a certain focus of reality as belonging to that reality. This is the fundamental nature of Judgment.
[1]Loc. cit.
Therefore, to draw our conclusion as to the Unity of the Judgment, it is not a transition from one mental state to another; the relation of which it consists is not between ideas in it, but is the content of the idea which forms it. Judgment is not primarily comparison between two things; it is a thing or content displayed as possessing some definite relation or quality within its identity. Every Judgment is the content of one idea, but you may of course distinguish relations between ideal elements within this idea. “Fire causes heat” is a single content or idea, the nature of fire, expanded into one of its properties.
Distinction between Subject and Predicate
5. But then, if the whole Judgment is a single content, what is the difference between Subject and Predicate, and is it necessary to distinguish Subject from Predicate at all? IfsomeJudgments can be made without explicit Subjects, cannotallbe made in that way?
This suggestion is very useful as carrying on the simplest type of Judgment throughout the whole theory of Judgment. By a little torture of expression any Judgment can be thrown into a form in which undefined Reality is the general subject, and the whole mass of the Judgment is the Predicate. “William Pitt was a great statesman” = “There was a great statesman named William Pitt”; “The three angles of every triangle are equal to two right angles” = “There are figures known as triangles with their three angles equal to two right angles”; “All citizens are members of a moral order” = “There is a moral order, including the {108} relations of citizenship”; “All trespassers will be prosecuted” = “Here are conditions which ensure the prosecution of possible trespassers.” Or you might always put a subject, “Reality is such that”—“Reality is characterised by.”
Thus we see that, as we have said before, in every Judgment the ultimate subject is Reality, the world in contact with us as we have already qualified it by previous Judgment. It is a less mistake to reject the Subject and Predicate in the Judgment altogether, than to think that they are separate things or ideas, and that in judging you pass or change from one to the other. Always bear in mind that it is possible to mass the whole Judgment as a single Predicate directly or indirectly true of Reality.
Having said this much, to make the Unity of the Judgment unmistakable, we may now safely distinguish between the Subject and Predicate in the Judgment. And we shall find the safest clue to be that the explicit Subject, when there is one, marks the place at which, or the conditions under which, Reality accepts the Predicate. The natural Subject is concrete, and the Predicate abstract; the Subject real, and the Predicate ideal, but pronounced to be real. The reason of this is that every Judgment is the connection of parts in a whole, and to be a whole is the characteristic of reality. In other words, the natural course of thought is to define further what is already in great part defined, and our real world is that which we have so far defined. The isolated judgments of the text-books make it very hard to grasp this, because you seem to begin anywhere for no connected reason at all. But if we reflect on actual thought, {109} we find that, as Mr. Stout very cleverly says, we are always developing a “subject” which is in our minds (in the ordinary sense of a “subject of conversation”), and this subject is some region or province of the world of reality.
Now the explicit Subject in Judgment or the grammatical Subject in Proposition does not always set out the full nature of this, but merely some mark or point in it which we wish to insist upon. So that we may find in Judgment almost anything serving as explicit Subject. Thus, as Aristotle said quite plainly and sensibly, it is natural to say “The horse is white,” but wemayhave occasion to say “This white is a horse”; it depends on the way in which the Subject comes into our minds. [1] Usually the Subject will be what Dr. Venn calls the heavier term,i.e.the term with more connotation. When there is no difference of concreteness between parts and whole, the Judgment becomes reversible as in the equation 7 + 5 = 12. There is no distinction here between Subject and Predicate. The real underlying unity or Subject is the numerical system.
[1] See Prof. Bain, p. 56, upon the Universe, and Universe of Discourse,i.e.the general subject which you have in your mind.
Therefore by recognising Subject and Predicate we represent the organisation of knowledge, and the connection of inherence or consequence within the content of our knowledge. If we do not recognise this distinction we throw the whole of Judgment into an undifferentiated mass of fact, running all assertion into the same mould, “It is the case that,” etc. One difficulty still remains. If the relation between Subject and Predicate is within an idea, and not between ideas—that is, if the whole explicit content, Subject and {110} Predicate together, can be regarded as predicated of reality,—why is the act of predication expressed by a verb,i.e.a sign of activity within this content? Why is a verb often if not always the form of predication which connotes Subject and Predicate? Not because it is a time-word. On the contrary, we want to get rid of the tense in Logic. The time of a Judgment ought to be determined only by the special connection between Subject and Predicate, not by tense, because tense is always subjective, merely relative to the time of speaking, and is accidental to the content of Judgment. Action seems nearer to what we want; theverbexpresses both action and predicate. But theideaof action again does not make a predication, and the verb “is” does notreally indicateaction. Perhaps it is the demonstrative element in a finite verb that makes it the vehicle of predication,i.e.in a finite verb you have a meaning referred by a demonstrative element to something else. Originally the meaning was always an action; “is” of course meant “breathes.” But now the verb has lost vitality by wear and tear, and only refers something to something else. The puzzle is that the Judgment is not referred to us who make it, but is expressed as if it was accomplished by something outside us. That puzzle points to the essential feature which we insisted on, viz. its objectivity; in predication we refer what is mentally our act to a subject that represents the real world, not to ourselves at all. When I say “Gladstone comes to London this week,” the verb which expresses Gladstone’s action also expresses that my real world in his person accepts the qualification “coming to London this week.” Because of this objectivity of thought, I attribute to {111} the real world and not to myself the connection which is presented to my mind, and so it takes its place as an act of the real world. But I might throw the whole content into the Predicate by saying, “The ideal content ‘Gladstone coming to London this week’ is a predication true of Reality.” Thus though the distinction between Subject and Predicate best exhibits the living structure of knowledge, we must beware of the notion that two ideas or two things are needed for Judgment.
{112}
Some criticism on the ordinary scheme[1]
1. We will first consider why we want to examine the types of Judgment, and then what arrangement of them best fulfils our want.
[1] Read Mill, ch. iv. (Bk. I.), on Propositions; Venn,Empirical Logic, ch. ix., x. Cf.Knowledge and Realitypp. 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 followmereeveryday 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 DisjunctiveJudgments. Judgments, Judgments.includingSingularJudgments.
The defects of this scheme from our point of view are—
(i.) Our Impersonal and Demonstrative Judgments are omitted. Theymightbe 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 [1] papers have been looked over” should be distinguished from “All triangles have their three angles equal to two right angles.”
[1] “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 [1] is said to consist of two categorical propositions, or to be “complex” But of course it is a simple judgment,prima facieexpressing a relation of reason and consequent. Its parts are not Judgments, for they are not such as to stand alone.
[1] 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. [1] 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.
[1] 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.” [1] This does notmeana certain number of engines, though of course theyarea 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.
[1] 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 itcanassert this, its Subject being a name for an existence that has limited reality within the temporal series, andcannotassert anything else, not having any general fixed content or connotation which could imply ageneralconnection 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 afact. When we come to the ordinary universal affirmative, we see at once that it may express very different meanings. In its natural meaning it stronglyimpliesthat 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 takenmorein Denotation (not solely, which is unmeaning), and the Predicatemorein 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 [1] {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. [2] If indeed we take the Universal Affirmative in the pure sense of aggregate formed by enumeration, and therefore finite, itmaybe 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 theCollective JudgmentorJudgment 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.” Thismightbe Categorical, but need not be so.
[1]Lectures, vol, iii. p. 327.
[2] 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. [1] 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.
[1]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 boilsunder 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 withdoubt. In Dr. Venn’sEmpirical Logicthe 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 ofall 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 afact? No, I should say not, although common usage varies. I remember aPall Mallleading 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 whichifMr. Gladstone, etc., etc.” Are mathematical truths facts, and in what sense? Abstract truth need not, and perhaps cannot express fact, but implies fact indirectly.