The natural and the true interpretation of " Dogs are mammals " is that dog and mammal are different attributes, and that these differences co-exist within the same things; or again, that, though the things are certainly the same, for all that they possess two different attributes, dog and mammal. But this natural interpretation involves the abandonment of the theory of inclusion within the predicate.
§ 20. And if you understand extension in a different sense, the result is the same. The class of mammal may be taken to contain, not only the collection of individuals which are mammals, but also the kinds of thing which are mammal. " Dog is one kind, and the judgment includes it among all the other kinds." It is doubtful what this means, but, whatever it means, the extension is not affirmed as a predicate. If I have in my mind a known or unknown aggregate of kinds, and say that dog is in the midst of this aggregate, then I assert of dog a spatial relation to a set of elements or the area they occupy. But this relation is surely an attribute. If again I mean that dog is an unit which, taken in addition with other units, amounts to the sum which I call " mammal," then I assert a relation to the other units, and a further CHAP. VI THE QUANTITY OF JUDGMENTS 179 attribute that results from this relation. If I mean that dog possesses mammal, and that other kinds, known or unknown, do so, or that dog is like these other kinds in possessing mammal, then again I assert an attribute of dog, the having an attribute, and the identity in this respect with some other kinds.
These interpretations are all forced and unnatural. They none of them are really what I have in my mind when I say " Dogs are mammals." Inclusion is not what I mean to assert. But, if I assert it, then my predicate is an attribute. The whole or part of the extension of mammals is not the real predicate. The predicate is that which I either affirm or deny of the subject, and a thing is not the same as a relation between itself and something else.
§ 21. If you say, " The dogs, with other things, make up a certain amount we know as mammals," then this contribution to a certain number is an undeniable attribute. If you say, " The dogs share a quality mammal with a heap of other things," this again is an attribute. If you suppose dogs and mammals to be two different lots in two adjoining folds, and if you pull up the mental hurdles which separate them, then you can not say, " The dogs are in the mammals," unless you are prepared to embrace a marsupial or some other such hypothesis. They are related locally to the other mammals or to the area or fence within which all mammals are circum scribed. And this local relation is an attributive predicate.
The mythology you invoke is not strong enough to save you, and, if you throw yourself into the arms of Nominalism, then you have not only an account of the fact which is absurdly insufficient, but the difference of names is still an attribute.
And if, in the end, to escape from your difficulties, you say "The class is no real collection in my head or out of it. It is a name that stands for the possible objects that have a certain attribute," then the answer is simple. If the class is no longer an aggregate or collection, it has become little else than a mere description. " Dogs are included in a possible group of things which are mammals," " Dogs are of the description mammal," " Dogs possess the attribute mammal " — what is the difference between these three assertions? I ask you, is ISO THE PRINCIPLES OF LOGIC BOOK I there any, and if so, what? To include real dogs among mere possibilities can hardly be the end you have in view.11 You must mean, " The dogs possess this attribute, and by virtue of this attribute are related to other possible mammals." The last part of the sentence calls for interpretation. " Dogs," we must read it, "are not only mammals but, supposing anything else to be mammal, then we may argue a relation between this thing and dogs." What relation? Surely not juxtaposition; that is too preposterous. The relation meant must surely rest on nothing whatever but the joint possession of the attribute. The inclusion in the class of possible mammals means nothing but the having the attribute mammal, and in addition, a hypothetical relation of identity with anything else of the same description. We predicate two things, in the first place a quality, and then a relation to possible objects supposed to have the same quality. Both of these predicates are attributes, and the last is an addition which may be superfluous. It is a mistake to think that the phrase " possible " will help us anywhere into anything but bad metaphysics. And the fa vourite prey of this delusion is the men who think themselves above metaphysics.
We may briefly sum up this matter thus. The only way to read the whole judgment in extension 12 is to take it as asserting a relation of identity between different individuals. Two individuals are one though their attributes differ.13 This is simply the other side of the judgment that different attributes are interrelated within the same individual. To take the sub ject as included in the predicate is in the first place to sub stitute fiction for fact, and in the next place is to predicate an attribute and is not to read the whole judgment in ex tension. But if the subject alone be taken in its extension, then what is asserted is obviously a connection of attributes within an individual or individuals.
§ 22. 14 Every judgment can be read in extension. Al though some present two or more subjects in relation, yet all can be reduced to the affirmation of a connection of content within one subject. In " A is to the right of B," the whole presentation is the subject, and the spatial relation of A to B is an attribute of that. In " Caesar is sick," the same person is CHAP. VI THE QUANTITY OF JUDGMENTS l8l said to be sick as well as Caesar. And in " Dogs are mam mals," there are certain things which are declared to be both. In this sense of extension every proposition can be read ex- tensionally.
We have now to ask if every judgment can be taken in intension. Can not only the predicate, but also the subject be reduced to mere content? Do they all assert a connection of attributes? And this question at first sight may be answered in the negative. In " Caesar is sick," we certainly have a junction of adjectives, but it will be said, " We have some thing else beside. There is the individual of whom these qualities are predicated; and. this individual is finite and deter mined. Admitted that in every intensional judgment you have a reference to the ultimate reality, and that this reality is individual, yet the ultimate subject does not affect the judg ment.15 It is given undetermined except so far as it is deter mined by the judgment: and hence it does not interfere with the connection of the adjectives. But when you have a finite subject, then that subject interferes. In ' Caesar is sick,' the judgment is not true unless you make it of this one Caesar. You can not get rid of the individual person, and, while he remains, he prevents your reading the judgment in intension."
§ 23. We have already cut the ground from under this objection by proving that every such judgment is hypothetical and strictly universal (Chap. II.). If the subject is taken as an existing individual or set of individuals, then no doubt the judgment is categorical, and can not possibly be read inten- sionally. " All these six sheep have got the rot," " William invaded England," " I have a headache ": if " these sheep," or " William," or " I," are taken as sensible individuals in the series of time, then that character enters into the assertion, and we can not reduce it to a hypothetical synthesis of ad jectives. But then our analysis in Chapter II. has shown us that the reduction is demanded. When we press for the final truth of the judgment, the particular subject becomes an unspecified condition of the content. The Assertion is thus hypothetical. It conjoins mere adjectives, though what it conjoins is vague and undetermined. The true subject of the judgment is, not this or that finite person or thing, but the ultimate reality. All the qualities of the ostensible subl82 THE PRINCIPLES OF LOGIC BOOK I ject pass into the condition of a universal connection of attributes. It would be idle to repeat the painful enquiries which have established this result. It stands or falls with our second chapter, and while it stands it carries the conclusion that every judgment can be read in intension.
§ 24. Thus, when the ostensible subject is a particular phenomenon 16 or collection of phenomena, no ordinary means will reduce the judgment. To take it in intension we must apply the drastic treatment we discussed in Chapter II. But in other instances the remedy is more obvious, and is easier to administer. " Some trespassers must be prosecuted," " Some English citizens are to be hung," " In some impossible cases right would be wrong." These assertions would, I pre sume, be called particular, but none of them need refer to this or that phenomenon. The " some " may mean " under some condition." It may describe the attribute, not point to the individuals.
There are cases where " some " most clearly does not indicate this or that particular or set of particulars. " Some crimes are deserving of capital punishment," " In some dis eases the patient should be secluded ": we mean here that, given a crime or disease of a certain sort which we do not specify, then something else would in that case follow. The judgment couples mere attributes with attributes. It does not assert the existence of this or that crime or disease. It is hypothetical, and is naturally read at once in intension.17 § 25. " Some " again may mean an unknown number. " Some English citizens will be hung next year," may mean, not one sort, but one unspecified quantity of English citizens will suffer this fate. A particular event is here asserted, and the proposition must in the end be reduced by the method laid down in Chapter II. But the event it foretells has al ready in part been stripped of particularity. The forming a number, or contributing to an amount, is an universal at tribute: it is a general adjective, and to this extent the subject has been already purified. When read in intension the judg ment runs thus, " Given certain conditions, part unspecified, part specified as the attribute of English citizen and the at tribute of amounting to a certain number, then" etc.
It is an elementary mistake to suppose that number18 CHAP. VI THE QUANTITY OF JUDGMENTS 183 confers particularity and destroys intension. And the error reveals a deep foundation of bad metaphysics. Number is surely nothing but an attribute. And how can the addition of an universal quality force us to take a judgment merely in extension? How can it even help towards such a result? You may say, perhaps, that nothing is numbered save actual phenomena, but such an assertion would be incompatible with fact. " In the single case of two men being three men, four men would be six men" — this is, I presume, an hypothetical judgment. Not only can you take it as connecting attributes, but I do not see how you can take it otherwise.19 It is idle to object that the subject is really the imagined example, where two is three, and that this example is a particular event. For it is nothing of the sort. It is a supposed condition which, if it existed, would really be single, but does not exist and will never be anything real at all.
§ 26. The idea that a numerical subject is particular van ishes as soon as we confront it with facts. The numerical character is nothing but a character. It is nothing but an adjective, and no adjective or accumulation of adjectives will make anything else than an abstract universal. Suppose that a phenomenon is capable of division in fact or in idea. Its divisibility is a general quality, which other phenomena might also possess, and which would not difference one from the other. To be regarded as a collection of units summed by means of addition to a certain quantity, is an attribute not special to any single phenomenon: it can in no sense bestow uniqueness. And again, if the subject is taken as a quan tity which stands in a certain fractional relation to another quantity, it is absurd to think that, on the strength of these mere qualities, you leave universals and get to existence.20 " If a penny is thrown one thousand times, half the number of throws will most probably give head ": we have here a purely intensional judgment. There is nothing contained in it but bare universals: there is nothing but hypothetical junctions of adjectives. Of course, if you say, " This penny in half its throws will now give heads," the case is altered: but the num bers have not changed it. The subject is particular, not be cause it is numerical, but because it is not so, because over and above it has now been taken as a particular fact. It must 184 THE PRINCIPLES OF LOGIC BOOK I be reduced by the method laid down in Chapter II. But so far as it is numerical it is already reduced, and is already nothing whatever but attributes.
§ 27. We may pass on to consider another superstition. If the intension signifies the meaning of a word, and the ex tension is the number of actual objects of which the meaning can be truly predicated, then both extension and intension are relative to our knowledge, and naturally fluctuate with altering experience. For instance, " mammal " is a term whose meaning has changed and will change. We can fix no limit to the possible information the word may convey, for we do not know how many attributes in the end may be found to be implied in the quality of giving suck. And the number of objects we denominate " mammal " is of course not stationary. Such considerations may seem too obvious to be ignored, but their neglect has given rise to a serious mistake.
In certain judgments, where the predicate is not of the " essence " of the subject, we are warned that an intensional reading is impossible. " All American citizens know the name of their President," is, we are told, to be taken in extension (Venn, Symbolic Logic, p. 395 ).21 It can not connect one set of attributes with another set of attributes, because the con nection it asserts is accidental. But the mistake here is obvious. If I know every single American citizen, so as on this knowledge to make my assertion, I surely must know by the selfsame process that the attribute I assert exists in each. After I have noticed each single citizen, it is one of his at tributes and part of his meaning to know the name of his President, and, before I have done so, I can say nothing at all. If the extension is increased, so also is the meaning. And the objection that, if the mark were part of the intension of " American," we should assert it of American citizens in the future as well as at present, may at once be dismissed. If the subject stands also for " all Americans in the future," then the attribute becomes at once part of their meaning. But, if the subject is confined to the present time, then the mark is the meaning of "present Americans," and you have no right to apply it beyond.
The judgment is particular, not in the least because it is " accidental," but because American citizens are facts in time.
CHAP. VI THE QUANTITY OF JUDGMENTS 185 It would be just as particular if I changed it into " American citizens are Americans." And of course if the citizens meant by the subject are neither real men, nor real images, but mere possibilities, the judgment is hypothetical at once, and we need not have recourse to Chapter II. to effect its reduction.
§ 28. This same mistake lay at the foundation of the doc trine (§4) that proper names have no " connotation." 22 The meaning is not fixed, and this leads to the idea that no mean ing exists. The simple enquiry "Is the denotation fixed?" leads at once to the result that, here as everywhere, intension and extension fluctuate together.
Both are relative to our knowledge. And the perception of this truth is fatal to a well-known Kantian distinction. A judgment is not fixed as " synthetic " or " analytic ": its character varies with the knowledge possessed by various persons, and at different times. If the meaning of a word were confined to that attribute or group of attributes with which it set out, we could distinguish those judgments which assert within the whole one part of its contents from those which add an element from outside (p. 142); and the distinc tion thus made would remain valid for ever. But in actual prac tice the meaning itself is enlarged by synthesis. What is added to-day is implied to-morrow. We may even say that a synthetic judgment, so soon as it is made, is at once analytic. Kant has really no need of this unfortunate division, which he seems to have inherited. The real question which he means to ask is, What kind of synthesis does each judgment contain, and what in each synthesis is the principle of unity?23' § 29. To sum up the result 24 — a proposition is read in- tensionally, when both subject and predicate are taken as attributes hypothetically related. Whenever the ostensible subject is no individual or collection of individuals the judgment is naturally understood in intension. Where the subject is one or more actual phenomena, the judgment can not be interpreted naturally as a hypothetical connection of attributes. But although not natural, this interpretation is legitimate, and is also necessary. When we leave first appear ances and ask for truth, we find that any phenomenal judg ment, whose subject refuses to be taken as content, is a judgment which is false (Chapter II.).
l86 THE PRINCIPLES OF LOGIC BOOK I The error we must avoid is the idea that a class is a mere aggregate of individuals.25 Such aggregates in my head or outside my head are barren mythology: they do not really exist. And if we mean by a class a possible aggregate of possible * individuals, we have no longer any collection. For possibilities occupy no place in the series of events connected with perception. They are not actual individuals, but merely ideal. A possible horse is anything which might conceivably possess the qualities, first of general uniqueness, and then of equine nature (Chap. VII.). Thus if the class means the attribute with reference to a hypothetical collection, to in clude in the class is to predicate an adjective. It is to assert an attribute, and through that attribute to assert a relation of identity and difference with any other instance.
§ 30. We have by this time had perhaps more than enough of the quantity of judgments, and yet there is a question we have not fully cleared up. The distinctions " universal," " particular," and " singular," fall under quantity, and it may be well that we should more definitely state here the meaning in which we take these terms. The common logic, we shall all remember, ranks singular and universal judgments to gether, and opposes the particular to both of these. A par ticular judgment is a judgment which fails to take the subject explicitly and avowedly in the whole of its extension; and other judgments are considered universal because in them you have all of the subject. This arrangement we shall not pro ceed to discuss. It is sufficient for the technical use of the syllogism, and it is perhaps in itself not so foolish as it seems to be. We need not however pause to examine it. We may be satisfied if we succeed in making clear our own interpretation.
§ 31. The subject is not only beset with ambiguities, but it tends at each moment to cross the border and to enter the field of metaphysics. I am afraid it is impossible for me here to defend the interpretation which I have adopted. I must content myself with trying to exhibit clearly the doctrine which seems metaphysically true, and which agrees with the logical results we have arrived at.
*I suppose we do not always mean "judged possible." Cf. p. 4 note.
CHAP. VI THE QUANTITY OF JUDGMENTS 187 We may realize some difficulties which obscure the sub ject, if we state them in the form of thesis and antithesis. (i) Nothing that is real is universal, (ii) All that is real is universal, (iii) Nothing that is real is particular, (iv) Most that is real is particular. I believe in the truth of all these propositions, and will endeavour to show that they are not in conflict. But first it is better to advocate each.
§ 32. (i) Nothing that is real is universal. Indeed, how should it be? What is real is substantial and exists by itself: it is individual. But the universal is nothing whatever but an adjective. It is an epithet divorced, a shadow which apart from its body is nothing, and can not exist.
(ii) Everything that is real is universal. How can it be otherwise? For what exists must be individual, and the indi vidual is no atom. It has an internal diversity of content. It has a change of appearance in time, and this change brings with it a plurality of attributes. But amid its manyness it still remains one. It is the identity of differences, and there fore universal.
(iii) And so we see that No real is particular. For if particular, then not individual, and if not individual, then non-existent. The particular is atomic. It excludes all dif ference. It is itself and nothing beyond itself. And that self is simple: it is so far as it is nothing else. The true particular in respect of quality is shut up in one quality; relations it can not be said to have; in respect of time it has no con tinuance, and in space it can not occupy extension. Its exist ence in space is nothing but a point, in other words, is nothing spatial. Such a particular is of course not to be verified in experience. It is a metaphysical ens rationis, an abstract universal26 which can not be real.
(iv) And it can not be real because, if not all, at least Most reality must be particular.27 For in existence the indi viduals which are real are finite. To some extent at least they are defined by their limits. It is because they repel other things that they are what they are. Exclusion by others, and exclusion of others, enters into their substance; and where this is there is particularity.
§ 33. It is obvious here that in thesis and antithesis words have been used with different meanings. And this result we l88 THE PRINCIPLES OF LOGIC BOOK I desired to establish. The abstract universal and the abstract particular are what does not exist. The concrete particular and the concrete universal both have reality, and they are different names for the individual.
What is real is the individual; and this individual, though one and the same, has internal differences. You may hence regard it in two opposite ways. So far as it is one against other individuals, it is particular. So far as it is the same throughout its diversity, it is universal. They are two dis tinctions we make within it. It has two characters, or aspects, or sides, or moments. And you consider it from whichever side you please, or from the side which happens for the pur pose of the context to be the emphatic or essential side. Thus a man is particular by virtue of his limiting and exclusive rela tions to other phenomena. He is universal because he is one throughout all his different attributes. You may call him particular, or again universal, because, being individual, he actually is both, and you wish to emphasize one aspect or side of his individuality. The individual is both a concrete particular and a concrete universal; and, as names of the whole from different points of view, these both are names of real existence.
§ 34. The abstract universal and abstract particular are both unreal, because neither are names for the individual. They take the two aspects or characters of the whole, and, turning them into independent existences, then assert their reality. But one side of a whole can not stand by itself except in our heads. It is nothing but an adjective, an internal distinction which we try to take as substantial fact. We can all see that this holds good of abstract universals. The oneness or identity of a man, we know, is not found when we search the series of mental phenomena. But the same is true of the abstract particular. If you take atoms seriously, and deny their extension, you find at once you are dealing with something which can not be fact. Mere exclusion in space of other spaces is nothing real. A reality in space must have spatial diversity, internal to itself, and which it does not ex clude. And this holds again with psychical atoms. For, as observed, they have internal multiplicity, duration in time, quality, and degree; and as anything else they could not be CHAP. VI THE QUANTITY OF JUDGMENTS 189 observed. An atom which really was particular, which was not divisible at least in idea, could not possibly be fact. It is one aspect of fact torn away from the rest, and is nothing in itself and apart from the act which tears it away.
§ 35. The abstract particular and the abstract universal are mental creations, which, if taken as fact outside our heads, are different examples of the same mistake. Both are dis tinctions within a whole, hardened into units that stand by themselves. And not only do they spring from the same mistake, but we may even say that they are the same error. The abstract triangle in and by itself is found to exclude all further predicates (cf. p. 119). Determined by that division and consequent exclusion which gave it its origin, it has be come particular. And the particular itself, because produced by mental separation, is really no more than an adjective divorced, or abstract universal. The dialectical method has laboured to show that, here as everywhere, insistence upon a onesided view brings out by negation the opposite onesided- ness. The universal, the more we emphasize its character, divides itself the more from the whole. We make its being depend on exclusion, and it turns in our hand into its logical contrary. The particular again, excluding others, and being so far as it merely excludes, is its own negative relation to other particulars. It falls beyond itself into a series of units pervaded by an universal identity, and itself has there become