its own opposite. In this speculative movement, if we take it in the character it claims for itself,28 I neither myself profess belief nor ask it from the reader. But I think we may go so far as this, that in the end the individual is real, and that ab stract universal and abstract particular are distinctions taken within that reality, which a mistake has afterwards turned into divisions and hardened into units. If we do not admit that each is a moment which, by negation of itself, affirms the other and begets the whole, we may certainly say that each has sprung from the same mistake, and is an illusion of the self-same kind. And we may muster courage, perhaps, to profess that the individual is the identity of universal and particular.
§ 36. We must keep in view the following distinctions. We have first the abstract universal and particular, and IQO THE PRINCIPLES OF LOGIC BOOK I neither of these can exist in nature.29 On the other side we have the individual, and the individual is the only thing which is real. But where this real is finite it may be taken from two points of view: it is concrete particular or concrete universal. In so far as it is a finite individual which excludes all others, so far it is a relative particular. But because it includes a diversity of content, it is therefore also a relative universal.
There is here, I confess, a doubtful point I am forced to .leave doubtful. It might be urged that, if you press the enquiry, you will be left alone with but a single individual. An individual which is finite or relative turns out in the end to be no individual; individual and infinite are inseparable characters. Or again, it might be said, the individual is finite, and there can not be an absolute individual. Meta physics, it is clear, would have to take up these questions, and in any case to revise the account which is given in this chapter. But that revision must be left to metaphysics; and for the pur poses of logic we may keep the distinctions already laid down. We have (i) the real, supposed to fall into (a) absolute indi vidual or concrete universal, (b) relative individual or con crete universal or concrete particular; and (ii) the unreal, con sisting (a) of the abstract universal, and (b) of the abstract or absolute particular.
§ 37- We may now attempt to lay down what we mean by universal judgments. Such a judgment is one whose subject is universal. And it is obvious that here we have more than one meaning. An universal judgment may be (i) absolute, or (ii) relative.
(i) In the first case we have again two divisions. Such a judgment may (a) be abstract, or again (b) may be concrete. If (a) the judgment is abstract, the ostensible subject will of course be an attribute. The statement will truly be hypo thetical,30 since the actual subject is non-phenomenal reality. The ordinary kind of universal judgment such as " The angles of a triangle are equal to two right angles " is, as we have seen (Chap. II.), of this description. And it is universal for two reasons. The grammatical subject is an abstract universal: while the actual subject, the ultimate reality, is a concrete uni versal and is also absolute. This is the first and more ordi nary kind of judgment which we are able to call absolutely CHAP. VI THE QUANTITY OF JUDGMENTS IQI universal. But (b) it is necessary to mention another sort. Any statement made concerning a reality which is not con sidered finite will also be an absolute universal judgment. Nothing will fall outside the subject, and the predication will be categorical. I do not say that such judgments are prac ticable; but they are logically possible,31 and must be provided for.
§ 38. (ii) A judgment is relatively universal where the subject is a finite individual or collection of individuals. It is universal, because the subject is the identity of its own internal diversity. In " Caesar is sick," Caesar is not affirmed to be nothing but sick: he is a common bond of many attributes, and is therefore universal. But this judgment is relative, because Caesar is one man among other men; and, if you take him so, he himself is particular.
§ 39. 32 A judgment which is absolutely particular can not exist. It would have a subject completely shut up and con fined in the predicate. And such a judgment, if it came into being, would not be a judgment. For it obviously would say nothing else of the subject or predicate than themselves. " This is this " may be taken as the nearest example.
A relative particular judgment is one where the subject is this or that singular or collection. It is the same as the relative universal judgment, but is taken from another side of its nature. The subject excludes all other individuals, and so is particular; but within itself it has a diversity, and so is universal. It possesses attributes other than the predicate, and may be taken within another context. It thus serves as a middle term in reasoning, as is shown in the third of the syllogistic figures.
§ 40. We have seen before (Chap. II. § 45) that no logical difference separates the singular and collective judgments.33 It is ridiculous to think that if one individual is not universal, you reach universality by adding on others. The number of units is quite irrelevant, since, however many they become, each remains a singular. And this or that collection of indi viduals is as hard a particular as any individual found in the collection. Nay, from this point of view, the single individual himself turns out to be a mere collection. Considered logi cally they are both alike. Excluding others, they are relative IQ2 THE PRINCIPLES OF LOGIC BOOK I particulars. Common to all their internal diversity and iden tical throughout it, they both alike are relative universals.
§41. No judgment has or can have a subject shut up within the limits of one single predicate. If we remain at the popular point of view, and admit those judgments where the subject is nothing but a finite phenomenon or set of phenomena, yet even these judgments are universal relatively. The sub ject will serve as a middle in reasoning. It is hence the iden tity of differences, and it could not be that if it were only particular. Every judgment is thus universal, and in the end they all may be said to be universal absolutely. For, if we exclude the possibility of non-phenomenal finite individuals, we have shown (Chap. II.) that every judgment to be true must predicate of the absolute individual, either hypothetically or categorically. And the former of these cases must, in the end, be reduced to the latter. The finite subject changes in our hands into a heap of mere adjectival conditions, and, since these conditions can never be complete, the statement loses its categorical force. But becoming hypothetical it predicates indirectly a latent quality 3* of the ultimate reality, and so once more is categorical, true categorically of the absolute subject.
§ 42. All judgments are thus alike universal, but it can not be said they are universal equally. If the subject of one judgment is a whole which includes the subject of another, the first is certainly the more universal. And again, if we take two abstract judgments, they are both hypothetical, but the one may assert a more abstract connection than is affirmed in the other. The purer hypothesis, the one most set free from irrelevant conditions, will be also more true. It will predicate in a higher sense of the universal subject, and therefore may be called the more universal. But if the connection, although less concrete, is not more pure, we must then not call one judgment more universal than the other, unless we qualify uni versal by abstract.35 § 43. I will repeat in conclusion the distinctions it is right we should keep in mind. The real is individual. The merely universal or merely particular are unreal abstractions. Con crete universal and concrete particular are the individual from different points of view. But we could not say that an abso- CHAP. VI THE QUANTITY OF JUDGMENTS IQ3 lute individual was really particular, since it would have no relation to anything outside.
Particular judgments, if taken categorically, are precisely the same as relative universal. The phenomenal individual, or collection of individuals, is the identity of diverse relations and qualities. Universal judgments are relative or absolute. If relative, they are the same as particular judgments. If absolute, they are either hypothetical or categorical. In the first the ostensible subject is an abstraction: in the second it must be the ultimate reality. Particular categorical judgments may all be reduced to abstract or hypothetical universals, and these again to categorical universals. In the end all truth, if really true, is true of the ultimate non-phenomenal fact.
ADDITIONAL NOTES 1 " Its content," i.e. in abstraction from its reference.
2 " Ideal or actual." By "actual " I evidently meant here " existing in our " real world." But the " ideal " instance, though not in this sense " real," must be taken as an individual or particular. The ex tension always means the particular object or objects to which the meaning is applicable. We may note that the word " any " implies always, if strictly used, a number of individuals (Cf. Essays, p. 286). The statement, in the footnote to this page, as to "possible horses" is wrong. It forgets that the " imaginary " also is " real " and can be individual. Cf. on Chap. II, §45, note.
3 " The fact is &c." The " fact," however, may be " imaginary."
* "The indiscriminate use— person." This detestable misuse— as well as that of "distinctly" for "clearly" or " undoubtedly "—seems now gone out of fashion.
5 " Unnecessary and objectionable." Dr. Keynes (Formal Logic) has not induced me to alter my opinion. He is, I presume, right in saying that what Mill meant by "connotation" was merely "conven tional meaning"; and I very possibly also in some other point may not have represented Mill's view fairly. But that his innovation was useless and objectionable I remain convinced, and why it should not be quietly buried, Dr. Keynes, I think, has failed to show. For the meaning of Proper Names I refer the reader to Bosanquet's 6 Cf. here Bosanquet, Logic, I, 47.
7 "False or frivolous." Cf. p. 486. The doctrine clearly, except within certain limits, is false. But to call it everywhere worthless is, on the other hand, to fall into error. Subsumption (§9) has its own value. See Bosanquet, Logic I. 55 foil.
194 THE PRINCIPLES OF LOGIC BOOK I 8 " Has ceased to lie in the individuals." But see Note 2.
9 " There are few readers." This perhaps, even in 1883, was an exaggeration.
10 On the subject of §§ 11-29 see further T. E. III.
11 " To include real dogs &c." should be " to include dogs, perhaps real, &c."
12 " The only way...extension." I do not, by " in extension," mean " merely in extension "; for this on my view is not possible.
13 "Two individuals...differ." We should add, "And, where you have only one individual, you can still, by more or less of vio lence, bring it under the above head. For, dividing it by a distinction, you can so make the one individual into two."
14 Sections 22 foil, require correction. No judgment can on my view be read merely in intension (see Note 10). Any passage in the text therefore, which seems to imply that possibility, should be amended. In § 22, par. 2, the words " reduced to mere content " are ambiguous and misleading. Though nothing but " content " enters into a judgment, the question as to the reference and the extension remains (cf. Notes i and 2).
15 How far and in what sense "the ultimate subject" does, and does not, enter into the judgment is discussed elsewhere (see on Chap. I, § 12). It is true that, so far as the judgment depends on Designation, it remains conditional (see Index, s. v. Designation). But to pass from this to the assertion of a mere conjunction of ad jectives is at least misleading. What in the text I really was attacking is the position of any one who takes the content of the judgment as depending on individuals or particulars, known merely by Designation so as to preclude an intensional reading of the judgment. Anything beyond this was to overshoot the mark, if not to fall into error. On Designation see the Index, s. v., and Appear ance and Essays, the Indexes. On "the ultimate subject" see on 16 " A particular phenomenon " should have been " a merely par ticular &c."
17 " Naturally read at once in intension," but not merely inten- sionally, however much the emphasis falls on the intension. The words " It is hypothetical " are again misleading here, as is also the reference to " existence," if that means " existence in my real world."
18 " Number." The mark here is once again overshot. I was really concerned to deny that mere "numerical" sameness and difference is possible, and that particulars, diverse in this sense, and so unique, can enter into a judgment and so exclude an intensional reading.
19 "How you can take it otherwise." (Cf. the "impossible cases" of §24.) These words should be corrected in accordance with what has been laid down in previous Notes. And so again with "nothing of the sort." There is aways an extensional side in judgment, how ever much this side may be wrongly emphasized or misinterpreted.
20 "And get to existence," i.e. in such a sense as to exclude an intensional reading.
CHAP. VI THE QUANTITY OF JUDGMENTS 195 21 It is, I think, unnecessary to ask if I here represent Dr. Venn's contention fairly. If "all American citizens" means "all that now exist," the extensional aspect, I can agree, is naturally emphasized, though the statement becomes, I presume, obviously false. But in any case the intensional aspect of the judgment is there. I would add that the use of " hypothetical " and " hypothetically " (in §§ 27 and 29) would better have been here avoided. Cf. Note 17.
22 " Proper Names." See Note 5.
23 Kant is not a writer whom I can suppose myself to understand, but my criticism seems, at least in part, to be unfair both in the foot note to Chap. I, § 7 and also here. However insufficient his answer, Kant did not, I presume, neglect " the real question " as to the nature of the synthesis within the idea, and as to how far, and by what right, this limited synthesis can be transcended.
On the real importance of the distinction between the essential and the accidental, see Bosanquet, K & R, pp. 59 foil.
24 The statement here is far less correct than that in § 12. After "actual phenomena" add "real or imaginary." And, after "judg ment which is false," add " In any case, even where we refer to one or more particulars and the emphasis is on the extension, the inten sional aspect is still there."
25 On Class see Essays, pp. 283 foil. A class is an aggregate, but is also more. The mere aggregate is that which here and everywhere is mythical.
" Possible individuals." The statement here is, at the least, mis leading. Possible horses, as actually imagined, are real individuals, though, except as psychical events, they do not enter into my "real" world. The footnote here repeats an error for which see Note 2. " Possible horses," again, are not the same as the possibility of horses, which latter is, itself as such, hardly a particular fact, except, once more, in the sense of a psychical event.
"A relation of identity, &c.," should have been "a relation of identity with, and difference from, every &c." For the Collective Judgment see Chap. II, §45.
26 " An abstract universal." Though this statement is correct, it might have been better to have said merely " an abstraction."
2.7 "Most reality." All reality, that is, except the Universe itself. In the next sentence, and again lower down, "existence" is not to be confined merely to " my real world." See Chap. II, Note 3. And (in §33, line 4) to "what does not exist" we should add "as such." For everything conceivable has existence in some sense.
2» " Character it claims for itself," should be, I think, " character so often claimed for it."
29 "Exist in nature" should be "as such be real." And, in the following paragraph, "as such" should again be added to "and (ii) the unreal."
so " Hypothetical." Here (in §37 (0, and again in §41) "con ditional " would be a better term to use, if either term is required.
IQ6 THE PRINCIPLES OF LOGIC BOOK I 31 "Logically possible." But even here the judgment will be sub ject to a condition. See Essays, pp. 228 foil., and T. E. II.
32 1 have in §§ 39-41 assumed that merely external relations are impossible or at least would be useless.
33 " No logical difference." This seems to be unnecessary, and is incorrect (see on Chap. I, §45). And the sentence "Nay...collec tion," though true, seems to be here more or less parenthetical.
35 This § 42 seems wanting in clearness, and I can not recall what exactly was in my mind when I wrote it. It appears to contemplate first (i) the case of two concrete wholes, and to lay down that the one which includes the other, or (we should add) is, generally, the more inclusive, is the more universal. We have next (2) the case of two abstract judgments, one of which is higher than the other (as being more general, and also "purer," in the sense of containing fewer unanalyzed, and perhaps irrelevant, conditions. The former judgment is therefore more universal as really covering and including more ground. Then we have (3) apparently two cases. In one of these (a) the judgment should be more universal in the sense of No. 2, but fails really to be so, because, though in a more general sphere — and, in this sense, more abstract — it contains as much or even more internal irrelevancy than is found in the other. Or (b) we have the case of a judgment which holds in a narrow, and so abstract, region, and therefore does not really cover more or even as much ground as is covered by a less " pure " and more concrete, but in effect wider, judgment.
We should here remember that, if our knowledge were completely systematic, these distinctions, at least in part, would cease to hold. But, as things are, our pure and abstract knowledge is really, though not ostensibly, conditioned by that enormous mass which it fails to explain and comprehend, and so really to include. Hence the knowl edge (say) of a mathematician may in one sense be far narrower and less universal than the knowledge (say) of a biologist. The above remarks may perhaps serve to explain, and, where necessary, to correct the text of §42 in detail. The subject is perhaps too difficult to admit of any brief statement.
CHAPTER VII THE MODALITY OF JUDGMENTS* § i. Modality is not an alluring theme. I should be glad to plead the fragmentary nature of the present work as an excuse for passing it by in silence. But for the sake of clear ness it is necessary to make an excursion into the subject, neglecting those parts of it which do not seem to concern us here.
We must begin by stating an erroneous view. Modality may be supposed to affect the assertion in its formal character, and without regard to that which is asserted. We may take for instance a content S — P, not yet asserted, and may claim for modality the power of affirming this content S — P, un altered and unqualified, in several ways. S — P, it is sup posed, may be asserted, for instance, either simply or prob lematically or apodeiktically, and may yet remain throughout S — P: and thus, though the content is unmodified, the asser tion is modal.
§ 2. This doctrine rests on a misunderstanding. There are no degrees of truth and falsehood.1 If S — P is fact, it can not be more than fact: if it is less than fact, it is nothing at all. The dilemma is simple. S — P is affirmed or it is not affirmed. If it is not affirmed, it is not judged true at all. If it is affirmed, it is declared to be fact, and it can not be more or less of a fact. There clearly can be but one kind of judg ment, the assertorical. Modality affects not the affirmation, but what is affirmed. It is not mere S — P that is asserted modally: it is another content, a modified S — P. In other words, you do not say that the mere idea S — P holds good in fact; you first say something else about S — P, and it is then this new and different idea which really is asserted.
§ 3. Modality in this sense, it has been rightly observed, has no natural limits. There are endless ways of modifying a judgment so as to make a fresh judgment. You may take * Cf. Sigwart, Logik, pp. 189 and following.
198 THE PRINCIPLES OF LOGIC BOOK I the idea of a judgment S — P and express any attitude of your mind towards it. You may say " I make it," or " wish to make it," or " fear to make it," or " can not make it," or " am inclined to make it," or " am forced to make it." All these are simple assertorical statements about my condition of mind. They have a psychological not a logical bearing, and may at once be dismissed.
§ 4. The different ways in which we can stand to a judg ment S — P are a matter for psychology rather than for logic. Logical modality must be limited to that which seems to affect the idea S — P, and to affect it in its relation to the world of reality. If we say, " I wish S — P were a fact," this once more is a psychological mode. The content S — P is not here first modified and then attributed to the ultimate subject. Neither itself nor anything we can call a modification of itself, pretends to be either true or false. The judgment in fact is concerned with nothing but my mental attitude.
Either logic has nothing to do with modality, or modality affects S — P from the side of truth and falsehood. The ideal content must be referred to or else denied of reality. But the reference or denial itself is simple, and can not be modified.2 What therefore must in some way be modified is the content itself. Not S — P but a transformed and conditioned S — P is the assertion made by logical modality.
§ 5. The modes of S — P which logic has to consider are three in number. In each case we assert, we refer some idea to ultimate fact, we begin the judgment by saying, " It is true," — but we go on to fill up the blank in each case by a different idea. It is true that S — P is actual, or is possible, or again is necessary. The idea pronounced true is " actual S — P," or "possible S — P," or "necessary S — P." These modes we retain for consideration, dismissing all others. But our choice is not really so arbitrary as it seems. We have here in a veiled and hidden shape the distinction of categorical and hypothetical assertion. The possible and the necessary are special forms of the hypothetical; and between the assertorical and the categorical there is no difference whatever.3 I shall begin by asking (i) the general meaning which in logic we assign to the predicates possible, necessary, and real. I shall then point out (ii) that the possible and the necessary CHAP. VII THE MODALITY OF JUDGMENTS 199 have no real existence. But on the other hand I shall show (iii) that these modal assertions, though as such and in them selves they are not true of fact, must always rest on a basis of assertion which is true or false of actual reality.
§ 6. (i) We need not ask what we mean by (a) asser- torical judgment. It is judgment categorical or unconditioned. " S — P is real," attributes S — P, directly or indirectly, to the ultimate reality. And on this point we have nothing to add to the explanations already given in Chapter II. The asser- torical judgment may be dismissed from our thoughts. To draw a difference between a categorical judgment on the one hand, and on the other a judgment which asserts reality, is plainly impossible. The assertorical is simply the categorical, taken in contrast with the possible and the necessary.
§ 7. And these are nothing but phases of the hypothetical. What may be and what must be involve a supposition. Neither is declared to be actual fact: they both are inferred on the strength of a condition, and subject to a condition.
(b) It is easy to give the general sense in which we use the term necessity. A thing is necessary if it is taken not simply in and by itself, but by virtue of something else and because of something else. Necessity carries with it the idea of media tion, of dependency, of inadequacy to maintain an isolated position and to stand and act alone and self-supported. A thing is not necessary when it simply is; it is necessary when it is, or is said to be, because of something else.
And where necessity is " internal," this meaning is re tained.4 For it is not the totality which in this case is necessi tated. There is a diversity of elements contained in the whole, and these elements are divided into that which constrains and that which follows. In an unseparated world there could be no necessity.
§ 8. In a work on metaphysics the word " because " 5 would lead us straight to some fundamental difficulties, which will meet us again in our concluding Book. Is there any because outside of our heads? Is it true that one thing is by means of another, and because of another? Or are we forced to admit that every fact, while it is no doubt and is also perhaps together with others, is not an adjective depending on these others, has no real bond that fastens it to its environment, 2OO THE PRINCIPLES OF LOGIC BOOK I nor is subject to any alien influence? The objection would assail us: " ' One fact is and another fact is/ so much is true; but ' One fact is and so another fact is/ must always be false. It is giving reality to mere ideal connections." And, if we escaped this objection, we should find another lying in wait for us. " You may say that one reality is the cause of another, and you may, if you please, add to this that the second is because of the first. But, if you venture to convert this asser tion, and assume that whenever you have a because you have also a cause, you fall into error of the worst description. A cause is real, a because is ideal; you may have the one and do often have it, where the other is impossible. They do not always co-exist; and where they do co-exist, they do not always coincide; and where they coincide, they are not identi cal. They are not the same thing: they are not even two different faces of the same thing. They are nothing but coun terparts, two parallel series which have no common points but possess some terms which have a constant relation " (Book III.).
§ 9. In a work of this kind we can not grapple with the problems offered us. We must here admit the objection and retire before it. We must admit that in logic " because " does not stand for a real connection in actual fact; 6 we must allow that necessity is not a bond between existing things. For logic what is necessary is nothing beyond a logical conse quence. Necessity is here the force which compels us to go to a conclusion, if we start from premises. The " because " expresses an ideal process of mental experiment, which gives as its result a certain judgment. It does not guarantee the truth of this judgment, if you take it by itself. It does not guarantee the truth of the data which the process starts from, and on which it operates. A necessary truth may be, and commonly is, categorical, but, so far as its necessity goes, it is hypothetical. It ceases to be hypothetical only when it ceases to be merely necessary.7 § 10. I admit it is not the same thing to affirm " // M is P then S is P," and " Since M is P therefore S is P." 8 And the difference is obvious. In the latter case the antecedent is a fact, and the consequent is a fact: they are both categorical (Chap. II. §71). In the former case the antecedent may be CHAP. VII THE MODALITY OF JUDGMENTS 2OI false and the consequent impossible. But the necessity in each case is one and the same. S — P must be true, if you take M — P, and take S — M, and draw the conclusion. That is all the necessity it is possible to find. The knowledge that S — M M — P are both true, and that S — P is a statement which holds of fact, falls outside the necessity and does not increase it. The hypothetical result becomes categorical by an implied addition. And the hypothetical connection may not even then become categorical. The bond of necessity is a logical passage, and to say that this logical passage itself exists in fact demands an assumption which can not be hazarded in the face of objections. In logic we must be content to say that, if the premises are categorical, the result is categorical. We can not add that this result is necessary, unless for a moment we treat the data as hypotheses, and mean no more than // S — MM — P are given, then S — P must follow.
§ ii. We are able to urge a two-fold argument to show that necessity is hypothetical. We can reason from principle, and again from usage. The argument from principle 9 we may repeat as follows. Logical necessity is an ideal process, and you can not assume that either ideas or process are facts. Even if the ideas exist in fact, and exist in corresponding sequence, you can not assume that in this sequence your process exists. Your ideal operation works with ideas, and, so far as you know, it works only with ideas. The idea may be more than a mere idea, but it is as an idea that it goes into the experiment. And a mere idea is no more than a mere sup- posal. The result, so far as necessitated, is therefore so far not categorical. This we may call the argument a priori.