*The books from which on this subject I have learnt most are Lotze, Logik; Sigwart, Logik; Wundt, Logik; Jevons, Principles of Science; Venn, Logic of Chance; De Morgan, Probabilities.
236 THE PRINCIPLES OF LOGIC BOOK I § 63. We shall have to return hereafter to this point, but have been right to anticipate here the conclusion. We have indeed begun some time back to anticipate the conclusions we have to reach in the following Books, since already unaware we have entered their territory. Silently before in the second Chapter, and now almost explicitly we have made the transi tion from judgment to inference. In both the latter kinds of modality we reason openly. The possible is that which we argue would follow from certain premises, part of which are taken as true. The necessary is that which we infer must follow, if its grounds are premised. It was in this sense that possibility was one kind of necessity. In both alike we deal with conclusions, reasoned results from given data. In logic we find that a necessary truth is really an inference, and an inference is nothing but a necessary truth. This is the secret which we hardly have kept, and with the discovery of which we may pass at once to our Second Book.
ADDITIONAL NOTES ADDITIONAL NOTES doctrine...falsehood." This statement needs correc tion. It is true that there are no degrees of the fact of logical assertion (cf. Chap. I, § 15 (rf)). It is true that you can not alter the logical mode of asserting S — P without altering S — P itself. On the other hand it is not true that you can abstract the assertion from the asserted content See Bosanquet, Logic, I, 363 foil. On the doctrine of degrees of truth I may refer the reader to my Appearance and Essays.
2 " The reference or the denial itself," i.e. taken in abstraction as a mental fact.
3 " The possible...whatever." This sentence must be corrected. It is better, once more here, to substitute " conditional " for " hypo thetical." Further, both " conditional " and " categorical " should be taken as falling under " necessary." The merely categorical is the lowest form of necessary (Chap. II, §§75 foil.) On the whole subject see Bosanquet, Logic (loc. cit.), and K & R, pp. 114 foil.
4 "Where necessity is internal &c." So far as the totality is a system which is because of its internal necessity, and is viewed in that character, the above statement will not hold.
6 " We must admit — fact." This, I think, is wrong. Logic, I agree, should abstain from dealing with the ultimate problem. But on the other hand logic most certainly should not admit and assume that its "because" is not real. To regard logical implication as merely CHAP. VII THE MODALITY OF JUDGMENTS 237 " ideal " is an error. See T. E. I. And we must remember that " fact," like "existence," is ambiguous. See on Chap. II, §§2 and 4.
7 " When it ceases to be merely necessary." " Merely " here seems misleading. The "necessity" itself is in any case not hypothetical.
8 On the difference between " if " and " because " see T. E. II. This § 10 is largely erroneous. It wrongly identifies " reality " and " fact," and it wrongly assumes the existence of judgments which really are not mediated. See ibid.
9 " The argument from principle." This surely is vicious. There are no "mere ideas" (see on Chap. I, § 10). Logic must assume that the ideal is real somehow and somewhere. The idea that did not qualify Reality would certainly fail to be an idea.
As to the " argument from usage " I agree that " must " can be used to weaken an assertion. But this is where we have an implica tion that our " because " is only partial and is so defective. In an immediate certainty (e.g.) we are sure that we are right somehow though the " how " is not specified. At times, again, we specify the "how" in order to throw doubt on it. We mean that we have this reason, and no more than this. Cf. Bosanquet, Logic I, 379, and K & R, pp. 122 foil. As to the " ultimate premises " which are known immediately, such things I consider to be illusions.
11 "Assumed to be compatible." These words (Cf. §§13, 14, and 21 ) were overlooked by some critics, who in consequence objected to my account on the ground that I had overlooked the possibility of incompatible conditions. But on the contrary my account assumes, not only that I have all the conditions, one part of which is taken as actual, but also that the rest are, in my knowledge, not incom patible. This point, however, should have been brought out more clearly, as it was later in Appearance, Index, s. v. Possible.
12 " Taken to exist " should be " taken to be actual."
13 "Our basis of fact &c." But we must remember that, for an idea to be an idea at all, it can not, so far, be unmeaning. We have therefore with every idea an assertion that it possesses, so far, the character of Reality, and further is real somehow. No possibility can rest fundamentally on mere privation. The assumption that, be yond the above, an idea is possible further, may, however, in a sense, be so grounded. Cf. on Chap. Ill, § 9- What is certainly wrong is to use " possible," where we are simply ignorant as to impossibility abso lute or relative. See Appearance, Chaps. XXIV and XXVII. For the meaning of "possible" cf. T. E. XI and the Index of the present volume.
14 "We have no reason &c." This must be corrected. For in the first place (i) if the idea has a meaning it, so far, is real. And (ii), if there are any facts which suggest a further reality, we have in these surely an additional ground. The "most unfavourable view," to be rational, would have, I think, to rest on the positive knowledge that 238 THE PRINCIPLES OF LOGIC BOOK I body and mind are in themselves, directly or indirectly, inseparable. The following words, " are idle frivolities...men," are almost certainly a quotation, and are so marked. But I can not recall the source.
15 « ]7or t m m supposed." This statement goes too far. The cor rect account of " hypothetical possibility " is, I think, as follows. If you take the actual (or fully grounded), to which the possible is anywhere opposed, and degrade this actual to possible — your first possibility becomes then possible at a further remove. Or (it is the same thing) take a possibility as actual — and then, in consequence, (on and against this) an even less grounded possibility may be doubly or possibly possible. Cf. T. E. XI.
16 For this question see Note 6.
17 " May claim no existence...possibility." But, since it must be thinkable, it must also to a certain point be real and possible. See preceding Notes.
18 " Complete revolution," which revolution I consider necessary.
19 By " men " I meant here " finite beings." And the same remark applies lower down to " human." In §§ 18 foil, we should bear in mind the following. The ordinary abstract judgment does not deal ostensibly with possibles, since it assumes a world in which these are actual. And it is better not to call it "hypothetical," since the attitude of supposal is not there. We need not, again, take the supposed as possible, though clearly, if in no sense it were so logically for us, we could not in fact suppose it.
The possible, as the partly grounded, is negative of a limited known reality, in the sense that not all of the possible is there. A part falls beyond and is actual only in another world. Thus the possible belongs to both of these worlds at once. But it is not a member of the first limited world, because it is only that in part and also is more. And hence alternative possibilities (r1, r2, r3) are all possible, though they can not all at once simply qualify our limited reality. Thus the possible and the actual may or may not exclude one another. The assertion, e.g. that the actual Universe is not possible is ambiguous. And it is false if it means to go beyond the denial of mere possibility, and to suggest that the "more" must, in every sense and everywhere, exclude the " less." Cf. T. E. XL I shall return (§ 28) to the dangerous error which takes " possible " as the contradictory of "impossible." Cf. ibid.
20 Sections 20 foil, need correction throughout, but I need not repeat everywhere in detail what has now been laid down in general.
21 " Less actuality than...the necessary." But obviously, if and so far as the " necessary " is taken as the " fully grounded," this is the case.
22 "Privative judgment." This must be corrected. See above on §§ 13, 14. " Bare possibility " is that which is general as against that which is possible here or there. Or it is that which possesses no more than the least amount of the character required for possibility.
CHAP. VII THE MODALITY OF JUDGMENTS 239 23 On " real possibility," and on the " potential " see Appearance and Essays (the Indexes), and cf. the Index of this work.
24 On Ground and Conditions cf. T. E. II. This section (24) is in part wrong because it once more ignores the various orders of reality (see Chap. II, Note 3). The conditions are the diverse elements of a grounded whole, and therefore are, in some sense and somewhere, actually real. Where in a limited "actual" you have a part of the above totality taken as there present — this limited reality is the "real possibility "of the rest, though the rest is not actually there present, or at least is not taken as being so. In what follows, on "the cause," I had in mind, I presume, the cause taken as mere existing fact. But some correction is required here. See Bosanquet K & R, 25 " Permanent Possibilities." Cf. Appearance, pp. 124-5.
26 I was not denying here that the Hedonistic End can be formu lated correctly. I was merely giving another instance where the use of the same delusive phrase takes the place of thought.
27 " The assertion &c.," that is, " apart from designation." See the Index, s. v. Designation.
28 "These predicates— reflection." But see Note 6. Further, with regard to the statement, "And to a knowledge...possible," we must ask, How far and in what sense would perfect knowledge contemplate unreality at all? It would do so, I presume, only so far as it remained discursive knowledge, and then only so far as the un reality is relative.
In the next paragraph for "directly vanishes" "simply and directly" would, I think, be better.
29 "On the Impossible see Appearance (Index), and T. E. VII. The impossible must of course have enough meaning to be what might perhaps be called " possibly possible."
30 " The real does not...incompatible." Under " incompatible " here will fall the case of the absence of some predicate. In the next sentence the words "Because...else is" go, I think, certainly beyond the first appearance of necessary impossibility. All that, so far, is present there, seems to be re-assertion with an exclusion on the ground of a " must."
si On Privation cf. Note 13. And see T. E. VII and VIII and Appearance (Index). The main point here is this— that a mere absence or exclusion is nothing at all. " Possible " and " impossible " are hence not mere contradictories. If the impossible is not possible enough to have a meaning, it is logically nought. Total absence of compatibility with the Real means sheer nothingness. The real ques tion is as to further compatibility, and whether we have positive reason, and if so, how much, to assume that, if there were "incom patibility," that would appear. In other words a mere failure to exclude is logically nothing, and so again is all mere exclusion whether of what has sense or is senseless.
The doctrine of §§ 28-9 is, I think, right in the main though some 24O THE PRINCIPLES OF LOGIC BOOK I correction is needed. For "pass unabridged" (§28) see Note n. For the rest, no suggestion, if it is a logical suggestion, can be meaningless and elicit no answer at all from Reality. Whether an utterly meaningless suggestion is possible as a psychological fact it would be idle here to ask. In logic the suggested must have a meaning, and must to some extent be real, and the question will be as to its further reality. Here, if we have but one possibility, that is real. If, on the other hand, we have counter-possibilities, the question will be as to the value to be attached to each of these upon positive grounds.
Apart from this, the doctrine of § 29 seems correct. We have a vicious identification of the real, as it is, with the real as we find it now mentally present; and we have a vicious conclusion that, if there were incompatibility, I should know of it. The reductio ad absurdum seems also correct. If anything is possible, then, if there is no counter-possibility, it is necessary and real.
32 " The universal...nothing." " Nothing " here should be " nothing special." And, in the next sentence, " The universal tri angle " should be qualified by "thus held in abstraction." Cf. Chap.
33 On the doctrine of § 31 see above, Note 31. The statement " then, I admit...judgment" is, we have seen, incorrect, unless we under stand what follows to deny the privative character of the foundation.
34 On Probability cf. Bosanquet, Logic, Chap. VIII. 2.
35 Instead of " any ground " — " any further ground " would be more accurate.
36 The reason of course is that in the latter case b (for instance) becomes a common heading of b1 b2 &c.
37 1 think that " perhaps " should here be omitted.
38 " The same as any one " — would better have been " the same as any particular one."
ao " Cause" is taken here not as pure cause (where there is reciprocity between cause and effect), but in that looser sense which admits " plurality of causes." See T. E. X and Index s. v. Cause.
40 The " other cause " might, e.g. be loaded dice or some art in the thrower. The question thus raised is answered by considering the comparative probability of each " cause "; and no new principle is involved here.
41 in " Within the probability " " within " is to be emphasized.
42 In " true or false in fact " we must here, once more, give a wide sense to "fact" (see Chap. II, Note 3). What in probability is "sub jective" is in short merely the amount of my ignorance and knowledge.
43 The word " now " should be omitted, as it might be wrongly taken in reference to "go beyond."
44 The words " or often " can not, I think, stand. For, even if they were true, they would be superfluous.
45 By " be a suggestion " what I meant was " be at least a sugges tion.
CHAP. VII THE MODALITY OF JUDGMENTS 24!
46 Cf. § 59. I should also have said that I do not pretend to know the sense in which within mathematics the word "infinite" is taken. But, so far as I have been able to understand the meanings in which, outside mathematics, some mathematicians wish to use the term — I am clear that these are self-contradictory.
With regard to " an infinite number," see Bosanquet, Logic, II, pp. 161 foil. He points out that it involves the fallacy of counting where you have nothing in particular to count, where, that is, you count in abstraction from any presupposed whole. This objection is in principle the same as that usually urged, which insists on the necessary external determination, and consequent internal incomplete ness, of any mere counted sum. If you are led in principle beyond any whole which you take, that is really the same thing as counting without any whole.
If I may be permitted a word of criticism on the later work of Prof. Royce, I would add that whether by the study of mathematics he really was carried over to a better world of ideas — I am quite unable to judge. But the passage by that Lethe, where he crossed, led him (so far as I see), here and elsewhere, simply to forget that way of understanding (good or bad) which he once shared with those who still are able to remember what they learnt.
47 By aiming at an unnecessary reductio ad absurdum, and also perhaps by a misunderstanding of Lotze, I was led here to injure a good case by a superfluous and serious blunder. This was noticed by Dr. Bosanquet, K & R, pp. 108 foil., and Logic, I, 108 foil. If the series is broken off at such a point that it can not exactly coincide with the ratio, to take this as being in any sense a deviation is plainly wrong. See Bosanquet, Logic I, 350.
48 Essendi should have been fiendi.
49 The statement here seems at least wanting in clearness. It would be better after "all should show once" to proceed as follows. "It is not that each face has a claim to show itself once, or that no face has a claim to appear twice. It is that there is less ground for the presence than for the absence of deviation from the ratio. This is why we think &c."
50 The words "But the first assumption...impossibility" need some correction. They should, I think, have been "But the first assumption is based on partial ignorance, and the second, as to the unknown residue, is not true. We have some reason here to expect irregularity, and we find nothing here about a balance."
51 On § 59 cf. the Note on § 53- 62 The sentences " But...the world," and the two preceding sentences are partly incorrect (see on § 17). But, since the ques tion here is as to existence in fact, the conclusion remains unaffected 53 "Without any mixture of" should be "freed, so far, from." And, in the next sentence, for "so universal," it would be better to write "in this sense universal." I should have added here that 242 THE PRINCIPLES OF LOGIC BOOK I necessity has no meaning outside a whole which is a concrete universal. Lower down " hypothetical " should, once more, be " conditional."
54 1 am unable to remember against what doctrine or writer I was arguing here, and I can not even say that the error noticed exists outside of some misapprehension of my own. See Bosanquet, BOOK II— I NFERENCE AT the end of our First Book we made a transition to the subject of our Second. Modality took us from judgment to reasoning. An inference is either a result or a process. If we take it as a result, we saw that it is the apprehension of a necessary truth. If we take it as a process, it is simply the operation which leads to that result. A truth judged true because of something else, and the going to a truth from the ground of a judgment or supposition x are what we mean by conclusion and reasoning. And this starting-place being reached, our right course may seem plain. We should first make quite clear the general character of inference, and should exemplify this by the necessary detail. And then we might proceed at our ease to remove the erroneous doctrines which cumber the ground.
There is an objection to this way of dealing with the sub ject. The reader would find his difficulties increased. I do not indeed know, after my first Book, if at this stage I have any actual reader; but I am sure, if I have one, that he is not eager to make a great effort. We have perhaps nothing in front of us so hard to cross as what we have passed over, and yet we shall find there are obstacles enough. It is better to make a gradual advance. Instead of going at once from the facts to the truth, and from that to the removal of erroneous theories, I shall aim at reaching an easy vantage-ground, from which we may disperse the mass of mistakes which bar our progress and harass each movement. This will be the object we shall try to gain first. Secure in our rear, we may then proceed upon the final position.
244 THE PRINCIPLES OF LOGIC BOOK II We must therefore in the first of the two following Books be content with a truth which is only partial. We must assume that in every valid inference no less than three terms are given to the reasoner. We shall hereafter see that this assumption is not tenable, but it will serve as a basis from which to operate. It may be a high thing to have no order of convenience, to follow the development of the subject matter, and to let the reader follow if he can. But it is an end more possible, and perhaps not much lower, to help the reader by any means whatever to a better understanding.
The arrangement of this Book as well as its basis must be considered arbitrary. I shall begin by setting down some characteristics of inference which perhaps are likely to be accepted by all. And to these I shall add a few examples of actual reasoning. I shall then proceed to deal with some mistakes, confining myself in the main to the syllogism. In the next place I will point out that inference consists in an ideal construction. And fourthly I will state some principles of synthesis by which we operate to effect that construction. One essential factor in valid inference will then be indicated, and will be seen to rest on a serious assumption; and we shall further show that in every inference at least one premise must be universal. Having reached this point we shall conclude our First Part, and take a fresh departure; and throughout the rest of this Second Book we shall be engaged in the work of clearing the ground. We shall have to criticize in general the alleged Association of Ideas, and especially the Associa tion of Similars. We shall briefly dispose of the supposed way of arguing from particulars to particulars; and shall show by an examination of J. S. Mill's Canons that his Inductive Logic is theoretically invalid. After this, having declined to enter on a discussion of Mr. Spencer's doctrine, we shall end with a review of Professor Jevons' theory of Equational Logic. The position we shall have reached, and the negative results we shall have been forced to gain, will have served to prepare us for a completer view.
ADDITIONAL NOTE " Judgment or supposition." Cf. p. 245, footnote. But to take "supposition" as excluding "judgment" is wrong. There are no "mere ideas." See on p. 4.
PART I THE GENERAL NATURE OF INFERENCE CHAPTER I SOME CHARACTERISTICS OF REASONING § i. When we first consider the subject of reasoning we seem to have nothing but a conflict of opinion. But a second glance reveals some agreement. There are three characteristic features of inference as to which in our hearts we are really at one. I do not mean that we should not deny them if our theories required it, but we should do so unwillingly and with a sense of compulsion. The first of these is a negative mark. There is a difference between reasoning and mere observa tion; if a truth is inferred it is not simply seen, and a conclu sion is never a mere perception. The latter may seem to be given to us bodily, but the former involves some other ele ment. It may indeed be thrust upon us, we may be compelled and constrained to make it, but we can not passively take it in. The fancies we cherish in respect of perception desert us as soon as we come to inference. The external fact or the reflec tion it throws off can violently break into and enter our minds, or the reality can stamp our yielding substance with its image and superscription. But we can hardly apply these ideas to a conclusion, for we feel that in this there is something that repels them. An inference can not wholly come in from with out or be passively received. It is not mere vision, it is more than observation.
§ 2. There is another mark which a conclusion possesses. It is not a mere fragment or isolated unit; it does not exist in and by itself, but is the result of a process. It rests upon a basis, and that basis is something we already know.* In inference we advance from truth possessed to a further truth; * For the sake of clearness I here ignore the hypothetical character of inference.
THE PRINCIPLES OF LOGIC BOOK II. Pi. I and the conclusion would never be reached at all if it were not for knowledge already attained. It is therefore dependent and in a sense adjectival.
§ 3. But there is another attribute which a conclusion has got. It must convey some piece of information, and must tell us something else than the truths it depends upon. We have no inference at all, we have simply a frivolous show and pretence, if taking something we already know we assert the whole or part of this once more, and then say, " I have rea soned and got to a conclusion." An inference must be more than a vain repetition, and its result is no echo of senseless iteration. It is not mere observation yet it gives us something new. Though not self-existent it is more than a shadow. To those who delight in discrepant metaphors we may bring conviction when we so express ourselves: The truth which is seen in the mirror of inference has not wandered in through the window-pane of sense, nor yet is it merely a reflection cast by an article of furniture already in the mind.
§ 4. Except in the interest of a preconceived theory, I think that these statements, at least so far, will not be denied. But I can hardly hope that the examples of reasoning I am about to produce will all escape unchallenged. Yet I shall not defend them, for I do not know how. They are palpable inferences, and the fact that they are so is much stronger than any theory of logic.
(i) A is to the right of B, B is to the right of C, therefore A is to the right of C. (ii) A is due north of B, B due west of C, therefore A is north-west of C. (iii) A is equal to (greater or less than) B, B is equal to (greater or less than) C, therefore &c. (iv) A is in tune with B, and B with C, there fore A with C. (v) A is prior to (after, simultaneous with) B, B to C, therefore A to C. (vi) Heat lengthens the pendulum, what lengthens the pendulum, makes it go slower, therefore heat makes it go slower, (vii) Charles I. was a king; he was beheaded, and so a king may be beheaded, (viii) Man is mortal, John is man, therefore John is mortal. We shall go from these facts to ask how far certain theories square with them.
CHAPTER II SOME ERRONEOUS VIEWS