§ 56. (ii) But why, it may be asked, does the length of the series increase this probability? Does the greater length add any new ground to those we have for believing in the correspondence of the events with the chances? No, it does not add any. Does it decrease any ground we had before for thinking the opposite? Yes, it does do that; and it does it, I think, in the following way. The unknown residuum in the cause of each throw was assumed to be indifferent. But it was not at all assumed to be passive. It supplies the determining element in the cause. It decides for one face, though we do not know for which face it decides. Now how does it de cide? Does it act regularly and in strict rotation, or is it ir regular? That we do not know; but, taking the possibilities, we believe that those in favour of irregularity are more than those in favour of rotation. It is therefore most probable that our series will turn out to be irregular. But, since we know no reason to prefer any one face, we can not say that any pro portion other than strict equality is the most probable. How are these assertions to be reconciled? Very easily in this way. Owing to the assumed indifference of the causal residue the faces will probably appear in their right numbers; but, because of its irregularity, their appearance will probably be irregular, and irregular to an extent to which we can assign no limit. To combine these attributes it is necessary to sup pose that the whole series will be most probably regular, but will contain periodic irregularities. The greater the irregu larity becomes, the less grows the chance of a final regu larity, unless the series is proportionately lengthened. There fore, since we can fix no limit to the irregular sequence of the faces, we conclude that, the longer the series becomes, the greater becomes the probability of a regular result. And this is a rational, and necessary conclusion from our imperfect data.
§ 57. It is true that, if you make a series longer, you de crease the chance of irregularity. It is true that, if per impossibile the series were so long that, in comparison with its length, every possible abnormal run was a period which other periods might easily balance in the completed cycle — if, I say, per impossibile this phantom could be real, it is true that the above chance of irregularity would vanish. If we as sume that what we do know gives us reason to believe in a series correspondent to our fractions; if we next assume, by virtue of a fiction, that the unknown residue gives no reason to believe in an unbalanced irregularity, then on these assump tions we may go to a conclusion, and we have no ground to disbelieve the statement that the series will exhibit the relations of the chances. But the first assumption is based on ignorance, and the second is based on a known impossibility.50 If we mean to speak about a series of events that could ever happen, we can say but this. It is certain there will be a series, each throw of which will give a single face. It is possible that in a series of any length but one single face should appear throughout. No arrangement is impossible. It is most prob able that the events will answer to the fractions, but against that probability there still remains another consideration, the chance arising from the possible irregularity of one part of the causal elements. This fraction is diminished by each increase of the series, but it does not disappear and it can not disappear.
§ 58. We do not know that in the long run the events will correspond to the probabilities. We do not know that, if we go on long enough, every chance will be realized. It is mere superstition which leads us to believe in the reality of the fiction which gives birth to these chimaeras. When I see the demonstrations, offered to gamblers against a bank, which prove to them that in the long run they can not but lose, I say to myself, On which side do I see the darker illusion? And I answer, On both sides the illusion is the same. For what is the root of the gambler's " system "? Is it not his belief that independent events are affected by each other? But this belief is a strict deduction from the premises offered him. If he really must lose, if there really is a cycle in which the chances must all be realized, then, let him observe the begin ning of the cycle, and mark the irregularities, and he surely must win. Since to equalize the numbers the end of the cycle must balance the beginning, he can speculate on that balance and his " system " is right. " Oh, but it is wrong, for the series is not finite. It is only after an infinite duration of play that the balance is struck. It is absurd to say he can be sure of winning." But is it not then equally absurd to say that he is sure to lose? If you mean he must have lost by the end of his life, you have just admitted your assertion to be false. If you mean he must have lost when he has got to the end of infinite time, confess that your meaning is something like nonsense, and that the gambler is right in imagining that you, as a rational man, must mean something else. The truth is that your common assumption is false. There is no must about it. The chances consist of grounds for belief in the nature of a series no event of which is known. And all they tell us is this: that we have more reason to expect one thing than we have to expect another, and that the increased length of the series proportionately decreases a reason for doubt, which never quite vanishes.
§ 5Q.51 I must not be suspected of a desire to intrude into mathematics if, in this connection, I venture to remark on a well-known paradox. I am to toss a coin, and to go on toss ing so long as I throw heads and nothing but heads. I am to receive £2 if I throw head once; if I throw head twice I am to win £4; for three successive heads I get £8, and so on accordingly. The series is supposed to have no limit except the appearance of a tail. And the question arises, how much am I to pay for the privilege of one single trial? The answer given is, An infinite sum; for it is possible I may throw an infinite series of nothing but heads (vid. De Morgan, Proba bilities, p. 99). The reasoning on which this conclusion seems to rest is exceedingly simple, and I need hardly say that I do not doubt its perfect validity within mathematics. And I think I see that no other answer can possibly be given. Unless an arbitrary limit is fixed, I may be allowed to say in all humility that I think I understand that, if this possibility has any value at all, then the worth of my chance is either incalculable or else is infinite. If this answer is given me by a special science, I dutifully receive it as true— within that science. But if I am told that in actual fact the result is true, I must be allowed to protest. I must be permitted to remark that the reasoning is absurd and the result is nonsense. I do not mean merely that it is absurd if we take it as a practical precept, because a man can not live for ever, and all the money in the world is finite. I mean that it is a theoretical absurdity. It is not true ideally any more than really. Since an infinite sum is an impossibility, the infinite series can not possibly be thrown. There is no chance whatever. There is no fraction at all. It is nothing I could win. It is nothing I can expect. It is nothing for which I can reasonably pay. The result is a deduction from premises known to be false and impossible.
It is idle to answer that the problem is " stated in the ideal form " (Venn, ibid. p. 137). There is a difference surely between ideals which as such do not exist, because they are abstractions, and ideals which are downright self-contradic tions. It is one thing to say, " There is a connection between abstract elements, so that when one of these is found as a real quality we shall have the other," and another thing to continue this assertion, when we know that the first of these elements is self-contradictory and could not possibly be any quality of reality. In this latter case what is true of fact can not be the consequence of an impossibility, but only the basis of the hypothetical judgment. Neither antecedent nor con sequent is taken as real or even as possible. But in a com mon abstract judgment the antecedent is taken as at least a possible quality of the world.52 Mr. Venn perhaps would question this difference between an abstraction and an im possibility, and would perhaps assert that an infinite series is really possible. In any case I must be allowed to protest against the invasion of logical reason by mathematical fic tions. If an infinite series is thought possible, we should be told how it can be possible. If it is not thought possible, it should not be offered us as if it were.
§ 60. There are other points in the theory of chances which have logical interest, but we have no space to discuss them here. We have said enough to make clear the relation in which that theory stands to our general principles. We have to avoid the fiction of the infinite long run, and the vicious alternative of " objective " and " subjective," and the false assumption that the essence of chance involves a series of events in time. If we keep clear of these pitfalls, the truth is by no means difficult to reach, and we hope above to have stated it clearly in its general form.* § 61. There is an aspect of modality we have neglected to notice. The omission was intentional, and the mention of this aspect has been reserved for the present place. There is an old doctrine which connects universality with necessity, and that doctrine is true. The necessary we saw was the ideal consequent, and such a consequent can not come except from an ideal antecedent. You never can say " B follows from A," " is because of A," " must be, given A," unless A is present in a determinate form. A must be a content without any mixture of mere sensuous conditions.53 It must be ideal, abstract, and so universal. If the ancient doctrine on its logical side may suffer some loss, since necessity becomes for logic hypothetical, yet it stands all the firmer. The " because " can not couple anything but universals.
§ 62. We may notice an error which creeps in with this truth.5* The antecedent in necessity must be universal, but it need not be more universal than the consequent. Where we say " because " we do not always appeal to anything more abstractly general than that which follows from our reason. " A must be equal to B, because C is equal to both B and A," " A must be removed by one foot from C, since B, which touches both in a certain manner, is one foot long." The consequence is not less general than the antecedent, and we deceive ourselves in thinking it always must be so.
No doubt in the cases where you say " because " you may find what we call the principle of the sequence, and that of course must be more abstract than the actual consequent. But the principle is not the antecedent itself. It is the base of the general connection, not the sufficient reason of the particular consequent. There is no more need for the con sequent to be more concrete than the antecedent, than there is for the effect to be more special than the cause. These ideas are nothing but kindred illusions (Book III. Chap. II.).
*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.
§ 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.
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 " 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 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.
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 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 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 SOME CHARACTERISTICS OF REASONING