§ 6. It is useless to attempt to lay down rules for either part of this process. It is the man who perceives the points of union within his premises — who can put (as the saying is) two and two together — who is able to reason. And so long as he secures the unity of his construction he has reasoned rightly. In the next Chapter we shall see that no models for construction can possibly be invented. And for the process of inspection one wants a good eye; for there are no rules which can tell you what to perceive.
We must free ourselves from these superstitions, if we can, and there are others beside which have oppressed us too long. It is ridiculous for instance to think about the order of our premises. The construction when made need have no order in time, and the order of its making may be left entirely to private convenience or else to chance.
And there is another superstition we may here dispose 26O THE PRINCIPLES OF LOGIC BOOK II. PT. I of.14 The number of terms is not limited to three. In the geographical example of the previous section we certainly do not argue thus C- B* , and D C but we first complete our construction C A , and then go to D A. It is true no doubt that in making a con struction we are forced to establish one link at a time; but it is wholly false that we are compelled to conclude before we take in another premise. Logic sets no limit to the number of premises which may precede the conclusion, and it is the weakness of our heads which narrows our constructions and narrows them sometimes to the prejudice of our inference. There is no branch of science where constructive power is wholly uncalled for, and certainly some where it is of the first importance. And perhaps we may say without exaggera tion that a man, who can not use more than three terms in reasoning, is unlikely to do much in any subject. But, how ever that may be, the limit is psychological and is not logicaL ADDITIONAL NOTES ^•This chapter must be taken as no more than a provisional clearing of the ground. Not only is the warning in the footnote to § i to be borne in mind, but, in addition, the chapter contains serious errors the correction of which can only be indicated in passing.
2 " Into a whole" should be "into a connected whole," and (in the next line) " not related " should be " not so related."
3 " Demonstration is merely pointing out." This is a grave mis take, and the term is, I think, nowhere so used in practice. It every where and always means showing the necessary and ideal connection and sequence. Whether and how far you have before you external fact and its alteration, or deal merely with what is "in your head," is utterly irrelevant. The " demonstration " in every case has to bring out — not the fact — but the ideal bond and process. Cf. on Bk.
4 " In a logical construction " should be " in and as the result 5 On " data " and " premisses " see Index, s. v. Premisses, and cf. Bosanquet, Logic, II, pp. 12 and 203.
CHAP. Ill A GENERAL IDEA OF INFERENCE 26l 6 The words " actual or suggested " should be omitted. See the first Note on Book II. And (at the end of this paragraph) it would be better to insert " new " before " individual," in the words " one individual whole."
7 " All this " should have been " Much of this."
8 " Different " should have been " merely different."
9 The " selective action " is really quite essential. See the Index s. v. Selection. What I meant here was merely that "elimination" is not always necessary. You do not always in the conclusion omit part of the construction. See Bk. III. I. I. § 2.
10 " This intuition is the conclusion." Certainly not so, unless the new relation appears in it as " following." The " conclusion " means seeing as part of the whole and because of the whole. See Note 4.
11 " So far no inference" — except so far as the analytic judgment itself involves inference. See Index, s. v. Analysis.
12 " If I draw the figure &c." This and what follows is seriously wrong. See Note 3.
13 "We hardly infer, etc." Yes, but how far the "we hear" is already itself inferential, still remains a question. See Note II.
14 "And there is another &c." On this see Bosanquet, K & R, p. 307, and Logic, II, pp. 12 foil. My statement here was wrong in forgetting that the necessary establishment by synthetic construction of each link, one at a time, itself is inference. On the other side I was right in insisting that in the final conclusion there is an inference from the whole construction without regard to the number of terms contained in that. Cf. Bk. Ill, I. II. § 5.
CHAPTER IV THE PRINCIPLES OF REASONING1 § I. We have seen in outline the main character of infer ence and we naturally recur to a former question, Is there any axiom or principle of reasoning? The result of our enquiry in the Second Chapter was that we could find nothing quite satisfactory. The syllogistic maxims were all too nar row, and the axiom that " Things which are related to the same are related to each other," we found on the other hand was much too wide. It may serve us however as a point of departure. When properly restricted it will express the truth, so far as is required by the present Book.2 I will repeat the result we arrived at before. The principle that elements which stand in relation to a common point are themselves related, is not the actual principle that operates in any given special inference.3 In its abstract form it is useless for the purpose of getting a conclusion. It assures us, before any construction is made, that anything which we have as an element of knowledge stands in some relation with every other element. But it will not enable us to go beyond this, and by combining our premises to get a definite relation. If A is prior to B in time, and B is west of C in space, then on the strength of B we can put these together, but we can not by means of our combination get a definite relation of A to C. We knew long ago that A and C po-existed as members within the universe of knowledge, and we desire to learn now not that general connection, but some special attitude of A to C. But in order to get this, and to be able so to speak to draw a new line from A to C, it is necessary first to connect A and C in a special manner. They must be interrelated not generally and in the universe at large, but in some special world. If one is merely in time and the other merely in space, they have so far not got any binding centre. To be specially related they must be related to the same, and under conditions which secure an unity of construction.
CHAP. IV THE PRINCIPLES OF REASONING 263 If what operates in inference is the principle of the indi viduality of synthesis, the axiom of that operation must not be taken too widely, and at the cost of clumsiness we must state it in two pieces. " Where elements A and C are related homogeneously to a common B, A and C are related within the same genus. Or where one relation only (either A — B or B — C) is within the category of subject and attribute, there is a valid conclusion within the category of either A — B or B — C." To express the same otherwise, " There is no conclusion where the relations are heterogeneous unless one of the two joins an attribute to a subject. In the latter case an inference is possible even outside the category of subject and attribute."
§ 2. We found first in our examination of the syllogism that there were inferences which fell outside its single cate gory of subject and attribute. We found again that if we kept outside all special categories, mere interrelation was much too vague to form a bond. The conclusion, which in the next place naturally offers itself, is that inference must take place within several special categories (such as time, space, subject and attribute, &c.), but must always be confined in each case to one category. To get a relation of time in the conclusion you would have to keep in your premises to time-relations, and the same thing again with other kinds of relation. And, if this were true, the axiom would run, " Things related to the same within one kind will be interrelated within that kind."
But there are inferences which will not submit to this principle. " Gold is heavier than lead and lead is a metal," " A runs faster than B and B is twice as tall," " A is stronger than B and B is full grown," " A is equal to B in weight and B is moved with such or such velocity " are premises which certainly will yield conclusions, and yet their relations are heterogeneous. And this shows that we may cross from cate gory to category. On the other hand we are unable to do this unless there exists a special condition; one relation must be that of attribute to subject. From " A is equal to B and B has such velocity " we have seen you can not get to the conclusion " A has such velocity." You can not do so till you predicate of A that point in B which brought it into 264 THE PRINCIPLES OF LOGIC BOOK II. PT. I relation with the other element (C). And from "A is equal to B and B is in my pocket " you can not infer that A is in my pocket, since the spatial relation which is affirmed of B is not true of B as equal to A. You can not argue to a relation of A to my pocket, but your conclusion must be " A is equal to something which is in my pocket." We have still the old relation of A to B, but qualified by the addition of an ad jective of B. And it is true, I think, in all possible cases that the relation between a subject and attribute is the only one which, if used with another category, is able to give us a new relation.* The remarks we let fall in a previous chapter (II. § 7) may have prepared the reader for our result. The categories do not stand on one and the same footing.5 It is possible after all to express unconditionally the principle of inference, and it is possible to do this within the one category of subject and attribute (p. 296). But we are not yet arrived at the stage where this is possible, and must content ourselves here with the formula that ended the foregoing section, " Related to the same within the same kind are interrelated within that kind," with a further axiom of possible inference where one relation is that of subject to attribute.
§ 3. Our main principle, it is obvious, will have as many forms as there happen to be categories or kinds of relation. It is not the business of this work to elaborate any theory as to how these kinds are connected or are subordinated. It is again not our purpose to draw out and defend a complete enumeration or scheme of such classes. But in order to make clear the general result, I will state and illustrate four or five main principles which operate in inference. We may call them the principles (i) of the synthesis of subject and attri bute, (ii) of identity, (iii) of degree, (iv) of space, and (v) of time.
I. Principle of synthesis of subject and attribute.
* Other examples are "A has a voice (B), that voice overpowers Z's voice (C), therefore A overpowers C." "A has a voice (B) which is in tune with C, therefore A has something in tune with C." In the first of these the relation of the conclusion is hardly between a subject and attribute.4 A by virtue of its attribute, which attribute acquired a momentary independence, has got a new relation to another subject.
CHAP. IV THE PRINCIPLES OF REASONING 265 (a) The attributes of one subject are interrelated.
(/3) Where two subjects have the same or a different attri bute they are alike or different.
(y) (i) Where the attribute is not taken as distinct from every subject, what is asserted of the attribute is asserted of its subject, (ii) Where the subject is not taken as distinct from every attribute, what is affirmed of the subject is affirmed of any attribute considered as its attribute.
Examples, (a) This man is a logician, this man is a fool, therefore a logician may be * (under some conditions is) a fool.
(13) This dog is white, this horse is white (or brown), this dog and this horse are alike (or different).
(y) (i) This figure is a triangle, a triangle has the angles equal to two right angles, this figure has the angles equal to two right angles, (ii) Gold is heavier than lead; lead is a metal. Therefore lead-metal (or some metal) is lighter than gold, or metal may be lighter than gold.
I may remark on (y) that, if we were to say " What is true of the attribute is true of the subject, and what is true of the subject is true of the attribute," we should fall into an error. The subject qua subject and the attribute qua attribute have each predicates which can not be applied to the other. Thus " Iron is heavy, heavy is a quality " is no ground for the assertion " Iron is a quality," nor from " Iron is heavy, iron is a substance," can you go to the conclusion " Heavy may be a substance" (cf. Book I. Chap. III. § 10). If on the other hand we laid down as a condition of the inference that this attribute and this subject must be taken together, we should then have become circular.6 II. Synthesis of Identity.
Where one term has one and the same point in common with two or more terms, there these others have the same point in common.
Examples. " Coin A has the same inscription as coin B, and coin B as coin C, therefore A as C; " " Instrument A is in tune with my tuning-fork (B), and so too are instruments C and D, therefore they are all in tune with one another;" *May be because, the subject being undefined, the conditions are partly unknown. Vid. Book I. Chap. VII. §26.
266 THE PRINCIPLES OF LOGIC BOOK II. Px. I " If A is the brother of B, and B of C, and C is the sister of D, then A is the brother of D."
III. Synthesis of Degree.
When one term does, by virtue of one and the same point in it, stand in a relation of degree with two or more other terms, then these others also are related in degree.
Examples. " A is hotter than B and B than C, therefore A than C; " " Colour A is brighter than B and B than C, there fore A than C; " " Sound A is lower in tone than B and B than C, therefore A than C." I will not enquire here whether " A = B and B = C, therefore A = C," falls under this head or under the previous head of the synthesis of identity.
IV. and V. Synthesis of Time and Space.7 Where one and the same term stands to two or more other terms in any relation of time or space, there we must have a relation of time or space between these others.
Examples. " A is north of B and B west of C, therefore C south-east of A; " "A is a day before B, B contemporary with C, therefore C a day after A."
This list, as we have said, does not pretend to be complete, and it would not be possible for us here to discuss the ques tions which any such pretence would at once give rise to. Take for instance the synthesis of cause and effect. Does this fall entirely under the head of time? Does it fall under the head of subject and attribute? Does it fall under both or again under neither? The answers to these questions would be hard to get, and, if we got them, they would be of no use to us here. They would not much serve to confirm the result we already have reached; they would possibly supply one more illustration, where I hope enough have already been given.
§ 4. But there is another question which can not be passed by. We have called these syntheses Principles of inference, and have ejected the syllogism to enthrone them in its stead. But how are we to understand the title they lay claim to? We know what the syllogism tried to accomplish, for it professed to control from a central office every possible event in all parts of its kingdom. It issued some two dozen forms of reasoning, to which all inference was expected to conform. Thus you had always some model with relations ready drawn between all the terms both in premises and con- CHAP. IV THE PRINCIPLES OF REASONING 267 elusion, and no liberty was left you save to fill up the blanks with terms of your own. The moods and figures were a bed of Procrustes into which all arguments had somehow to be forced, and they were therefore not merely principles of rea soning, but actual canons and tests of inference. Within this pale you were secure of salvation, and on the outside it was heresy to doubt you were lost. Such was the claim which the syllogism put forth, and enforced as long as it had any strength.
Like some other chimseras that have had their day, the syllogism is effete and its realm is masterless; and the question for us who aspire to the inheritance is to know in what charac ter we mean to succeed. Do we wish to substitute one des potism for another? Are our principles of inference to be tests and canons? Most assuredly not; for if the thing were desirable, and I am much too staunch a Protestant to desire it, it is at all events thoroughly impossible.
§ 5. Our principles give us under each head of inference the general and abstract form of the operation. They do not profess in all cases to give us the individual operation itself which is necessary. It is not merely that the terms are left blank, for the special relations of the premises and conclusion are also left blank. The kind of construction is indicated generally, and the kind of conclusion you will find within it; but the actual construction, and the actual new relation to which that will give rise, are left entirely to private judgment.8 From such premises as " A to the right of B and B to the right of C," there is and there can be no form of reasoning which will give you the conclusion. It is true that the axiom goes so far as to assure you that A and C must be related in space, for 9 you do not know that unless you know that the two space-relations belong to one world. And you do not know this unless you are sure that they have a common meeting-point in space (Book I. Chap. II. §21). But the axiom will not tell you anything beyond. It will neither give you the definite relation, nor even assure you that you will be able to attain to any such relation. A is greater than B, and C is greater than B, therefore (if the point in B is the same) A and C must certainly be related in degree; but you do not know how. B is south of both A and C, therefore A and C are 268 THE PRINCIPLES OF LOGIC BOOK II. PT. I related in space; but you have no means of getting to know their particular relation. For the individual construction can not here be drawn, and it is that alone which can supply the conclusion.
Where the inference is valid, the special operation by which it is performed falls outside the axiom, and it is impossible therefore that the axiom can supply any test of validity. Where the inference is invalid, what makes it invalid may fall without the axiom, and the axiom is therefore no test of invalidity. If I like to argue that, because A and C are both greater than B, they are equal to one another, the principle has nothing to say against it. If I choose to go from " B is south of both A and C " to, " therefore A and C lie east and west," again the principle is perfectly satisfied. It can no more tell me that here I am wrong than that I am right if I say, " A is due north-west of C, because B is five miles south of A and again the same distance west of C." The general form is valid in either case, but the actual operation, whether erroneous or correct, is in either case beyond the scope of the principle. It is not a matter for superior direction; it is a matter for private inspiration and insight.
§ 6. It is impossible that there should be fixed models for reasoning; you can not draw out exhaustive schemata of valid inference. There are principles which are tests of the general possibility of making a construction: but of the actual con struction there can be no canons. The attempt to manufacture them would lead to the search for a completed infinity; for the number of special relations has no end, and the possible connections in time, space, and degree are indefinite and inex haustible. To find the canons of valid inference you must first make a list of valid inferences. You will manufacture a major premise for each, and that major premise derived from each operation will appear as its canon. Your success, if you succeeded, would be the capture of a phantasm, but in the endlessness of the field you would be for ever eluded, No canon will fix for us the pale of orthodoxy, until that day comes when the nature of things will change itself to gratify our stubborn illusions.
§ 7. The popular belief in logic endows it with ability to test all reasonings offered it. In a given case of given premises CHAP. IV THE PRINCIPLES OF REASONING 269 the logician is thought to be a spiritual Director who, if he can not supply, at least tests right and wrong. Thus, if logic is no art which provides us with arguments, yet, once give it the premises, and it is both the art of extracting conclusions and of assaying all those which amateurs have extracted with out its authority. But, understood in this sense, logic has no existence, for there is and there can be no art of reasoning. Logic has to lay down a general theory of reasoning, which is true in general and in the abstract. But when it goes beyond that, it ceases to be a science, it ceases to be logic, and it becomes, what too much of it has already become, an effete chimsera which cries out for burial.
§ 8. It should not lie alone. There is another false science more unlovely in life and more unpleasant in decay, from which I myself should be loath to divide it.10 Just as Logic has been perverted into the art of reasoning, so Ethics has been perverted into the art of morality. They are twin delusions we shall consign, if we are wise, to a common grave.
But I would not grudge Casuistry a Christian burial. I should be glad to see it dead and done with on any terms; and then, if all the truth must be spoken, in its later years it has suffered much wrong. That it became odious beyond parallel and in parts most filthy, is not to be denied; but it ill becomes the parents of a monster, who have begotten it and nourished it, to cry out when it follows the laws of its nature. And, if I am to say what I think, I must express my conviction that it is not only the Catholic priest, but it also is our Utilitarian moralist, who embraces the delusion which has borne such a progeny. If you believe, as our Utilitarian believes, that the philosopher should know the reason why each action is to be judged moral or immoral; if you believe that he at least should guide his action reflectively by an ethical code, which provides an universal rule and canon for every possible case, and should enlighten his more uninitiated fellows, then it seems to me you have wedded the mistake from which this offensive offspring has issued. It may be true that the office of pro fessional confessor has made necessary a completer codifi cation of offences, and has joined doctrinal vagaries to ethica blunders. We may allow that it was the lust for spiritual tyranny which choked the last whisper of the unsanctified 27O THE PRINCIPLES OF LOGIC BOOK II. PT. I conscience. It may be true that, in his effort theoretically to exhaust the possibilities of human depravity, the celibate priest dwelt with curious refinement on the morbid subject of sexual transgression. But unless his principle is wholly unsound I confess that I can hardly find fault with his practice; for if there is to be an art and a code of morality, I do not see how we can narrow its scope beforehand. The field is not limited by our dislikes, and whoever works at the disgusting parts, is surely deserving not of blame but of gratitude. Hence if the Utilitarian has declined to follow the priest, he has also de clined to follow his own principles; he has stopped short not from logical reasons but from psychological causes.
§ 9. It is natural to think that logic has to tell us how we are to reason from special premises; and it is natural to think that ethics must inform us how we are to act in particular cases. Our uncritical logic and our uncritical ethics naturally assume these doctrines as self-evident. But the mistake, if natural, is in both cases palpable. Unless you artificially limit the facts, then models of reasoning can not be procured, since you would need in the end an infinitude of schemes to parallel the infinitude of possible relations. And a code of morality is no less impossible. To anticipate the conclusion in each special case you would have to anticipate all possible cases; for the particular condition which makes this conduct right here and wrong elsewhere, will fall outside the abstractions of the code. You are thus committed to a dilemma: at a certain point you must cease to profess to go right by rule, or else, anticipating all possible combinations of circumstances, you must succeed in manufacturing countless major premises. The second alternative is in the first place illusory, since the principle is really got from the intuition, and in the next place it is impossible, since the number of principles will be limitless and endless. But if you accept the first alternative, and admit that only in certain cases it is possible to deduce the conclusion from a principle, you have given up the hope of your " prac tical reason," and denied the axiom from which you set out.
The syllogistic logic possesses one merit. If its basis is mistaken and its conclusion false, at least it has not stopped short of its goal. In Barbara Celarent its code is perfected, and it has carried out the purpose with which it began. We CHAP. IV THE PRINCIPLES OF REASONING 271 can not say so much of the Casuistry of Hedonism. The con fident dogmatism of its setting-out has been lost in vagueness and in hesitation. It flies to ambiguities it does not venture to analyze, and sighs faintly to a Deity which it dares not invoke. But if the principle of our most fashionable Ethics is true, then an art of Casuistry and a Science of Sin are the goal of that Ethics, and the non-recognition of this evident result, if creditable to the heart, does no honour to the head. If the popular moralist will not declare for a thorough-going Casuistry, if he retires in confusion from the breath of its impurity, he should at least take courage to put away the prin ciples which have given it life. We may apply to him as he stands a saying of Strauss, " He partly does not know what he wants, and partly does not want what he knows." * § 10. If we return to the subject of the syllogistic logic, we may see on the one hand that its moods and figures will not take in any one of our syntheses except the synthesis of subject and attribute. The fifth, the fourth, the third, and the second, refuse to enter the traditional limits. On the other hand the first of our syntheses covers every argument of the syllogistic logic. An inspection of the figures would at once assure us that with positive reasoning this assertion holds good, and we must now proceed to test our conclusion by applying it to the subject of negative inference.
* Compare on the subject of Casuistry my pamphlet, Mr. Sidgwick's Hedonism, § 8, and Ethical Studies, pp. 142, 174, foil (Ed. II. pp. IS7, ADDITIONAL NOTES