Disjunctive Judgment
(5) The Disjunctive Judgment “A is either B or C,” is again not a judgment of doubt but a mode of Knowledge, It may be taken as numerical; then it gives rise to the statement of Chances. But in its perfect form it is appropriate to the exposition of a content as a system, and it may be taken as returning to the Categorical Judgment, and combining it with the Hypothetical, because its {124} content is naturally taken as an individual, being necessarily concrete.
The peculiar point of the Disjunctive is that it makes negation positively significant.
“This signal light shows either red or green.” Here we have the categorical element, “This signal light shows some colour,” and on the top of this the two Hypothetical Judgments, “If it shows red it does not show green,” “If it does not show red it does show green.” You cannot make it up out of the two Hypothetical Judgments alone; they do not give you the assertion that “it shows some colour.” [1]
[1] The example in the text, chosen for its simplicity, may be objected to as involving perceptive concreteness by the pronoun “this.” You can have a disjunction, it may be said, dealing with “the triangle” as such; and why should this be more “Categorical” than the assertion that the triangle has its angles = three right angles? Still, it might be replied, the development of a single nature into a number of precise and necessary alternatives, always gives it an implication of self-completeness.
Does this state a fact? I think it implies a fact much more distinctly than the hypothetical does, but of course it is a question whether an alternative can be called a fact. It seems a precise expression of some kinds of reality, but it is not a solid single momentary fact. It is very appropriate to the objects of philosophy as the higher concrete science, which are conceived as systems of facts bearing definite relations to each other;e.g.“Society is a structure of individual characters, having positions which are not interchangeable.” Taken all as a mass, they are conjunctively connected, but taken in distinguishable relations they are disjunctively related. A human being as such has some position and no other, and this is ultimately determined by {125} the nature of the social whole to which he belongs. He is if this, nothing else, and if nothing else, then this. A more artificial example, which illustrates the degree in which actual abstract knowledge and purpose can be embodied by man in machinery, is the interlocking system of points and signals at a great railway station. I suppose that the essence of such a system lies in arrangements for necessarily closing every track to all but one at a time of any tracks which cross it or converge into it. The track X receives trains from A, B, C, D; if the entrance for those from A is open, B, C, and D areipso factoclosed; if A, B, and C are closed, D is open, and so on. This is a disjunction consciously and purposely incorporated in material fact, and differs from a Disjunctive Judgment only in so far as existence necessarily differs from discursive thought.
The disjunction seems to complete the system of judgments, including all the others in itself, and it is wrong in principle to distinguish,e.g.between a hypothetical and categorical disjunction, or to consider how a disjunction can be denied. For disjunction in itself implies a kind of individuality which is beyond mere fact and mere abstract truth, though allied to both; and all intelligible negation is under, not of, a disjunction. Negation of a disjunction would mean throwing aside the whole of some definite group of thoughts as fallacious, and going back to begin again with a judgment of the simplest kind. It amounts to saying, “None of your distinctions touch the point; you must begin afresh.”
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Distinction between Contrary and Contradictory opposition[1]
1. The only important point in the traditional diagram of opposition of Judgments is the distinction between contrary and contradictory opposition, the opposition, that is, between A and E, and the opposition between A and O, or E and I.
[1] Read Bain, pp. 55-6, on “Negative Names and the Universe of the Proposition,” also on “Negative Propositions,” p. 83 ff.; Venn,Empirical Logic, pp. 214—217; Jevons,Elementary Logic, ix., on “Opposition of Propositions”; Mill, ch. iv. § 2.
InContraryOpposition the one Judgment not only denies the other, but goes on to deny or assert something more besides. The mere grammatical shape “No man is mortal” conceals this, but we easily see that it says more than is necessary to deny the other, “All men are mortal.”
InContradictoryOpposition, the one Judgment does absolutely nothing more than is involved in destroying the other.
TheContraryNegation has the advantage in positive, or at least in definite import.
TheContradictoryor pure Negation has the advantage in the exhaustive disjunction which it involves.
This is plain if we reflect that Contrary Negation only {127} rests on the Law of Contradiction, “X is not both A and not A.”
Ordinary Diagram of Opposition of Judgments.
[The diagram has diagonal lines, not represented here, from corner A to corner O, and from corner E to corner I, each labelled “Contradictory Opposition”. Tr.]
A EContrary Opposition.
Sub-contrary Opposition.I O
A = Universal Affirmative. All men are mortal.E = Universal Negative. No men are mortal.I = Particular Affirmative. Some men are mortal.O = Particular Negative. Some men are not mortal.
Sub-contrary Opposition has no real meaning; the judgments so opposed are compatible.
It is nottrueboth that “All M.P.’s are wise,”andthat “No M.P.’s are wise,” but both may be false; while Contradictory Negation implies the Law of Excluded Third or excluded Middle, “X is either A or not A,” the principle of disjunction, or rather, the simplest case of it. It is not {128}falseboth that “All M.P.’s are wise” and that “Some M.P.’s are not wise.” The point is, then, on the one hand, that in Contradiction you can go from falsehood to truth, [1] while in Contrariety you can only go from truth to falsehood; but also that in Contradiction the Affirmative and Negative are not at all on a level in meaning, while in Contrariety they are much more nearly so. Then if we leave out the relations of mere plurality, of All and Some, which enable you to get contrary negation in pure negative form in the common Logic, we may say generally that in contrary negation something is asserted, and in contradictory negation taken quite literally nothing is asserted, but we have a “bare denial,” a predicate is merely removed. In actual thought this cannot be quite realised, because a bare denial is really meaningless, and we always have in our mind some subject or universe of discourse within which the denial is construed definitely. But this definite construing is not justified by the bare form of contradiction, which consists simply in destroying a predication and not replacing it by another. In as far as you replace it by another, defined or undefined, you are going forward towards contrary negation.
[1]I.e.Contradictory alternatives are exhaustive.
Contrary Negation
2. Thus, Contrary Negation in its essence is affirmation with a negative intention, and we may take as a type of it in this wider sense the affirmation of a positive character with the intention of denying another positive character.E.g.when you deny “This is a right-angled triangle” by asserting “This is an equilateral triangle,” you have typical contrary negation. It is not really safe to speak of contraries except with reference tojudgments, intended to deny each {129} other; but it is common to speak of species of the same genus as contraries or opposites, because the same thing cannot be both. [1]
[1] Bain, p. 55 ff.
We must therefore distinguishcontraryfromdifferent. Of course the same thing or content has many different qualities, and even combines qualities that we are apt to call contrary or opposite. But as Plato was fond of pointing out, a thing cannot have different or opposing qualities in the same relation, that is to say, belonging to the same subject under the same condition. The same thing may be blue in one part of it and green in another, and the same part of it may be blue by daylight and green by candlelight. But the same surface cannot be blue and green at once by the same light to the same eye looking in the same direction.Differentqualities becomecontrarywhen they claim to stand in the same relation to the same subject. Right-angled triangles and equilateral triangles do not deny each other if we leave them in peace side by side. They are then merely different species of the same genus, or different combinations of the same angular space. But if you say, “This triangle is right-angled,” and I say “It is equilateral,” then they deny each other, and become true contraries.
Then themeaningof denial is always of the nature ofcontrarydenial. As we always speak and think within a general subject or universe of discourse, it follows that every denial substitutes some affirmation for the judgment which it denies. The only judgments in which this is not the case are those called by an unmeaning tradition Infinite Judgments,i.e.judgments in which the negative predicate {130} includes every determination which has applicability to the Subject. This is because the attribute denied has no applicability to the Subject, and therefore all that has applicability is undiscriminatingly affirmed, in other words, the judgment has no meaning. “Virtue is not-square.” This suggests no definite positive quality applicable to virtue, and therefore is idle. You may safely analyse a significant negative judgment, “A is not B” as = “A is not B but C,” or as = “A is X, which excludes B.” For X may be undetermined, “a colour not red.” But then if the meaning is always affirmative or positive, why do we ever use the negative form?
Why use Negation?
3. In the first place, we use it because it indicates exclusion, and without it we cannot distinguish between mere differents on the one hand and contraries on the other. If you ask me, “Are you going to Victoria, London Chatham and Dover station?” and I answer, “I am going to Victoria, London Brighton and South Coast,” that will not be satisfactory to you, unless you happen to know beforehand that these stations are so arranged that if you are at one you are not at the other. They might be a single station used by different companies, and called indifferently by the name of either. To make it clear that the suggestion and the answer are incompatible, I must say, “I amnotgoing to Victoria, London Chatham and Dover,” and I may add or not add, “Iamgoing to Victoria, London Brighton and South Coast.” That tells you that the one predicate excludes the other, and that is the first reason why we use the generalised form of exclusion,i.e.negation.
But in the second place, it can give us more, and something absolutely necessary to our knowledge, and that is not {131} merely exclusion, but exhaustion. In literal form negation is absolutely exhaustive, that is to say, contradictory. The Judgment “A is not B” forms an exhaustive alternative to the Judgment “A is B,” so that no third case beyond these two is possible, and therefore you can argue from the falsehood of either to the truth of the other. Now this form is potentially of immense value for knowledge, and all disjunction consists in applying it; but as it stands in the abstract it is worthless, because it is an empty form. “A is red or not-red.” If either of these is false the other is true. But what do you gain by this? You are not entitled to put any positive meaning upon not-red; if you do so you slide into mere contrary negation, and the inference from falsehood becomes a fallacy. Make an argument, “The soul is red or not-red.” “It is not-red ∴ it is some other colour than red.” The argument is futile. We have construed “not-red” as a positive contrary, and that being so, the disjunction is no longer exhaustive. We had no right to say that the soul is either red or some other colour; the law of Excluded Middle does not warrant that.
I pause to say that the proof of the exhaustiveness of negation,i.e.that two negatives make an affirmative—that if A is not not-B, it follows that A is B—is a disputed problem, the problem known as double negation. How do you know that what is not not-red must be red? I take the law of Excluded Middle simply as a definition of the bare form of denial, or the distinction between this and not-this; “not-this” being the bare abstraction of the other than this. Others say that every negation presupposes an affirmation; so “A is not-B” presupposes the affirmation “A is B,” and {132} if you knock down the negative, the original affirmative is left standing. Sigwart and B. Erdmann say this. I think it monstrous. I do not believe that you must find an affirmative standing before you can deny.
Stage of Significant Negation. Combination of Contrary and Contradictory
4. Well, then, the point we have reached is this. What we mean in denial is always the contrary, something positive. What we say in denial—in other words, the literal form which we use—always approaches the contradictory,i.e.is pure exclusion. The Contrary of the diagram denies more than it need, but still its form is that of exclusion. Now we have seen that in denial, as used in common speech, we get the benefit ofboth affirmation and exclusion, but in accurate thought we want to do much more than this; we want to get the whole benefit of the negative form—that is, to get a positive meaning together with not only exclusion, but exhaustion.
I will put the three cases in one example, beginning with mere affirmations of different facts.
Different Affirmations
(1) “He goes by this train to-day.” “He goes by that train to-morrow.” This conjunction, as simply stated, gives no inference from the truth or falsehood of either statement to the truth or falsehood of the other.
Contrary Opposition, exclusive
(2) “He goes by this train,” and “He goes by that train,” with a meaning equivalent to “No, he goes by that.” If it is true that in the sense suggested by the context he goes by this train, then it is not true that he goes by the other, and if it is true, in the sense explained, that he goes by the other, then he does not go by this. Each excludes the other, but both may be excluded by a third alternative. If it isnottrue that he goes by this {133} train—nothing follows. There may be any number of trains he might go by, or he might give up going;i.e.your Universe of discourse, your implicit meaning is not expressly limited. If it isnottrue to say, “No, he goes by that”—taking the whole meaning together, and not separating its parts, for this combination is essential to the “contrary”—nothing follows as to the truth of the other statement. He may not be going at all, or may be going by some third train, or by road.
Combined Contrary and Contradictory Negation
But if you limit your Universe, or general subject, then you can combine the value of contrary and contradictory negation. Then you say,
(3) “He goes either by this train or by that.” Then you can infer not only from “He goes by this train,” that “He does not go by that,” but from “He does not go by this train” to “He does go by that.”
The alternative between “A is B” and “A is not-B” remains exhaustive, but not-B has been given a positive value,because we have limited the possibilities by definite knowledge. The processes of accurate thinking and observation aim almost entirely at giving a positive value C to not-B, and a positive value B to not-C, under a disjunction, because it is then that you define exactly where and within what conditions C which is not B passes into B which is not C. Take the disjunction, “Sound is either musical or noise.” If the successive vibrations are of a uniform period it is musical sound; if they are of irregular periods it is noise. This is a disjunction which assumes the form,
A is either B or C. That is to say, If it is B it is not C. If it is not B it is C.
{134} Therefore I think that all “determination is negation”—of course, however, not bare negation, but significant negation; the essence of it consists in correcting and confirming our judgment of the nature of a positive phenomenon by showing thatjust whenits condition ceases,just thensomething else begins, and when you have exhausted the whole operation of the system of conditions in question, so that from any one phase of their effects you can read off whatitis not but theothersare, then you have almost all the knowledge we can get. The “Just-not” is the important point, and this is only given by a positive negation within a definite system. You want to explain or define the case in which A becomes B. You want observation of not-B; but almost the whole world is formally or barely not-B, so that you are lost in chaos. What you must do is to find the point within A, where A1 which is B passes into A2 which is C, and that will give you thejust-not-Bwhich is the valuable negative instance.
Negative judgment expressing fact
5. You will find it said that a Negative Judgment cannot express fact;e.g.that a Judgment of Perception cannot be negative. This is worth reflecting upon; I hope that what has been said makes clear how far it is true. The bare form of Negation is not adequate to fact; it contains mere emptiness or ignorance; we nowhere in our perception come upon a mere “not-something.” No doubt negation is in this way more subjective than affirmation. But then as it fills up in meaning, the denial becomes more and more on a level with the affirmation, till at last in systematic knowledge both become double-edged—every affirmative denies, and every negative affirms. When a man who is both a {135} musician and a physicist says, “this compound tone A is a discord Y,” he knows exactly how much of a discord, what ratio of vibration makes it so much of a discord, how much it would have to change to become a concord (X which is not Y), and what change in the vibration ratio from a1 to a2 would be needed to make it a concord. To such knowledge as this, the accurate negation is just as expressive as the affirmation, and it does not matter whether he says “A is Y,” or “A is by so much not X.” It becomes, as Venn says, all but impossible to distinguish the affirmation from the negation. No doubt affirmative terms come in at this stage, though the meaning is negative. Observe in this connection how we sometimes use the nearest word we can think of, knowing that the negative gives the positive indirectly—“He was, I won’t say insolent,” meaningjust notor “all but” insolent; or again, “That was not right,” rather than saying bluntly “wrong.”
Operation of the denied idea
6. Every significant negation “A is not B” can be analysed as “A is X which excludes B.” Of course X may not be a distinct C;e.g.we may be able to see that A is not red, but we may not be able to make out for certain what colour it is; then the colour X is “an unknown colour which excludes red.”
How does the rejected idea operate in Judgment? I suppose it operates by suggesting a Judgment which as you make it destroys some of its own characteristics. It is really an expression of the confirmatory negative instance or “just-not.”Justwhen two parallel straight lines swing so that they can meet,justthen the two interior angles begin to be less than two right angles, which tells us that the {136} straight lines are ceasing to be parallel. Just in as much as two straight lines begin to enclose a space we become aware that one or other of them is not straight, so that A in turning from Y to X turnspari passufrom A1 to A2, and we are therefore justified in saying that A, when it is Y, cannot be X.
This lecture may pave the way for Induction, by giving some idea of the importance of the negative instance which Bacon preached so assiduously.
In a real system of science the conceptions are negative towards each other merely as defining each other. One of them is not in itself more negative than another. Such a conception,e.g., is that of a triangle compared with two parallel straight lines which are cut by a third line. If the parallels are swung so as to meet, they become a triangle which gains in its third angle what the parallels lose on the two interior angles, and the total of two right angles remains the same. Thus in saying that parallels cut by a third straight line cannot form a triangle, and that the three angles of a triangle are equal to two right angles, we are expressing the frontier which is at once the demarcation between two sets of geometrical relations, and the positive grasp or connection of the one with the other. The negation is no bar to a positive continuity in the organism of the science, but is essential to defining its nature and constituent elements. This is the bearing of significant negation when fully developed.
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Inference in general[1]
1. The Problem of Inference is something of a paradox. Inference consists in asserting as fact or truth, on the ground of certain given facts or truths, something which is not included in those data. We have not got inference unless the conclusion, (i.) is necessary from the premisses, and (ii.) goes beyond the premisses. To put the paradox quite roughly—we have not got inference unless the conclusion is (i.) in the premisses, and (ii.) outside the premisses. This is the problem which exercises Mill so much in the chapter, “Function and Value of the Syllogism.” We should notice especially his § 7, “the universal type of the reasoning process.” The point of it is to make the justice of inference depend upon relations of content, which are judged of by what he calls induction. That is quite right, but the question still returns upon us, “What kind of relations of content must we have, in order to realise the paradox of Inference?” This the “type of inference” rather shirks. See Mill’s remarks when he is brought face to face with {138} Induction, Bk. III. ch. f. § 2. An Inference, as he there recognises, either does not hold at all, or it holds “in all cases of a certain description,”i.e., it depends on universals.
[1] Read for Lectures IX. and X., Mill, Bk. II ch. i., ii., iii.; Bk. III. ch. i. and ii. at least; Venn, ch. xiv., xv.; Jevons,Lessonsxv. and xxiv.; De Morgan’sBudget of Paradoxes.
I ought to warn you at once that though we may have novelty in the conclusion of Inference (as in multiplication of large numbers), the necessity is more essential than the novelty. In fact, much of Inference consists in demonstrating theconnectionof matters that asfactsare pretty familiar. Of course, however, they are always modified in the process, and in that sense there is always novelty. You obtain the most vital idea of Inference by starting from the conclusion as a suggestion, or even as an observation, and asking yourself how it is proved, or explained, and treating the whole process as a single mediate judgment,i.e.a reasoned affirmation. Take the observation, “The tide at new and full moon is exceptionally high.” In scientific inference this is filled out by a middle term. We may profitably think of the “middle term,” as the copula or grip which holds the conclusion together, made explicit and definitely stated. Thus the judgment pulls out like a telescope, exhibiting fresh parts within it, as it passes into inference. “The tide at new and full moon,being at these times the lunar tide plus the solar tide, is exceptionally high.” This is the sort of inference which is really commonest in science. Such an inference would no doubt give us the conclusion if we did not know it by observation, but it happens in many cases that we do know it by observation, and what the inference gives us is the connection, which of course may enable us to correct the observation.
{139}Conditions of the possibility of Inference
2. In the strictest formal sense there can be no inference from particulars to particulars. When there seems to be such inference, it is merely that the ground of inference is not mentioned, sometimes because it is obvious, sometimes because it is not clearly specified in the mind. Suppose we say, “Morley and Harcourt will go for Disestablishment, and I think, therefore, that Gladstone will.” I do notexpressany connecting link, merely because every one sees at once that I am inferring from the intentions of some Liberal leaders to those of another. If the terms are really particulars, “X is A, Y is B, Z is C,” one is helpless; they do not point to anything further at all; there is no bridge from one to the other.
Inference cannot possibly take place except through the medium of an identity or universal which acts as a bridge from one case or relation to another. If each particular was shut up within itself as in the letters taken as an instance just now, you could never get from one which is given to another which is not given, or to a connection not given between two which are given.
Take the simplest conceivable case, which hardly amounts to Inference, that of producing a given straight line. How is it that this is possible? Because the direction of the straight line is universal and self-identical as against possible directions in space, and it acts as a rule which carries you beyond the given portion of it. This might fairly be called an “immediate inference.” So I presume that any curve can be constructed out of a sufficient portion of the curve, although, except with a circle, this is more than repeating the same line over again. The content has a nature which {140} is capable of prescribing its own continuation. A curve is not a direction; a truth which is a puzzle to the non-mathematician—it is a law of continuous change of direction.
System the ultimate condition of Inference
3.Ultimatelythe condition of inference is always a system. And it will help us in getting a vital notion of inference if we think, to begin with, of the interdependence of relations in space—in geometrical figures, or, to take a commonplace example, in the adjustment of a Chinese puzzle or a dissected map. Or any of the propositions about the properties of triangles are a good example. How can one property or attribute determine another, so that you can say, “Given this, there must be that”? This can only be answered by pointing to the nature of a whole with parts, or a system, which just means this, a group of relations or properties or things so held together by a common nature that you can judge from some of them what the others must be. Not all systems admit of precise calculation and demonstration, but wherever there is inference at all there is at least an identity of content which may be more or less developed into a precise relation between parts. For example, we cannot construct geometrically the life and character of an individual man; we can argue from his character to some extent, but the connection of facts in his personal identity is all that we can infer for certain; and even this involves a certain context of facts, as in circumstantial evidence. Yet this simplest linking together of occurrences by personal identity is enough to give very startling inferences. Thackeray’s story of the priest is a good instance of inference from mere identity. “An old abbé, talking among a party of intimate friends, happened {141} to say, ‘A priest has strange experiences; why, ladies, my first penitent was a murderer.’ Upon this, the principal nobleman of the neighbourhood enters the room. ‘Ah, Abbé, here you are; do you know, ladies, I was the Abbé’s first penitent, and I promise you my confession astonished him!’” Here the inference depends solely on individual identity, which is, as we saw, a kind of universal.
But in this case was there really an inference? Does not the conclusion fall inside the premisses? It must in one sense fall inside the premisses, or it is not true. But it does not fall inside them until we have brought them into contact by their point of identity and melted them down into the same judgment. I admit that these inferences from individual identity, assuming the terms not to be ambiguous, are only just within the line of rational inference, but, as we see in this case, they bring together the parts of a very extended universal. Whatisthe lower limit of inference?
Immediate Inference
4. In the doctrine ofimmediate Inferencecommon Logic treats of Conversion and the Opposition of judgments.
Is a mere transposition of Subject and Predicate, where the truth of the new judgment follows from that of the old, an inference? It is a matter of degree. [1] Does it give anything new? “The Queen is a woman.” “A woman is the Queen.” If we make a real difference between the implications of a Subject and a Predicate, we seem to get something new; but it is a point of little interest. {142} Comparison or Recognition are more like immediate inferences. Comparison means that we do not let ourselves perceive freely, but take a particular content as the means of apperception of another content,i.e.as the medium through which we look at it. I do not merely look at the second, but I look at it with the first in my mind. And so far I may be said to infer, without the form of proof, from data of perception to a relation between them. “You are taller than me,” is a result obtained by considering your height from the point of view of mine, orvice versâ. Recognition is somewhat similar. It is more than a mere perception, because it implies reproduction of elements not given, and an identification with them. I recognise this manasso-and-so,i.e.I see he is identical with the person who did so-and-so. It is a judgment, but it goes beyond the primary judgment, “He is such and such,” and is really inferred from it. It is a matter of degree. Almost every Judgment can be broken up into elements, and recognition fades gradually into cognition—we “recognise” an example of a law, a right, a duty, an authority; not that we knewit, the special case, before, but that in analysing it we find a principle which commands our assent, and with which we identify the particular instance before us.
[1] The collective or general judgment, as commonly explained, cannot be converted “simply,” because the predicate is “wider” than the subject, and the same rule is accepted for the relation of consequent to antecedent. The aim of science, it might almost be said, is to get beyond the kind of judgment to which this rule applies.
Number of Instances
5. The difference between guess-work and demonstration rests on the difference between a detached quality or relation striking enough to suggest something to us, and a system thoroughly known in its parts as depending on one another. This is so even in recognising an individual person; it is necessary to know that the quality by which you recognise him is one that no one else possesses, or else {143} it is guess-work. Still more is this the case in attempting a scientific connection. All scientific connection is really by system as between the parts of the content. A quality is often forced on our attention by being repeated a great many times in some particular kind of occurrence, but as long as we do not know itscausalconnection with the properties and relations involved in the occurrence it is only guess-work to treat them as essentially connected. This is a matter very easy to confuse, and very important. It is easy to confuse, because a number of instances does help us really in inference, as it always insensibly gives us an immense command of content; that is to say, without knowing it we correct and enlarge our idea of the probable connection a little with every instance. So the connection between the properties that strike us becomes much larger and also more correct than it is to people who have only seen a few instances. But this is because the instances are all a little different, and so correct each other, and show transitions from more obvious forms to less obvious forms of the properties in question which lead us up to a true understanding of them. If the instances were all exactly the same they would not help us in this way, but our guess would still be a guess, however many instances might have suggested it.
I remember that a great many years ago I hardly believed in the stone-age tools being really tools made by men. I had only seen a few bad specimens, one or two of which I still think were just accidentally broken flints which an old country clergyman took for stone-age tools. This was to me then a mere guess, viz. that the cutting shape proved {144} the flints to have been made by men. And obviously, if I had seen hundreds of specimens no better than these, I should have treated it as a mere guess all the same. But I happened to go to Salisbury, and there I saw the famous Blackmore Museum, where there are not only hundreds of specimens, but specimens arranged in series from the most beautiful knives and arrow-heads to the rudest. There one’s eye caught the common look of them at once, the better specimens helping one to interpret the worse, and the guess was almost turned into a demonstration, because one’s eyes were opened to the sort of handwork which these things exhibit, and to the way in which they are chipped and flaked.
Now this very important operation of number of examples, in helping the mind to an explanation, is always being confused with the effect of mere repetition of examples, which does not help you to an explanation,i.e.a repetition in which one tells you no more than another. But these mere repetitions operateprima faciein a different way, viz. by making you think there is anunknowncause in favour of the combination of properties which recurs, and lead up to the old-fashioned perfect Induction and the doctrine of chances, and not to demonstration. [1]
[1] Ultimately the calculus of chances may be said to rest on the same principle as Induction, in so far as the repetition of examples derives its force from the (unspecified) variety of contexts through which this repetition shows a certain result to be persistent. But in such a calculus the presumption from recurrence in such a variety of contexts is only estimated, and not analysed.
On the road from guess-work to demonstration, and generally assisted by great experience, we haveskilful{145} guess-work, the first stage of discovery. This depends on the capacity for hitting upon qualities whichareconnected by causation, though the connection remains to be proved. So a countryman or a sailor gets to judge of the weather; it is not merely that he has seen so many instances, but he has been taught by a great variety of instances to recognise the essential points, and has formed probably a much more complex judgment than he can put into words. So again a doctor or a nurse can see how ill a patient is, though it does not follow that they could always say why this appearance goes with this degree of illness. In proportion as you merelypresumea causal connection, it is guess-work or pure discovery. In as far as you cananalysea causal connection it is demonstration or proof; and for Logic, discovery cannot be treated apart from proof, except as skilful guess-work.In as far asthere is ground for the guess, so far it approaches to proof;in as far asthere is no ground, it gives nothing for Logic to get hold of—is mere caprice. A good scientific guess really depends on a shrewd eye for the essential points. I am not mathematician enough to give the history of the discovery of Neptune by Leverrier and Adams, “calculating a planet into existence by enormous heaps of algebra,” [1] but it must have begun as a guess, I should suppose it was suggested before Adams and Leverrier took it up, on the ground of the anomalous movements of Uranus indicating an attraction unaccounted for by the known solar system. And I suppose that this guess would gradually grow into demonstration as it became clear that nothing but a new planet would explain the anomalies of {146} the orbit of Uranus. And at last the calculators were able to tell the telescopist almost exactly where to look for the unknown planet. The proof in this case preceded the observation or discovery by perception, and this makes it a very dramatic example; but if the observation had come earlier, it would not I suppose have dispensed with the precise proof of Neptune’s effect on Uranus, though it might have made it easier.
[1] De Morgan,Budget of Paradoxes, p. 53.
Figures of Syllogism
6. In illustration of this progress from guess-work to science, [1] I will give an example of the three Aristotelian figures of the Syllogism. I omit the fourth. I assume that the heavier term, or the term most like a “thing,” is fitted to be the Subject, and the term more like an attribute to be the Predicate. The syllogistic rules depend practically on the fact that common Logic, following common speech and thought, treats the Predicate as wider than the Subject, which corresponds to Mill’s view (also the common scientific view), that the same effect may have several alternative causes (not a compound cause, but different possible causes), and that consequent is wider than antecedent. [2] It is this assumption that prevents affirmative propositions from being simply convertible,i.e.prevents “All men are mortal” from being identical with “All mortals are men,” and but for it there would be no difference of figure at all, as there is not for inference by equation.
[1] Cf. Plato’sRepublic, Bk. VI., end. [2] See p. 141, note.
This progression is here merely meant to illustrate the universal or systematic connection of particulars in process of disengaging itself. But I donotsay that the first {147} figure with a major premise is a natural form for all arguments.
I take the scheme of the first three figures from Jevons, and suggest their meaning as follows:—
X denotes the major term.Y denotes the middle term.Z denotes the minor term.
1st Fig. 2nd Fig. 3rd Fig.Major Premise YX XY YXMinor Premise ZY ZY YZConclusion ZX ZX ZX
Fig. 3.An observation and a guess.
Yesterday it rained in the evening.All yesterday the smoke tended to sink.∴ The smoke sinking ( may be ) a sign of rain.( is sometimes )
The conclusion cannot be general in this figure, because nothing general has been said in the premisses about the subject of the conclusion. So it is very suitable for a mere suggested connection given in a single content—that of the time “yesterday,” implying moreover that both the points in question have something to do with the state of the atmosphere on that single day.
Fig. 2.A tentative justification.
Smoke that goes downwards is heavier than airParticles of moisture are heavier than air.∴ Particles of moisture may be in the descending smoke.
A universal conclusion in this figure would be formally bad. But we do not care for that, because we only mean it to be tentative, and we do not draw a universal affirmative {148} conclusion. We express its badness by querying it, or by saying “may be.” The reason why it is formally bad is that nothing general has been said in the premisses about the middle term or reason, so that it is possible that the two Subjects do not touch each other within it,i.e.that the suggested special cause, moisture, is not connected with the special effect, the sinking of the smoke. The general reason “heavier than air” may include both special suggested cause and special suggested effect without their touching. Smoke and moisture may both sink in air, but for different and unconnected reasons. Still, when a special cause is suggested which is probably present in part, and which would act in the way required by the general character of the effect, there is a certain probability that itisthe operative cause, subject to further analysis; and the argument has substantive value, though bad in form. The only good arguments in this figure have negative conclusions,e.g.—
Smoke that is heavier than air goes downwards.Smoke on dry days does not go downwards.∴ Smoke on dry days is not heavier than air.
This conclusionisformal, because the negative throws the second Subject altogether outside the Predicate, and so outside the first Subject. The one content always has a characteristic which can never attach to the other, and consequently it is clear that some genuine underlying difference keeps them apart. Such an inference would corroborate the suggestion previously obtained that the presence of moisture was the active cause of the descending smoke on days when rain was coming.
Fig. 1.A completely reasoned judgment.{149}All particles that sink in the air in damp weather morethan in dry, are loaded with moisture when they sink.
Smoke that descends before rain is an example of particlesthat sink in the air in damp weather more than in dry.
∴ Smoke that descends before rain is loaded with moisture when it descends (and therefore its sinking is not accidentally a sign of rain, but is really connected with the cause of rain).
The major premise belongs only to this figure. In the other it is mere tradition to call it so, and their two premisses are the same in kind, and contribute equally to the conclusion, and for that reason the affirmative conclusion was not general or not formal. If your general conclusion is to follow by mere form, you must show your principle as explicitly covering your conclusion. But if you do this, then of course you are charged with begging the question. And, in a sense, that is what you mean to do, when you set out to make your argument complete by its mere form. If you havebonâ fideto construct a combination of your data, you cannot predict whether the conclusion will take this form or that form. Using a major premise meant, “We have got a principle that covers the conclusion, and so explains the case before us.” Granting that the major premise involves the minor premise and conclusion, that is just the reason why it is imperative to express them. The meaning of the Syllogism is that it analyses the whole actual thought; the fault is to suppose that novelty is the point of inference. The Syllogism shows you how you must understand either premise in order that it may cover {150} the conclusion. Or, starting from the conclusion as a current popular belief, or as an isolated observation or suggestion by an individual observer (and this is practically the way in which our science on any subject as a rule takes its rise), the characteristic process through the three stages described above consists in first noting the given circumstances under which, according to theprima faciebelief or observation, the conjunction in question takes place (“yesterday,”i.e.“in the state of the atmosphere yesterday”); secondly in analysing or considering those given circumstances, to find within them something which looks like a general property, a law, or causal operation, which may attach the conjunction in question to the systematic whole of our experience (the presence of something heavier than air in the atmosphere); and thirdly, in the exhibition of this ground or reason as a principle, in the light of which the primary belief or observation (probably a good deal modified) becomes a part of our systematic intelligible world.
{151}
Induction[1]
1. Induction has always meant some process that starts from instances; the Greek word for it is used by Aristotle both in his own Logic and in describing the method of Socrates. It meant either “bringing up instance after instance,” or “carrying the hearer on by instances.” And still in speaking of Induction we think of some process that consists in doing something with a number of instances. But we find that this notion really breaks down, and the contradiction between Mill and other writers (Jevons, ch. i.) shows exactly how it breaks down. The question is whether one experiment will establish an inductive truth. We will review the meanings of the term, and show how they change.
[1] Read N. Lockyer’sElements of Astronomy; Abney’sColour Measurement; Introduction toBain on Induction; Jevons’sElementary Lessons on “Observation and Experiment”p. 228, and onInduction, p. 214 (about Mill).
Induction by simple Enumeration
(a) Induction by simple enumeration was what Bacon was always attacking, and saying, quite rightly, that it was not scientific. It is the method which I stated in the Third Figure of the syllogism, almost a conversational method; the mere beginning of observation. “I am sure the influenza is a serious illness; all my friends who have had it have been dreadfully pulled down.” {152}
A B C have been seriously ill.ABC have had influenza.∴ Influenza is a serious illness.
Now this popular kind of inference, as Bacon says, “Precarie concludit, et periculo exponitur ab instantia contradictoria.” Suppose you come across one slight case of influenza, the conclusion is upset. This type of reasoning really appeals to two quite opposite principles; one the principle of counting, which leads up to statistics and the old-fashioned perfect Induction or the theory of chance, the other the principle of scientific system.
Enumeration always has a ground
(b) In counting, we do not think of the reason why we count, but there always is a reason, which is given in the nature of the whole whose parts we are counting. If I count the members of this audience, it is because I want to know how many units the whole audience consists of. I do not ask why each unit is there; counting is different from scientific analysis; but yet the connection between whole and part is present inmy reason for counting. So really, though I only say, “One, two, three, four, etc.,” each unit demands a judgment, “This is one member—that makes two members, that makes three members,” etc. Counting is the construction of a total of units sharing a common nature; measurement is a form of counting in which the units are also referred to some other standard besides the whole in question,e.g.the standard pound or inch.
Perfect Induction
(c)Merecounting or “enumeration” only helps you in induction by comparison with some other numerical result, and, if imperfect, only to the extent of suggesting that there {153} is a common cause or there is not a common cause.E.g.if you throw a six with one die fifty times running, you infer that the die is probably loaded. This is because you compare the result with that which you expect if the die is fair, viz. a six once in every six throws. You infer that there is a special cause favouring one side. The principle is that ignorance is impartial. If you know no reason for one case more than another, you take them as equal fractions of reality; if results are not equal fractions of reality, you infer a special reason favouring one case. [1] Pure counting cannot help you in Induction in any way but this.Perfect Inductionsimply means that the total is limited and the limit is reached; you have counted 100 per cent, of the possible cases, and the chance becomes certainty. The result is a mere collective judgment.
[1] See Lecture IX, p. 144, note.
System
(d) The principle of scientific system is quite a different thing. Essentially, it has nothing to do with number or with a generalised conclusion. It is merely this, “What is once true is always true, and what is not true never was true.” The aim of scientific induction is to find out “Whatistrue,”i.e.what is consistent with the given system. We never doubt this principle; if we did we could have no science. If observation contradicts our best-established scientific laws, and we cannot suppose an error in the observation, we must infer that the law was wrongly,i.e.untruly stated. Therefore, as Mill says, one case is enough,ifyou can find the truth about it. People object that you cannot make a whole science out of one case, and therefore you must have a number of instances. That is a {154}practicalpoint to be borne in mind, but it has no real scientific meaning. “Instance” cannot be defined except as one observation, which is a purely accidental limitation. The point is, that you use your instances not by counting cases of given terms, but by ascertaining what the terms really are (i.e.modifying them), and what is their real connection. This is the simple secret of Mill’s struggle to base scientific Induction, on Induction by simple Enumeration; the latter is not the evidence, but the beginning of eliciting the evidence—so that the Scientific Induction is far more certain than that on which Mill bases it. Aristotle’s statement is the clearest and profoundest that has ever been made. [1]
“Nor is it possible to obtain scientific knowledge by way sense-perception. For even if sense-perception reveals a certain character in its object, yet we necessarily perceivethis,here, andnow. The universal, which is throughout all, it is impossible to perceive; for it is not a this-now; if it had been it would not have been universal, for what is always and everywhere we call universal. Since then demonstration (science) is universal, and such elements it is impossible to perceive by sense, it is plain that we cannot obtain scientific knowledge by way of sense. But it is clear that even if we had been able to perceive by sense [e.g.by measurement] that the three angles of a triangle are equal to two right angles, we should still have had to search for a demonstration, and should not, as some say, have known it scientifically (without one); for we necessarily perceive in particular cases only, but science comes by knowing the universal. Wherefore if we could have been on the moon, and seen the earth coming between it and the {155} sun, we should not (by that mere perception) haveknownthe cause of the eclipse. Not but what by seeing this frequently happen we should have grasped the universal, and obtained a demonstration; for the universal becomes evident out of a plurality of particulars, and the universal is valuable because it reveals the cause;” and again, [2] “And that the search of science is for the middle term is made plain in those cases in which the middle term is perceptible to sense. For we search where we have had no perception,—as for the reason (or middle term) of an eclipse,—to know if there is a reason or not. But if we had been upon the moon, we should not have had to inquire if the process (of an eclipse as such, and not some other kind of darkness) takes place, or for what reason, but both would have been plain at once. The perception would have been, ‘The earth is now coming between,’ carrying with it the obvious fact, ‘The moon is now suffering an eclipse,’ andout of thisthe universal (connection) would have arisen.”
[1] Aristotle,An. Post.87, b. 28. [2]Ibid.90, a. 24.
Analogy
(e) I showed you a method on the way to this in the shape of Aristotle’s second figure, which we may callanalogy. The plain sign of it is, that you give up counting the instances and begin to weigh them, so that the attributes which are predicates fall into the middle term or reason. In the former inference about influenza we did not suppose that you had any ideawhyinfluenza was a serious illness; but in analogy there is some suggestion of this kind, so that the connection is examined into. Here at once you begin to get suggested explanations and confirmation from the {156} system of knowledge. You cannot have analogy by merely counting attributes.
I begin fromEnumerative Suggestiondrawn from observation ofButterflies.
1. Three species of genusxclosely resemble three species ofy.
2. The species ofxwould be protected by resemblingy(becauseyis distasteful to birds).
∴ The resemblance may be a “protective resemblance,”i.e.a resemblance brought about by survival of those thus protected.
On this there naturally followsAnalogy.
1. Protective resemblances naturally increase through series of species from slighter to closer resemblances.
2. The resemblances in question increase in genusxthrough series of species from slighter to closer resemblance toy.
∴ The resemblances in question show important signs of being protective resemblances.
When we get thus far, a single syllogism will not really represent the argument. It can only analyse with convenience a single step in inference. But now we have connected the reason of the resemblances with the whole doctrine of natural selection, the gradual approximation of the species is most striking, and we could set up a corroborative analogy on the basis of every feature and detail of these resemblances, the tendency of which would be to show that no cause or combination of causes other than that suggested is likely to account for the observed resemblances.
{157} I give a confirmatory negative analogy.
1. No protective resemblance can grow up where there is no initial tendency to resemblance.
2. The non-resembling species in the genusxshow no initial tendency towardsy.
∴ The non-resemblances observed are such as could not produce protective resemblances. This is a formally bad argument from two negative premisses justified by its positive meaning, which implies thatjust wherethe alleged effect ceases, the alleged cause ceases too.
If you look at the case in the Natural History Museum [1] you see the normal Pierinae down one side, not approaching Euploinae. They are the positive examples, negatively confirming the explanation of those which do approach Euploinae. These latter all start from some form which varied slightly, by accident we presume, towards Euploinae, and then this partially resembling series splits into three sets, each leading up to a different and complete protective resemblance.
[1] These cases in the entrance-hall of the Natural History Museum at South Kensington afford excellent practical illustrations of Inductive Method. I strongly urge the London student to try his hand at formulating them.
I saidmerenumber was no help in scientific Induction. But do not these three sets of resemblances make a stronger proof than any one would? Yes, because we need a presumption against accident. You would not want this if you could unveil what really happens in one case, but as infinite conditions are operative in such matters, and it is impossible to experiment accurately, [1] this cannot be done; {158} and it might be said thatonesuch resemblance was an accident,i.e.that it was owing to causes independent of the protection. But as the cases become more numerous it becomes more improbable that different circumstances produce the same effect, which would then be a mere coincidence, in so many different cases. If, however, we knew by positive and negative analysis what circumstance did produce the effect, this confirmation would be useless.
[1] Ultimately, no experiments are absolutely accurate. There is always an unexhausted background in which unsuspected causes of error may be latent.
Negative Instance
(f) In order to showexactlywhat circumstance produces a given effect, a system must be brought to bear on the phenomenon through negation. The only test of truth is that it is that which enables you to organise your thought and perception.
The first means of doing this is Observation, then Experiment, thenClassification and Hypothesis, which takes us into Deduction.
Observation is inaccurate, until you begin to distinguish what is connected from what is not connected. When you do this, you are very near experiment, the use of which is to introduce perfectly definite and measurable changes into what you are observing. [1] There is no absolute distinction between observation and experiment. Looking at a tissue through a microscope is observation; putting on a polariscope, though it changes theimagealtogether, is observation; if you warm the stage, or put an acid on the object, that, I suppose, is experiment, because you interfere with the object {159} itself. What should we say, for example, as to spectroscopic analysis of the Sun’s corona?
[1] Jevons,loc. cit., esp. quot. from Herschel (p. 234).
The moment you begin accurate observation you get a negative with positive value, which is really the converse by negation of your positive observation, a1 is b1; b2 (which isjustnot-b1) is a2 (which isjustnot-a1). Thus the two may be represented as the same judgment in positive and negative forms, which confirm one another. “Yellow is a compound of red and green”—in Experiment, “if, and as far as you take away the red or the green you destroy the yellow.” That describes an experiment with the colour-box. I have inverted the order in the conversions in compliance with the rule of common Logic, that Predicate is wider than Subject; but in accurate matter it is a false rule, and very inconvenient. The common rule means that a man who is drowned is dead, but a man who is dead need not have been drowned; but of course if he has the signs of death by drowning then he has been drowned.
Classification and Generalisation
(g)Classificationis a consequence of all systematic theory; it is not a separate method of science. It is merely the arrangement of positive contents negatively related. No doubt where we have a kind of family relations between individuals classification is more prominent, and in the theory of continuous matter or operation, where individualities are not remarkable—e.g.in geometry—it is less prominent. But both are always there—classification and theory. Classification which expresses no theory is worthless, except that intended for convenient reference, such as alphabetical classification.
Under classification I may say a word on generalisation. {160} The common idea of inference from many cases, because they are many, to all cases of the same kind, is quite without justification. The only genuine and fundamental law of generalisation is “Once true always true.” But this might fail to suffice for our practical purposes, because it might save its truth by abstraction. Let us take the example, “Water is made of oxygen and hydrogen.” If that is true once, it is always truein the same sense. If you find some fluid of a different composition which you are inclined to call water, then you must identify or distinguish the two, and this is a mere question of classification.Practically, however, we could not get on unless our knowledge had some degree ofexhaustiveness,i.e.unless we knew roughly that most ofwhat we take for waterwill have the alleged properties. But no Induction or analysis, however accurate, can assure us against confusion and error, viz. assure us that everything we take to be water will be made of oxygen and hydrogen, nor that water will always be found on the earth. I call this accurate analysis, whichmaybe made in a single instance only, and is the only perfectly scientific generalisation, generalisation by mere determination. Its classification is hypothetical,i.e.in it the individuals are merely possible individuals.
But this passes into another kind of generalisation, which may be called generalisation by concrete system, as when we attach scientific analysis to some extensive individual reality,e.g.to the solar system or the race of man. Then our judgments have a place in the real world, and our classification is categorical classification. The generalisation in this case does not follow from the judgment being extended {161} over a great plurality of possible similar subjects, but from the subject to which it applies having as an organised totality a large place in the world;e.g.“The human race alone gives moral interest to the history of bur planet.” These judgments come by making explicit the reality which underlies such hypothetical judgments as “all men are capable of morality.” It means that we actually venture to assign a place in the universe to the system we are speaking of. Then, though it is an individual, and unique, its name has a meaning, and is not a mere proper name. The solar system is good instance. Judgments about it or parts of it are universal but not purely hypothetical, and as our knowledge of this kind increases it becomes even a little exhaustive.
Generalisation by mere likeness or analogy, on the other hand, is precarious. It is what popular theory has in its mind in speaking of Induction, viz. a conclusion from a truth to judgments concerning all similar cases,e.g.from “Water is made of Oxygen and Hydrogen” to “All liquids which we choose to take for water are made of Oxygen and Hydrogen.” No scientific method can possibly give us this result. In as far as it has value it depends upon our guessing rightly by analogy. It may be replied, “that the signs of recognition are set down in the law or truth.” Well, if they are certain, generalisation by mere determination is enough; if they are doubtful, no induction can warrant your judgment of them in particular cases. Practically, of course, we get them right pretty often, although wrong very often.
Hypothesis
(h) Hypothesis is merely supposition; it consists in suggesting a fact as if it were real, when it is the only way of {162} completing given facts into a consistent system. If the hypothesis is proved that is a demonstration. It has been said that “Facts are only familiar theories.” If a bell rings in the house, I say unhesitatingly, “Some one rang that bell.” Once in ten years it may be rung, not by a person, but by some mechanical accident, in which case the “some one” is a hypothesis, but one always treats it as a fact. The only proof of a hypothesis is its being the only one that will fit the facts,i.e.make our system of reality relatively self-consistent. We believe many things we can never verify by perception,e.g.the existence of the centre of the earth, or that you have an idea in your minds; and if we go to ultimate analysis, perception itself involves hypothesis, anda fortioriall experiment involves hypothesis. Every experimental interference with nature involves some supposition as to a possible connection which it is intended to confirm or disprove.
Deduction
2. Classification and hypothesis bring us into Deduction, which is not really a separate kind of inference from Induction, but is a name given to science when it becomes systematic, so that it goes from the whole to the parts, and not from the parts to the whole. In Induction you are finding out the system piecemeal, in Deduction you already have the clue; but the system, and the system only, is the ground of inference in both. Induction is tentative because we do not know the system completely. Their relation may be fairly represented by the relation of the first figure of the Syllogism to the second and third. The difference is merely that in deduction we are sure of having knowledge which covers the whole system. If a man observed, “The difference {163} between the dark blood in the veins and the bright blood in the arteries calls for explanation,” that is the beginning of Induction. If a man states the circulation of the blood as an explanation, that is Deduction. Really Induction is only a popular name for such Inference as deals with numbers of instances. Mill’s experimental methods do not depend upon number of instances, but only upon content; they presuppose the instances already broken up into conditions A, B, C, and consequents a, b, c.
I must distinguish subsumption and construction as two forms of deduction. Only the formerproperlyemploys Syllogism in the first figure.
Subsumption
(a) Subsumption is argument by subject and attribute;i.e.when we do not know the system so as to construct the detail,—e.g.a man’s character,—and can only stateinwhat individual system the details occur. Then wereally wantthe major premise to lay down the properties of the system, and all deductioncantherefore be employed with a major premise,e.g.a mathematical argument might ultimately take the form, “space is such thattwo parallels cannot meet.”
Construction
But (b) when the nature of the subject is very obvious, and the combinations in it very definite, then the major premise is superfluous, and adds nothing to the elements of the combination.
“A to right of B, B to right of C.∴ A to right of C.”
This is clear, but it is not formal; as a syllogism it has four terms. It is simply a construction in a series of which the nature is obvious. And if you insert a major premise it would be, “What is to the right of anything is to the right {164} of that which the former is to the right of,” and that is simply the nature of the series implied in the inference stated in an abstract form. “Inference is a construction followed by an intuition.” [1] The construction, I think, however, must be a stage of the intuition. I am therefore inclined to suggest that a factor of general insight into principle is neglected in this definition, from which much may undoubtedly be learned.
[1] Bradley,Principles of Logic, p. 235.
Causation
3. I have said very little about causation. The fact is, that in Logic the cause necessarily fades away into the reason, that is, the explanation. If we follow Mill’s account, we see how this takes place. I will put the stages very briefly.
Cause
(a) We start, no doubt, by thinking of a cause as a real event in time, the priority of which is the condition of another event, the effect. Pull the trigger—cause—and the gun goes off—effect.
Complete conditions
(b) The moment we look closer at it, we see that this will not do, and we begin to say with Mill, that the cause is the antecedent which includesallthe conditions of the effect. The plurality of alternative causes breaks down, through the conditions defining the effect. Pull the trigger?—yes, but the cartridge must be in its place, the striker must be straight, the cap must be in order, the powder must be dry and chemically fit, and so on, and so on, till it becomes pretty clear that the cause is a system of circumstances which include the effect.
Law
(c) But then our troubles are not ended. Only the essential and invariable conditions enter into the cause, if the {165} cause is invariable. This begins to cut away the particular circumstances of the case. You need not use the trigger, nor even the cap; you may ignite powder in many ways. You may have many kinds of explosives. All that is essential is to have an explosion of a certain force and not too great rapidity. Then you will get this paradox. What is merely essential to the effect, is always something less than any combination of real “things” which will produce the effect, because every real thing has many properties irrelevant to this particular effect. So,if the cause means something real, as a material object is real, it cannot be invariable and essential. If it is not something real, and is essential, it fines down into a reason or law—the antecedent in a hypothetical judgment.
Ground, or real system with known laws
(d) We can only escape this by identifying both cause and reason with the complete ground; that is, the nature of a system of reality within which the cause and effect both lie. But even then, though the ground isreal, it is not antecedent in time. We see, indeed, that the conditions of an effect must be continuous through the effect. If the process were taken as cut in two at any point, its connection would be destroyed. Ifacause andbeffect were really detached events, what difference could it make if, instead ofa,cprecededb?
Postulate of Knowledge
4. The postulate of Knowledge, then, is very badly stated as Uniformity of Nature. That was due to the vulgar notion of Inductive “generalisation.” It must be stated in two parts: first, “Once true always true;” and secondly, “Our truth is enough for us,” that is, it covers enough of the universe for our practical and theoretical needs. The {166} two parts may be put together by saying, “The universe is a rational system,” taking rational to mean not only of such a nature that it can be known by intelligence, but further of such a nature that it can be known and handled by our intelligence.
Conclusion
5. These lectures have been unavoidably descriptive rather than thorough, and yet, as I warned you, descriptive of properties which are in a sense not at all new, but quite familiar, and even trite. You will not feel, at first, that the full interest which I claimed for the science of knowledge, really attaches to these dry relations of abstract thought. You will get no permanent good unless you carry the study forward for yourselves, and use these ideas as a clue to find your bearings in the great world of knowledge.