The Essentials of Logic, Being Ten Lectures on Judgment and Inference

by Bernard Bosanquet

LECTURE X INDUCTION, DEDUCTION, AND CAUSATION

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’s Elements of Astronomy; Abney’s Colour Measurement; Introduction to Bain on Induction; Jevons’s Elementary Lessons on “Observation and Experiment” p. 228, and on Induction, 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 in my 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) Mere counting 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 Induction simply 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 “What is true,” 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, if you 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} practical point 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 perceive this, here, and now. 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) have known the 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,’ and out of this the 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 call analogy. 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 idea why influenza 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 from Enumerative Suggestion drawn from observation of
Butterflies.

1. Three species of genus x closely resemble three species of y.

2. The species of x would be protected by resembling y (because y is 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 follows Analogy.

1. Protective resemblances naturally increase through series of species from slighter to closer resemblances.

2. The resemblances in question increase in genus x through series of species from slighter to closer resemblance to y.

∴ 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 genus x show no initial tendency towards y.

∴ 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 that just where the 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 said mere number 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 that one such 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 show exactly what 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, then
Classification 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 the image altogether, 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 is just not-b1) is a2 (which is just not-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) Classification is 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 true in 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 of exhaustiveness, i.e. unless we knew roughly that most of what we take for water will 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, which may be 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, and a fortiori all 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 former properly employs 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 state in what individual system the details occur. Then we really want the major premise to lay down the properties of the system, and all deduction can therefore be employed with a major premise, e.g. a mathematical argument might ultimately take the form, “space is such that two 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 includes all the 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 is real, 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. If a cause and b effect were really detached events, what difference could it make if, instead of a, c preceded b?

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.

And I would give you one hint about this. I do not suggest that you should neglect philosophy but yet you should remember that philosophy can tell you no new facts, and can make no discoveries. All that it can tell you is the significant connection of what you already know. And if you know little or nothing, philosophy has little or nothing to tell you. Plato says, “The synoptical man, the man who has a conspectus of knowledge, is the philosopher; and the man who is not synoptical, who cannot see two subjects in their relation, is no philosopher.” By all means read good logical books; but also and more especially read good and thorough systematic books on science, or history, or politics, or fine art—I do not mean on all of these subjects, but on some, wherever your interest leads you. You cannot learn the nature of inference, of systematic necessity, of the construction of reality, by reading logic exclusively; you must {167} feel it and possess it by working in the world of concrete knowledge. I give one example in passing. If you study social questions, test for yourselves the value of statistics—i.e. sets of enumerative judgments. Consider what the causal analysis of any problem demands; remember that all enumeration implies a ground or whole, on which its value depends; and contrast the exhaustive examination of an instance thoroughly known, with the enumeration of thousands of cases lumped under a general predicate. Determine always to know the truth; welcome all information and all suggestion, but remember that truth is always systematic, and that every judgment, when you scrutinise it, demands a fuller and fuller connection with the structure of life. It is not cleverness or learning that makes the philosopher; it is a certain spirit; openness of mind, thoroughness of work, and hatred of superficiality. Each of us, whatever his opportunities, can become in a true sense, if he has the real philosophic spirit, in Plato’s magnificent words, “The spectator of all time and of all existence.”

THE END

End of Project Gutenberg's The Essentials of Logic, by Bernard Bosanquet