Logic: Deductive and Inductive Part 21

But there are a good many general propositions, more or less trustworthy within a certain range of conditions, which cannot be methodically proved for want of a precise principle by which they may be tested; and they, therefore, depend upon Immethodical Induction, that is, upon the examination of as many instances as can be found, relying for the rest upon the undefinable principle of the Uniformity of Nature, since we are not able to connect them with any of its definite modes enumerated in chap. xiii. -- 7. To this subject we shall return in chap. xix., after treating of Methodical Induction, or the means of determining that a relation of events is of the nature of cause and effect, because the relation can be shown to have the marks of causation, or some of them.

-- 5. Observations and Experiments are the _material_ grounds of Induction. An experiment is an observation made under prepared, and therefore known, conditions; and, when obtainable, it is much to be preferred. Simple observation shows that the burning of the fire depends, for one thing, on the supply of air; but it cannot show us that it depends on oxygen. To prove this we must make experiments as by obtaining pure oxygen and pure nitrogen (which, mixed in the proportion of one to four, form the air) in separate vessels, and then plunging a burning taper into the oxygen--when it will blaze fiercely; and again plunging it into the nitrogen--when it will be extinguished. This shows that the greater part of the air does nothing to keep the fire alight, except by diminishing its intensity and so making it last longer.

Experiments are more perfect the more carefully they are prepared, and the more completely the conditions are known under which the given phenomenon is to be observed. Therefore, they become possible only when some knowledge has already been gained by observation; for else the preparation which they require could not be made.

Observation, then, was the first material ground of Induction, and in some sciences it remains the chief ground. The heavenly bodies, the winds and tides, the strata of the earth, and the movements of history, are beyond our power to experiment with. Experiments upon the living body or mind are indeed resorted to when practicable, even in the case of man, as now in all departments of Psychology; but, if of a grave nature, they are usually thought unjustifiable. And in political affairs experiments are hindered by the reflection, that those whose interests are affected must bear the consequences and may resent them. Hence, it is in physical and chemical inquiries and in the physiology of plants and animals (under certain conditions) that direct experiment is most constantly practised.

Where direct experiment is possible, however, it has many advantages over unaided observation. If one experiment does not enable us to observe the phenomenon satisfactorily, we may try again and again; whereas the mere observer, who wishes to study the bright spots on Mars, or a commercial crisis, must wait for a favourable opportunity. Again, in making experiments we can vary the conditions of the phenomenon, so as to observe its different behaviour in each case; whereas he who depends solely on observation must trust the bounty of nature to supply him with a suitable diversity of instances. It is a particular advantage of experiment that a phenomenon may sometimes be 'isolated,' that is, removed from the influence of all agents except that whose operation we desire to observe, or except those whose operation is already known: whereas a simple observer, who has no control over the conditions of the subject he studies, can never be quite sure that its movements or changes are not due to causes that have never been conspicuous enough to draw his attention. Finally, experiment enables us to observe coolly and circ.u.mspectly and to be precise as to what happens, the time of its occurrence, the order of successive events, their duration, intensity and extent.

But whether we proceed by observation or experiment, the utmost attainable exactness of measurements and calculation is requisite; and these presuppose some Unit, in multiples or divisions of which the result may be expressed. This unit cannot be an abstract number as in Arithmetic, but must be one something--an hour, or a yard, or a pound--according to the nature of the phenomenon to be measured. But what is an hour, or a yard or a pound? There must in each case be some constant Standard of reference to give a.s.surance that the unit may always have the same value. "The English pound is defined by a certain lump of platinum preserved at Westminster." The unit may be identical with the standard or some division or multiple of it; and, in measuring the same kind of phenomena, different units may be used for different purposes as long as each bears a constant relation to the standard.

Thus, taking the rotation of the earth as the standard of Time, the convenient unit for long periods is a year (which is a multiple); for shorter periods, a day (which is identical); for shorter still, an hour (which is a division), or a second, or a thousandth of a second. (See Jevons' _Principles of Science_, ch. 14.)

-- 6. The principle of Causation is the _formal_ ground of Induction; and the Inductive Canons derived from it are means of testing the formal sufficiency of observations to justify the statement of a Law. If we can observe the process of cause and effect in nature we may generalise our observation into a law, because that process is invariable. First, then, can we observe the course of cause and effect? Our power to do so is limited by the refinement of our senses aided by instruments, such as lenses, thermometers, balances, etc. If the causal process is essentially molecular change, as in the maintenance of combustion by oxygen, we cannot directly observe it; if the process is partly cerebral or mental, as in social movements which depend on feeling and opinion, it can but remotely be inferred; even if the process is a collision of moving ma.s.ses (billiard-b.a.l.l.s), we cannot really observe what happens, the elastic yielding, and recoil and the internal changes that result; though no doubt photography will throw some light upon this, as it has done upon the galloping of horses and the impact of projectiles. Direct observation is limited to the effect which any change in a phenomenon (or its index) produces upon our senses; and what we believe to be the causal process is a matter of inference and calculation. The meagre and abstract outlines of Inductive Logic are apt to foster the notion, that the evidence on which Science rests is simple; but it is amazingly intricate and c.u.mulative.

Secondly, so far as we can observe the process of nature, how shall we judge whether a true causal instance, a relation of cause and effect, is before us? By looking for the five marks of Causation. Thus, in the experiment above described, showing that oxygen supports combustion, we find--(1) that the taper which only glowed before being plunged into the oxygen, bursts into flame when there--Sequence; (2) that this begins to happen at once without perceptible interval--Immediacy; (3) that no other agent or disturbing circ.u.mstance was present (the preparation of the experiment having excluded any such thing)--Unconditionalness; (4) the experiment may be repeated as often as we like with the same result--Invariableness. Invariableness, indeed, I do not regard as formally necessary to be shown, supposing the other marks to be clear; for it can only be proved within our experience; and the very object of Induction is to find grounds of belief beyond actual experience.

However, for material a.s.surance, to guard against his own liability to error, the inquirer will of course repeat his experiments.

The above four are the qualitative marks of Causation: the fifth and quant.i.tative mark is the Equality of Cause and Effect; and this, in the above example, the Chemist determines by showing that, instead of the oxygen and wax that have disappeared during combustion, an equivalent weight of carbon dioxide, water, etc., has been formed.

Here, then, we have all the marks of causation; but in the ordinary judgments of life, in history, politics, criticism, business, we must not expect such clear and direct proofs; in subsequent chapters it will appear how different kinds of evidence are combined in different departments of investigation.

-- 7. The Inductive Canons, to be explained in the next chapter, describe the character of observations and experiments that justify us in drawing conclusions about causation; and, as we have mentioned, they are derived from the principle of Causation itself. According to that principle, cause and effect are invariably, immediately and unconditionally antecedent and consequent, and are equal as to the matter and energy embodied.

Invariability can only be observed, in any of the methods of induction, by collecting more and more instances, or repeating experiments. Of course it can never be exhaustively observed.

Immediacy, too, in direct Induction, is a matter for observation the most exact that is possible.

Succession, or the relation itself of antecedent and consequent, must either be directly observed (or some index of it); or else ascertained by showing that energy gained by one phenomenon has been lost by another, for this implies succession.

But to determine the unconditionality of causation, or the indispensability of some condition, is the great object of the methods, and for that purpose the meaning of unconditionality may be further explicated by the following rules for the determination of a Cause.

A. QUALITATIVE DETERMINATION

_I.--For Positive Instances._

To prove a supposed Cause: (a) Any agent whose introduction among certain conditions (without further change) is followed by a given phenomenon; or, (b) whose removal is followed by the cessation (or modification) of that phenomenon, is (so far) the cause or an indispensable condition of it.

To find the Effect: (c) Any event that follows a given phenomenon, when there is no further change; or, (d) that does not occur when the conditions of a former occurrence are exactly the same, except for the absence of that phenomenon, is the effect of it (or is dependent on it).

_II.--For Negative Instances._

To exclude a supposed Cause: (a) Any agent that can be introduced among certain conditions without being followed by a given phenomenon (or that is found without that phenomenon); or (b) that can be removed when that phenomenon is present without impairing it (or that is absent when that phenomenon is present), is not the cause, or does not complete the cause, of that phenomenon in those circ.u.mstances.

To exclude a supposed Effect: (c) Any event that occurs without the introduction (or presence) of a given phenomenon; or (d) that does not occur when that phenomenon is introduced (or is present), is not the effect of that phenomenon.

Subject to the conditions thus stated, the rules may be briefly put as follows:

I. (a) That which (without further change) is followed by a given event is its cause.

II. (a) That which is not so followed is not the cause.

I. (b) That which cannot be left out without impairing a phenomenon is a condition of it.

II. (b) That which can be left out is not a condition of it.

B. QUANt.i.tATIVE DETERMINATION

The Equality of Cause and Effect may be further explained by these rules:

III. (a) When a cause (or effect) increases or decreases, so does its effect (or cause).

III. (b) If two phenomena, having the other marks of cause and effect, seem unequal, the less contains an unexplored factor.

III. (c) If an antecedent and consequent do not increase or decrease correspondingly, they are not cause and effect, so far as they vary.

It will next be shown that these propositions are variously combined in Mill's five Canons of Induction: Agreement, the Joint Method, Difference, Variations, Residues. The first three are sometimes called Qualitative Methods, and the two last Quant.i.tative; and although this grouping is not quite accurate, seeing that Difference is often used quant.i.tatively, yet it draws attention to an important distinction between a mere description of conditions and determination by exact measurement.

To avoid certain misunderstandings, some slight alterations have been made in the wording of the Canons. It may seem questionable whether the Canons add anything to the above propositions: I think they do. They are not discussed in the ensuing chapter merely out of reverence for Mill, or regard for a nascent tradition; but because, as describing the character of observations and experiments that justify us in drawing conclusions about causation, they are guides to the a.n.a.lysis of observations and to the preparation of experiments. To many eminent investigators the Canons (as such) have been unknown; but they prepared their work effectively so far only as they had definite ideas to the same purport. A definite conception of the conditions of proof is the necessary antecedent of whatever preparations may be made for proving anything.

CHAPTER XVI

THE CANONS OF DIRECT INDUCTION

-- 1. Let me begin by borrowing an example from Bain (_Logic_: B. III. c.

6). The North-East wind is generally detested in this country: as long as it blows few people feel at their best. Occasional well-known causes of a wind being injurious are violence, excessive heat or cold, excessive dryness or moisture, electrical condition, the being laden with dust or exhalations. Let the hypothesis be that the last is the cause of the North-East wind's unwholesome quality; since we know it is a ground current setting from the pole toward the equator and bent westward by the rotation of the earth; so that, reaching us over thousands of miles of land, it may well be fraught with dust, effluvia, and microbes. Now, examining many cases of North-East wind, we find that this is the only circ.u.mstance in which all the instances agree: for it is sometimes cold, sometimes hot; generally dry, but sometimes wet; sometimes light, sometimes violent, and of all electrical conditions.

Each of the other circ.u.mstances, then, can be omitted without the N.E.

wind ceasing to be noxious; but one circ.u.mstance is never absent, namely, that it is a ground current. That circ.u.mstance, therefore, is probably the cause of its injuriousness. This case ill.u.s.trates:--

(I) THE CANON OF AGREEMENT.

_If two or more instances of a phenomenon under investigation have only one other circ.u.mstance (antecedent or consequent) in common, that circ.u.mstance is probably the cause (or an indispensable condition) or the effect of the phenomenon, or is connected with it by causation._

This rule of proof (so far as it is used to establish direct causation) depends, first, upon observation of an invariable connection between the given phenomenon and one other circ.u.mstance; and, secondly, upon I. (a) and II. (b) among the propositions obtained from the unconditionality of causation at the close of the last chapter.

To prove that A is causally related to _p_, suppose two instances of the occurrence of A, an antecedent, and _p_, a consequent, with concomitant facts or events--and let us represent them thus:

Antecedents: A B C A D E Consequents: _p q r_ _p s t_;

and suppose further that, in this case, the immediate succession of events can be observed. Then A is probably the cause, or an indispensable condition, of _p_. For, as far as our instances go, A is the invariable antecedent of _p_; and _p_ is the invariable consequent of A. But the two instances of A or _p_ agree in no other circ.u.mstance.

Therefore A is (or completes) the unconditional antecedent of _p_. For B and C are not indispensable conditions of _p_, being absent in the second instance (Rule II. (b)); nor are D and E, being absent in the first instance. Moreover, _q_ and _r_ are not effects of A, being absent in the second instance (Rule II. (d)); nor are _s_ and _t_, being absent in the first instance.