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CHAPTER 1,

On the Nature of Inductive Inference.

TWO bodies of unequal weight (say a guinea and a feather) are placed at the same height under the exhausted receiver of an air-pump. When released, they are observed to reach the bottom of the vessel at the same instant of time, or, in other words, to fall in equal times. From this fact, it is inferred that a repetition of the experiment either with these two bodies or with any other bodies would be attended with the same result, and that, if it were not for the resistance of the atmosphere and other impeding circumstances, all bodies, whatever their weight, would fall through equal vertical spaces in equal times. Now, that these two bodies in this particular experiment fall to the bottom of the receiver in equal times is merely a fact of observation, but that they would do so if we repeated the experiment, or that the next two bodies we selected, or any bodies, or all bodies, would do so, is an inference, and is an inference of that particular character which is called an Inductive Inference or an Induction 1.

1 The student must throughout bear in mind the ambiguous use of the words Induction, Inference, &c., as signifying both the result and

What assumptions underlie this inference, and on what grounds does it rest?

My object in placing the two bodies under the receiver was obviously to answer a question which I had previously addressed to myself: viz. whether, when subject to the action of gravity2 only, they would fall in equal or in unequal times. By exhausting the air in the receiver, I am able to isolate the phenomenon, and thus, by removing all circumstances affecting the bodies, except the action of gravity, to watch the effect of this cause operating alone. But in trying this experiment, in isolating the phenomenon, and asking what will be the effect of the action of gravity operating alone, I am evidently assuming that the effect, whatever it may be, will be entirely due to the cause or causes which are then and there in action; in other words, I am assuming that nothing can happen without a cause, that no change can take place without being preceded or attended by circumstances which, if we were fully acquainted with them, would fully account for that change. This assumption (which may be called the Law of Universal Causation) is universally admitted by mankind, or at least by the

the process by which the result is arrived at. See Deductive Logic, Preface, and Part III. ch. i. note 1.

2 When I employ the expression action of gravity' or 'force of gravity,' I must not be understood as adopting any particular theory on the nature of the phenomenon which we call 'gravitation.' I use these terms simply because they are short and recognised phrases for expressing the fact that all terrestrial bodies, when left entirely free, fall in the direction of the earth's centre.

reflecting portion of mankind, though the grounds on which it is admitted have been variously stated; some justifying it by an appeal to the continuous and uncontradicted experience not only of the individual himself but of the human race, others by an appeal to the necessities of thought.

Thus far, however, we have only ascertained that the fact of these two particular bodies, in this particular instance, falling to the ground in equal times is due to the action of gravity, unimpeded by any other circumstances. But why should I infer that they, if the experiment were repeated, or any other two bodies, if exposed to the same circumstances, would behave in the same way? It is not enough to feel assured that nothing can happen without a cause, and that the only cause operating in this particular instance is the action of gravity; I must also feel assured that the same cause will invariably be followed by the same effect, or, to speak more accurately, that the same cause or combination of causes, will, if unimpeded by the action of any other cause or combination of causes, be invariably followed by the same effect or combination of effects, or, to state the same proposition in somewhat different language, that, whenever the same antecedents, and none others, are introduced, the same consequents will invariably follow. This assump

The

3 The expression 'will' is used for the sake of brevity. argument, however, is not simply from the present to the future, but from cases within the range of our experience to all cases, past, present, or future, without that range. See p. 31, note 27.

tion (or law) is, like the former, universally admitted by mankind, or the reflecting portion of mankind, though the grounds on which it is admitted have been variously stated, some, as in the case of the former law, referring it to experience, others to certain necessities of thought arising from the original constitution of the human mind. This law may be called the Law of the Uniformity of Nature".

The argument, then, in the case which we have selected as our instance, may be represented as follows:

I observe that these two bodies (though of unequal weight) reach the bottom of the receiver at the same moment.

This fact must be due to some cause or com

bination of causes (Law of Universal Causation). The only cause operating in this instance is the action of gravity.

.. The fact that these two bodies reach the bottom of the receiver at the same moment is due to the

action of gravity, operating alone.

But, whenever the same cause or combination of causes is in operation, and that only, the same effect will invariably follow (Law of Uniformity of Nature).

It is, perhaps, necessary thus early to warn the student that the converse of the Law of the Uniformity of Nature does not hold true. Though the same cause, that is, the same antecedent or combination of antecedents, is never followed by different effects, the same effect may be due to different causes. We can, thus, always argue from the cause to the effect, but we cannot always argue from the effect to the cause.

.. Whenever these two bodies, or any other two or more bodies (even though of unequal weight), are subject to the action of gravity only, they will reach the bottom of the receiver at the same moment, or, in other words, will fall in equal times.

The induction just examined has been arrived at by a process of elimination, and takes for granted the conception of causation. It is representative of the inductions with which science is mainly concerned, and of which we shall have, for the most part, to treat in the present work. But there are other inductions of a simpler character, the validity of which is assured not by any artificial process of elimination, but merely by a series of uncontradicted experiences. This kind of induction is usually distinguished by logicians as Inductio per Enumerationem Simplicem. It is often (as will hereafter be pointed out in the 4th chapter) exceedingly untrustworthy, but, when the area of experience is very wide, the evidence which it affords may approach to, and even amount to, certainty. Often moreover, and especially in the case of our widest generalisations, it is our only resource.

Amongst inductions of this kind must be included, as we conceive, the Laws of Uniformity of Nature and Universal Causation themselves, as well as the axioms of mathematics and certain facts of coexistence which have not yet been resolved into, or possibly do not admit of being resolved into, facts of causation. As examples of the last class we may specify the coexistence throughout

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