PART III.-OF INFERENCES.

CHAPTER I.

On the Various Kinds of Inferences.

THE third and most important part of Logic treats of Inferences1. Wherever we assert a proposition in consequence of one or more other propositions, or, in other words, wherever we regard one or more propositions as justifying us in asserting a proposition distinct from any that has preceded, the combination of propositions may be regarded as an inference. Thus defined, inferences may be divided into inductive and deductive, and deductive inferences may be sub-divided into mediate and immediate. I shall attempt to make these distinctions clear by examples.

1 The word 'inference' is employed in no less than three different senses. It is sometimes used to express the conclusion in conjunction with the premiss or premisses from which it is derived, as when we speak of a syllogism or an induction as an inference; sometimes it is used to express the conclusion alone; sometimes the process by which the conclusion is derived from the premisses, as when we speak of Induction or Deduction as inferences or inferential processes. Except where the meaning is obvious from the context, I shall endeavour to confine the word to the first named signification. The terms Induction and Deduction will be appropriated to express processes which result, the former in inductions or inductive inferences, the latter in deductions or deductive inferences, these last being subdivided into syllogisms and immediate inferences.

I mix tartaric acid and carbonate of soda in certain proportions in water, and I observe that the mixture is followed by an effervescence; from this I infer that, whenever tartaric acid and carbonate of soda are mixed in water in these proportions, effervescence will follow. I put a poker into the fire, and I observe that after a time it becomes red-hot; from this I infer that incandescence can always be produced in iron by a certain degree of heat. I observe five points in the orbit of a planet, and, assuming that the orbit is a curve of the second degree, my knowledge of mathematics enables me to say that they are situated in an ellipse: from this I infer that the entire orbit of the planet is elliptical, and that, in all future revolutions of the planet, a similar orbit will be described. Now what in these cases do I mean by the word 'infer'? That the mixture is followed by effervescence is a matter of observation; but it is only an inferential process which justifies me in asserting that, inasmuch as it could have been produced by nothing else, the effervescence was produced by the mixture, and that, whenever in future I see a similar mixture, I may expect to see it followed by similar results. Two assumptions, it will be seen, underlie this inference: 1st, that every event has a cause, which leads me to assume that the effervescence must have been produced by some cause or other; 2nd, the belief in the uniformity of nature, which leads me to expect that, whenever similar circumstances are repeated, they will be followed by similar results. The reasoning therefore in these cases may be represented as follows:

The mixture of the tartaric acid with the carbonate of soda is followed by effervescence. (Original Proposition.)

.: (Owing to the special circumstances of the case and in accordance with the principle that every event must have a cause), the effervescence was produced by the mixture.

.. (In accordance with the principle of the uniformity of nature), a similar mixture will always be followed by an effervescence.

We may represent the reasoning in the third example in the same manner :—

We may assert (by virtue of our knowledge of

mathematics) that five points which we have observed in the orbit of the planet Mars are, on the assumption above stated, situated in the arc of an ellipse. (Original Proposition.)

.. As there are, comparatively speaking, no causes determining the position of the planet at any given moment, except the attraction of the sun and the continued effects of the initial velocity, we may infer that the fact of the five points observed in the planet's course being all situated in the arc of an ellipse is due to the combination of these

two causes.

.. (In accordance with the principle of the uniformity

of nature), it may be inferred that all other points in the orbit of the planet are situated in an ellipse, and that, in all future revolutions, a similar orbit will be described; i. e. the orbit of the planet

Mars may be regarded as elliptical.

Now inferences of this kind are called Inductive. The instances I have selected are remarkably simple, but they are sufficient to shew that an induction may be defined as an inference in which we argue from particulars to adjacent particulars, or (if we speak of the adjacent particulars collectively) from particulars to universals, in accordance with the laws of universal causation and of the uniformity of nature. As to the circumstances which justify us in asserting that one phenomenon or set of phenomena is the cause or the effect of, or is invariably conjoined with, another (for this is the problem of Induction), the student is referred to works specially treating of Inductive Inference. It is sufficient here to distinguish inductive from the deductive inferences which it is our more special business to explain 2.

2 An Analogy is a form of imperfect induction, and, though justifying a conclusion more or less probable, never leads to certainty. If two objects resemble each other in several important respects, and we argue that any particular attribute which we know to be predicable of the one, and do not know to be either predicable or not predicable of the other, is, on account of the general resemblance of the two objects, also predicable of the other, the argument is called an argument from analogy; and, in the same way, if two objects are dissimilar, we may argue that an attribute which is predicable of the one, is, on account of their dissimilarity, not predicable of the other. Thus, from the similarity between the earth and the moon, we might

Beginning where induction ended, we may state such All iron when heated to a

a proposition as this:

argue that the latter is inhabited, or, from their dissimilarity, that it is not inhabited. The value of the inference always depends on the ratio of the ascertained resemblances to the ascertained differences (it being understood that the resemblances which we take into account are none of them derived, as properties, from each other, and so with the differences), providing that our knowledge of the objects is sufficiently large to justify us in drawing any inference at all. For a more detailed analysis of this mode of reasoning, and an estimate of the value to be attached to its conclusions, the student is referred to the author's Elements of Inductive Logic, ch. iv., and to Mr. Mill's Logic, Bk. III. ch. xx., one of the most instructive and important chapters in his work.

It should be noticed that an analogy, as here described, is not identical with the Analogy of Aristotle, the Aristotelian Analogy being an equality of relations (ioórŋs λóywv). Thus the expression, The intellect the soul = the sight: the body,

is an ávaλoyía. From this analogy it is argued that anything which may be predicated of the one pair of terms may be predicated also of the other. Or, to take a non-Aristotelian instance, which will be more intelligible to beginners:

A colony the mother-country = a child: a parent.

From this analogy it is argued that the reciprocal rights and duties of a colony and the mother-state are the same as those of a child and a parent. In this form of argument, if the relations between the two sets of terms were precisely the same in all respects, the conclusion would be invariably valid; as it is usually found in practice, however, the relations are the same in some respects, but not in others, and, consequently, the conclusion is valid, when based on those points in which the relations are the same, and invalid, when based on those points in which the relations are not the same. Thus, it might be maintained that, in many respects, the relation of the child to the parent is not the same as that of a colony to the mothercountry, and, hence, that many of the rights and duties which exist