by analogy. We gradually come to learn the main classes of exceptions to it, and to feel some degree of confidence that, these apart, what is rigidly true in the limit will be sufficiently near the truth for practical purposes at some considerable distance from the limit.

The reader may think that it is unworthy of science to take notice of such considerations as this. But if we propose to systematize the principles on which we do actually depend when we are drawing our daily inferences about future or distant matters of concrete fact, surely no doubts can be raised as to the legitimacy of their introduction. The metaphysicians have been too much in the habit of treating the Law of Causation as if it was not only expressible in a rigidly accurate form, but also capable of practical appeal in that form, and this has set up an altogether false standard of certainty to the inductive logicians, who have naturally wished not to fall behindhand in respect of what they claim. Accordingly there has been too much of a tendency to omit whole classes of considerations upon which sound and reasonable persons unhesitatingly rely every day of their lives in speculation and practice alike.

A number more of generalizations, or wide uniformities, might easily be added to the above; but the attempt to enumerate them would soon lead us into the province of this or that special science, which is generally far more competent to treat them.

One of these indeed ought not to be passed by entirely without notice, since it has received the support of Mr H. Spencer. I allude to that tendency towards Differentiation, which he regards as of universal prevalence and as admitting of à priori proof, and which he terms "the Instability of the Homogeneous." That this principle holds true in a great variety of cases is indisputable, as no one has better shown than its author; but it seems to me to be of a highly derivative character, and to depend upon so many conditions that each separate science must determine to what extent it can be admitted within its borders. To glance at a couple of instances only. When we are dealing with bodies on the earth's surface, as in Geology or Physiography, this tendency is very prevalent. When a stream is started down a hill side each resultant change tends to breed further change, and thus to continually enlarge

the heterogeneity. But when we are dealing with molecules, what we know of their behaviour suggests that their tendencies mostly lie in the other direction. Take a quantity of different gases, and mix them with what heterogeneity we please in any confined space. They will tend continuously towards the homogeneous, and will not rest until they have obliterated every trace of the original disturbance or arrangement, and diffused themselves uniformly throughout.

CHAPTER V.

THE SUBJECTIVE FOUNDATIONS OF INDUCTION.

WE have now examined, with sufficient minuteness and care for our present purposes, what may be called the objective or material foundations of an Inductive system of Logic. But, in accordance with the general view already insisted on, such an examination deals only with one side of our subject. Logic is neither a purely objective nor a purely subjective science, but essentially and almost exclusively a science which involves both aspects of things. It concerns itself with the operations of the human mind when drawing inferences about the phenomena of nature. Accordingly we must now enter into some examination of the second, or mental, side of the enquiry, by ascertaining the nature of the postulates which have to be demanded from the regions of Psychology or Metaphysics before a System of Inference can be constructed.

I. To begin with; it is extremely obvious that the ordinary powers of observation must be taken for granted. Logic, by universal admission, in every application we make of it, starts from premises which have been obtained from observation, directly or remotely. We must therefore include, amongst our postulates, the existence of these powers of observation. As however this is in no way peculiar to Logic, but applies in an equal or even greater degree to many of the special sciences, we need not pause to examine it as a general postulate.

Where the question does force itself upon our notice, and indeed, as we are about to see, raises some very perplexing problems, is not so much in respect of the mere assumption of these powers, or in the assignment of their general character, ✓ but rather in the attempted determination of their boundary line. Where, in fact, are we to suppose that pure Observation

ends and true Inference begins? In a Science of Inference such a question as this is a serious one; and it must be frankly admitted that any doubts and difficulties which we encounter in answering it are a flaw in the theoretic perfection of the science. Unfortunately however there seems no way of completely removing such doubts, and all that we can do is to minimize their consequences.

Any simple example will serve to illustrate the difficulty. Suppose I am on a walking tour, and a stranger proposes to join our party; I give a glance at him and say to my friend, 'I can see plainly enough that he will not be fit for our excursion to-day'. Now though this remark is couched in the language of mere observation any one uttering it would not need to be reminded that it is a mixture of observation and inference; and if he spoke with less colloquial abbreviation he would intimate the distinction by expressing himself somewhat as follows,-'I can see that the man is ill, and therefore I conclude he cannot take a long walk'. In common parlance the present illness is an observation, and the inability to take the walk is an inference. We might not be consciously thinking of the distinction at the time, but this is the sort of analysis we should instantaneously make when attention was directed to the point. Our plain man would reply 'you can see for yourself the state he is in. Just look at him, how ill he is', and so forth.

Now it is a merely elementary step in analysis to point out that the whole state of the man, bodily and mental, which is involved in the 'illness', is largely a conclusion founded on data. The very expression 'symptom', so commonly applied to diseases, is an illustration that the distinction has been recognized as far as this by all but the rudest and most unobservant. So far then we have pushed the observation a stage further back, having resolved it into such elements as the paleness, the lax or stooping gait, perhaps the quickness of breathing, and so forth, which are considered to be the symptoms of the disease.

But then begins again the never-ending process of analysis as applied to these elements themselves. For shortness, take but one of these, the paleness, where we are purposely confining ourselves to a characteristic which seems about as simple and elementary as experience can furnish, viz. one of colour pure and simple. But the psychologist has something to say about

this. It admits of simple proof that the colour of the man's face, as perceived by us, varies vastly more according as we see it by daylight or candlelight, or even according as he stands somewhat more or less in the shade, than it can possibly vary according to the extremest conditions of health and sickness whilst the light remains the same. That is, our subjective estimate of such a simple and apparently ultimate datum as this of mere colour is in great part a judgment or inference. What we really saw is so instantly corrected and allowed for that it actually drops out of notice, whilst what is effectively retained is something so different from the former that it must be regarded as very largely consisting of inference. Again; suppose that by an effort of reflection, and comparison of the same shade under varying conditions, we had enabled ourselves to estimate the colour as it was, that is, as it should be under normal circumstances,-and the psychologist knows what a piece of work this would be,-was it really true that we saw, as we supposed, a surface of that colour? It is highly unlikely that we did so. What any ordinary glance takes in, when directed towards a surface, is nothing more than a succession of points which are supplemented and filled in by something else than sight. At least this is all that is perceived by the central spot of the retina which alone is capable of clear vision. How obstinately our senses refuse to undertake the drudgery of examining every separate detail in the objects we inspect, even when we are gazing upon them with some care, is only too well known to those who have ever worked through a proof sheet as it came from the press. The almost inevitable impulse is to take in a few letters and thence to infer the whole word, and even from a part of a sentence to infer the rest; and it requires a strong and persistent effort to insist that the eye shall not thus shirk its work of adequate observation.

Finally; take as minute a fragment of visible area as we choose, so as to avoid any such spatial filling in as that just indicated: is the impression really continuous, either in time or space? Confine ourselves, for the sake of brevity, to the former continuity. It is approximately certain in the case of sight, and quite certain in the case of sound, that what seems to us to be a continuous elementary impression is really made up of distinct nervous impulses or shocks. We are not referring here to the