Observation and experiment, therefore, are wholly outside the province of formal logic. The only question is, whether they have any claim to consideration under the head of applied logic; whether as means of adding to the propositions that we regard as certain and adopt as such, they should be examined into, and the results to which they lead tested. As to their other qualifications for admission into the mind, this depends on a further question. Do the various methods which were first inaugurated by Bacon and subsequently developed by those who have followed in his steps give us certainty at all, and if so, what sort of certainty ?

Probably no one in his senses will deny that external observation can give us certainty. That the sun will rise to-morrow morning, that a stone thrown into the air will fall to earth again, are as certain as anything can be that does not depend on the inner laws that regulate all being. But such a certainty is, strictly speaking, always a practical or hypothetical, never an essential or absolute certainty. It is within the bounds of absolute possibility. But some unknown comet might intervene between the earth and the sun during the coming night, or, some undiscovered and mysterious influence might whisk away our stone to the moon, not to mention the further possibility of Divine interference by what we call a miracle.

But in the case of a priori laws no miracle can intervene, no possible hypothesis can set them aside. God Himself cannot make five out of two and two, or prevent things equal to the same thing. from being equal to one another, or cause the exterior angle of any plane triangle to be less than either of the interior and opposite angles. It is beyond the utmost limit of Divine omnipotence to bring about either of these, because they are in themselves contradictory, and would, if they could be realized, make God a liar. These a priori laws are not merely laws of thought and of human reason, but of being and of the Divine nature. They are based upon the nature of God Himself, and thus on Eternal and Immutable Truth.

Not so the physical laws at which we arrive by observation and experiment. God could reverse them all to-morrow, if He chose. He does, from time to time, intervene and hinder their efficacy. They are not founded on the Divine nature, but in the Divine enactment. They are, therefore, liable to exceptions, and this is why we say that they have only a hypothetical or conditional certainty.

Not only can God

But they have another source of weakness. set them aside at any moment if He pleases, but we are not absolutely certain that they exist at all. All that we call physical laws

are but magnificent hypotheses. We have not the means of arriving at any absolute certainty when once we depart from those laws which are stamped on all being, and therefore on the human intellect, which are the very conditions under which we think, because the conditions under which all things, even God Himself, necessarily exist. When we come to laws that are purely a posteriori, we never can say more than that they are generalizations from experience, that they explain all the facts known to us, and that they satisfy every test we can apply to them. Such is the law of gravity, the undulatory theory of light, the laws of attraction and distance, etc. All this gives us physical certainty respecting them, but this is utterly inferior to absolute certainty. It is the attainment of physical certainty which is regulated by the various methods that have come in since the time of Bacon, and it cannot be denied that these methods were an object of comparative indifference and neglect to scholastic and Aristotelian philosophy. The pre-Reformation world did not recognize the importance of those modern discoveries and inventions which have revolutionized the world since the days of Bacon. With the Aristotelian philosophy dominant, the steam-engine, gas, the electric light, steam-looms, sewing-machines, and all the mechanical substitutes for human labor would either not have existed at all, or never arrived at their present perfection. The a priori method had no room for hypothesis, and hypothesis is the fertile mother of physical research and discovery. Whether all those have really fostered human progress, whether they have made men stronger, healthier, more honest, virtuous, and happy, is a point which does not concern us. We have already wandered too far away from the question before us, which is this: Are we to admit into logic, in its wider sense, what are called the inductive methods, and which are elaborated with wonderful skill and ability by John Stuart Mill?

Among the functions of natural or applied logic, one of the most important is to distinguish between certitude and probability, and also to separate the various kinds of certitude one from the other. But when once we have passed from the highest kind of certitude to a lower level, from metaphysical to physical certitude, it does not belong to the logician to elaborate with minute care the various conditions necessary for attaining to the latter. It would be misleading for him to dwell on them with too much detail; it would have a tendency to raise in the estimation of mankind the laws that are based on them to an equality with the a priori laws; to exalt hypothesis into law, to lead men to confound practical with absolute certainty, to obliterate the distinction between the eternal, the immutable, and the transitory, the contingent, the mutable. Yet in spite of all this, they cannot be passed over, and ought not

to be passed over unnoticed, in the present day. They are too important a factor in the present condition of human society to admit of our neglecting them; they are weapons which have been forged by what is called the march of human intellect, and it would be suicidal to deny their value and their efficacy. Besides, we ought to master them in order to protest against their abuse. We must give them their due in order that they may not usurp the whole field of human science. Mill and his followers drag down all the a priori laws to the level of the a posteriori, or rather deny the existence of a priori laws at all. This is the fatal result of the departure from the old scholastic method, which began at the" Reformation," and has been carried farther, day by day. But, fas est et ab hoste doceri; and the various methods set forth in detail by Mill have, in their own proper limits, a most important function to perform, and are of constant application to our everyday life.

We have now to return to our consideration of the premises which assert the representative nature of the instances on which we are going to base our law. Our methods are to give us the means of ascertaining this. They are to decide for us whether what is true of the instances under our consideration is true of all instances, real or possible; or, at least, they are to settle the question for us as far as it is possible in the nature of things to arrive at any certainty respecting it.

Our premisses then asserted that what was true of January 14th, etc., is true of all days on which the barometer falls, and the value of our argument depends on our being able to establish this proposition. What is necessary to prove it satisfactorily is to show that these days had nothing in common which could possibly be connected with the approach of rainy weather, save a certain heaviness in the air indicated by the fall in the barometer. If this could be ascertained beyond a doubt, then we should have a perfect physical certainty that there was a connection of cause and effect between the heaviness in the air and the subsequent rain. But in point of fact we never can be sure that there are not other characteristics common to these days which might be the source of the phenomenon of rain. To be absolutely certain would require a knowledge of the inner nature of things, which even the greatest scientist does not possess. All that we can say is, that we are unable to detect any common characteristic in the days in question which would account for the subsequent rain, save only the heaviness in the air and the consequent fall of the barometer, and therefore the connection between the rain and the heaviness in the air is at most but a strong probability.

Here, then, we have a case of the first of Mr. Mill's experimental methods, the Method of Agreement. We cannot do better than formulate it in his own words: If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon.

Our readers will observe that in this law Mr. Mill goes beyond the requirements we have given above, and exacts not only the presence of no common circumstance which could account for the result save one, but absolutely the presence of no common circumstance at all save one alone. To establish this will be still more impossible, therefore we can derive from the employment of this method nothing more than a strong probability. There are no two phenomena in the world which have not one common cir

cumstance.

But there is another method which comes in to supplement the former. Let us suppose that we find a day exactly corresponding to one of the days aforenamed in every circumstance save one, viz., the weight of the air. In all else they are exactly alike. When we examine the rain record of the year we find that on the day when the air was heavy rain followed, and on the day when it was light fine weather came after it. Here too we should again have perfect physical certainty, if only we could find two days corresponding exactly in every possible circumstance save one. There would be no doubt whatever as to the connection of the circumstance with the result that was present when the circumstance in question was present, absent when the circumstance was absent. But here, too, it is impossible to find any two such days; there must of necessity be a dozen points of difference between the two. All that we can have is a certain amount of correspondence, and the absence of any points of difference which seem likely to be connected with the result, save the single circumstance which is conspicuous for its presence in the one case and for its absence in the other. Here, therefore, we are again limited to a probable connection and can get no further.

In this case we have an instance of the Method of Difference; we will again give it in Mr. Mill's own words:

"If an instance in which the phenomenon under investigation occurs and another in which it does not occur have every circumstance in common save one, that one occurring only in the former, the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause of the phenomenon."

But this second method, as Mr. Mill very pertinently remarks, is applicable rather to experiment than to observation, that is, to

cases where we can artificially vary the antecedents instead of having to receive them ready made. We will, therefore, take another instance, which will moreover have the advantage of illustrating other methods of inductive research which cannot be so easily applied to the case of the weather.

We will take a familiar and very practical case: We have of late from time to time risen with a headache in the morning for which we cannot account. Somehow we fancy it must be connected with some sort of digestive disarrangement and that this disarrangement is the result of some food that we have taken and that does not suit our stomach. One day it occurs to us that our headache always follows upon a special dish, and that possibly this might be its cause. We therefore take note of what we have for dinner, and after a little experience we discover that in most cases when we have eaten of jugged hare for dinner, we have had a headache the next morning. We set to work to test the connection by means of the methods of agreement and difference. First of all, we take a number of days when our dinner has been as varied as possible; on one day we have taken soup, on another day not; on one day we have had beef for the chief dish, on another mutton, on another veal, and on another pork. On one day we have drunk port wine, on another sherry, on another hock, on another champagne, on another claret, on another nothing but water. On one day we have partaken of pastry, on another not; on one day cheese, on another not, and so on ad indefinitum, varying our dinner in every possible way on the days of trial. But on all these days there has been the common element of jugged hare, and on each of them there has been a headache following. Here we have a good instance of the method of agreement.

But we cannot be certain that there may not have been some other cause for our headache which happened to coincide with the jugged hare. We may have been rather tired on the evenings in question, or, perhaps, a little more thirsty than usual, and the port wine may have been more attractive than on other days. So we proceed to a further experiment. On two given days we take the same amount of exercise, and order exactly the same dinner, drink the same amount of wine and go to bed at the same hour. The only difference between these two days is that on the former we make jugged hare an item in our bill of fare, and on the other omit it. The result is that the former day is followed by a severe headache, whereas after the latter we rise fresh and ready for busi

ness.

Here we have the method of difference. At first the experiment seems decisive, but it is not so. It may be the mere addition of