who speak so much of the value of facts may understand the meaning of fact, but they evidently do not understand the meaning of value. For, the value of a thing is not a property residing in that thing, nor is it a component; but it is simply its relation to some other thing. We say, for instance, that a five-shilling piece has a certain value; but the value does not reside in the coin. If it does, where is it? Our senses can not grasp value. We can not see value, nor hear it, nor feel it, nor taste it, nor smell it. The value consists solely in the relation which the five-shilling piece bears to something else. Just so in regard to facts. Facts, as facts, have no sort of value, but are simply a mass of idle lumber. The value of a fact is not an element or constituent of that fact, but is its relation to the total stock of our knowledge, either present or prospective. Facts, therefore, have merely a potential, and, as it were, subsequent value, and the only advantage of possessing them is the possibility of drawing conclusions from them; in other words, of rising to the idea, the principle, the law which governs them. Our knowledge is composed not of facts, but of the relations which facts and ideas bear to themselves and to each other; and real knowledge consists not in an acquaintance with facts, which only makes a pedant, but in the use of facts, which makes a philosopher. Looking at knowledge in this way, we shall find that it has three divisions: Method, Science, and Art. Of method I will speak presently; but I will first state the limits of the other two divisions. The immediate object of all art is either pleasure or utility: the immediate object of! all science is solely truth. As art and science have different objects, so also have they different faculties. The faculty of art is to change events; the faculty of science is to foresee them. The phenomena with which we deal are controlled by art; they are predicted by science. The more complete a science is, the greater its power of prediction; the more complete an art is, the greater its power of control. Astronomy, for instance, is called the queen of the sciences, because it is the most advanced of all; and the astronomer, while he abandons all hope of controlling or altering the phenomena, frequently knows what the phenomena will be years before they actually appear; the extent of his foreknowledge proving the accuracy of his science. So, too, in the science of mechanics, we predict that, certain circumstances being present, certain results must follow; and having done this, our science ceases. Our art then begins, and from that moment the object of utility and the faculty of control come into play; so that in the art of mechanics, we alter what in the science of mechanics we were content to foresee. One of the most conspicuous tendencies of advancing civilization is to give a scientific basis to that faculty of control which is represented by art, and thus afford fresh prominence to the faculty of prediction. In the earliest stage of society there are many arts, but no sciences. A little later, science begins to appear, and every subsequent step is marked by an increased desire to bring art under the dominion of science. To those who have studied the history of the human mind, this tendency is so familiar that I need hardly stop to prove it. Perhaps the most remarkable instance is in the case of agriculture, which, for thousands of years, was a mere empirical art, resting on the traditional maxims of experience, but which, during the present century, chemists began to draw under their jurisdiction, so that the practical art of manuring the ground is now explained by laws of physical science. Probably the next step will be to bring another part of the art of agriculture under the dominion of meteorology, which will be done as soon as the conditions which govern the changes of the weather have been so generalized as to enable us to foretell what the weather will be. General reasoning, therefore, as well as the history of what has been actually done. justify us in saying that the highest, the ripest, and the most important form of knowledge, is the scientific form of predicting consequences; it is therefore to this form that I shall restrict the remainder of what I have to say to you respecting the influence of women. And the point which I shall attempt to prove is, that there is a natural, a leading, and probably an indestructible element, in the minds of women, which enables them, not indeed to make scientific discoveries, but to exercise the most momentous and salutary influence over the method by which discoveries are made. And as all questions concerning the philosophy of method lie at the very root of our knowledge, I will, in the first place, state, as succinctly as I am able, the only two methods by which we can arrive at truth. The scientific inquirer, properly so called, that is, he whose object is merely truth, has only two ways of attaining his result. He may proceed from the external world to the internal; or he may begin with the internal and proceed to the external. In the former case he studies the facts presented to his senses, in order to arrive at a true idea of them; in the latter case he studies the ideas already in his mind, in order to explain the facts of which his senses are cognizant. If he begin with the facts his method is inductive; if he begin with the ideas it is deductive. The inductive philosopher collects phenomena either by observation or by experiment, and from them rises to the general principle or law which explains and covers them. The deductive philosopher draws the principle from ideas already existing in his mind, and explains the phenomena by descending on them, instead of rising from them. Several eminent thinkers have asserted that every idea is the result of induction, and that the axioms of geometry, for instance, are the product of early and unconscious induction. In the same way Mr. Mill, in his great work on Logic, affirms that all reasoning is in reality from particular to particular, and that the major premiss of every syllogism is merely a record and register of knowledge previously obtained. Whether this be true, or whether, as another school of thinkers asserts, we have ideas antecedent to experience, is a question which has been hotly disputed, but which I do not believe the actual resources of our knowledge can answer, and certainly I have no intention at present of making the attempt. It is enough to say that we call geometry a deductive science, because, even if its axioms are arrived at inductively, the inductive process is extremely small, and we are unconscious of it; while the deductive reasonings form the great mass and difficulty of the science. To bring this distinction home to you, I will illustrate it by a specimen of deductive and inductive investigation of the same subject. Suppose a writer on what is termed social science, wishes to estimate the influence of different habits of thought on the average duration of life, and taking as an instance the opposite pursuits of VOL XLIV.-NO. II. poets and mathematicians, asks which of them live longest. How is he to solve this? If he proceeds inductively he will first collect the facts, that is, he will ransack the biographies of poets and mathematicians in different ages, different climates, and different states of society, so as to eliminate perturbations arising from circumstances not connected with his subject. He will then throw the results into the statistical form of tables of mortality, and on comparing them will find, that notwithstanding the immense variety of circumstances which he has investigated, there is a general average which constitutes an empirical law, and proves that mathematicians, as a body, are longer lived than poets. This is the inductive method. On the other hand, the deductive inquirer will arrive at precisely the same conclusion by a totally different method. He will argue thus: poetry ap peals to the imagination, mathematics to the understanding. To work the imagination is more exciting than to work the understanding, and what is habitually exciting is usually unhealthy. But what is usually unhealthy will tend to shorten life; therefore poetry tends more than mathematics to shorten life; therefore on the whole, poets will die sooner than mathematicians. You now see the difference between induction and deduction; and you see, too, that both methods are valuable, and that any conclusion must be greatly strengthened if we can reach it by two such different paths. To connect this with the question before us, I will endeavor to establish two propositions. First, That women naturally prefer the deductive method to the inductive. Secondly, That women by encouraging in men deductive habits of thought, have rendered an immense though unconscious service to the progress of knowledge, by preventing scientific investigators from being as exclusively inductive as they would otherwise be. In regard to women being by nature more deductive, and men more inductive, you will remember that induction assigns the first place to particular facts; deduction to general propositions or ideas. Now, there are several reasons why women prefer the deductive, and, if I may so say, ideal method. They are more emotional, more enthusiastic, and more imaginative than men; they therefore live more in an 13 ideal world; while men, with their colder, | more ideal world, and therefore prefer a harder, and austerer organizations, are method of inquiry which proceeds from more practical and more under the do- ideas to facts; leaving to men the oppominion of facts, to which they consequent- site method of proceeding from facts to ly ascribe a higher importance. Another ideas. circumstance which makes women more deductive, is that they possess more of what is called intuition. They can not see so far as men can, but what they do see they see quicker. Hence, they are constantly tempted to grasp at once at an idea, and seek to solve a problem suddenly, in contradistinction to the slower and more laborious ascent of the inductive investigator. That women are more deductive than men, because they think quicker than men, is a proposition which some persons will not relish, and yet it may be proved in a variety of ways. Indeed, nothing could prevent its being universally admitted except the fact, that the remarkable rapidity with which women think is obscured by that miserable, that contemptible, that preposterous system, called their education, in which valuable things are carefully kept from them, and trifling things carefully taught to them, until their fine and nimble minds are too often irretrievably injured. It is on this account, that in the lower classes the superior quickness of women is even more noticeable than in the upper; and an eminent physician, Dr. Currie, mentions in one of his letters, that when a laborer and his wife came together to consult him, it was always from the woman that he gained the clearest and most precise information, the intellect of the man moving too slowly for his purpose. To this I may add another observation which many travelers have made, and which any one can verify; namely, that when you are in a foreign country, and speaking a foreign language, women will understand you quicker than the men will; and that for the same reason, if you lose your way in a town abroad, it is always best to apply to a woman, because a man will show less readiness of apprehension. These, and other circumstances which might be adduced-such, for instance, as the insight into character possessed by women, and the fine tact for which they are remarkable-prove that they are more deductive than men, for two principal reasons. First, Because they are quicker than men, Secondly, Because, being more emotional and enthusiastic, they live in a My second proposition is, that women have rendered great though unconscious service to science, by encouraging and keeping alive this habit of deductive thought; and that if it were not for them, scientific men would be much too inductive, and the progress of our knowledge would be hindered. There are many here who will not willingly admit this proposition, because, in England, since the first half of the seventeenth century, the inductive method, as the means of arriving at physical truths, has been the object, not of rational admiration, but of a blind and servile worship; and it is constantly said, that since the time of Bacon all great physical discoveries have been made by that process. If this be true, then of course the deductive habits of women must, in reference to the progress of knowledge, have done more harm than good. But it is not true. It is not true that the greatest modern discoveries have all been made by induction; and the circumstance of its being believed to be true, is one of many proofs how much more successful Englishmen have been in making discoveries than in investigating the principles according to which discoveries are made. The first instance I will give you of the triumph of the deductive method, is in the most important discovery yet made respecting the inorganic world; I mean the discovery of the law of gravitation by Sir Isaac Newton. Several of Newton's other discoveries were, no doubt, inductive, in so far as they merely assumed such provisional and tentative hypotheses as are always necessary to make experiments fruitful. But it is certain that his greatest discovery of all was deductive, in the proper sense of the word; that is to say, the process of reasoning from ideas was out of all proportion large, compared to the process of reasoning from facts. Five or six years after the accession of Charles II., Newton was sitting in a garden, when (you all know this part of the story) an apple fell from a tree. Whether he had been already musing respecting gravitation, or whether the fall of the apple directed his thoughts into that channel is uncertain, and is immaterial to my present fall of the apple was the cause of the discovery, and then to adduce that as a confirmation of the idle and superficial saying "that great events spring from little causes," only shows how unable such writers are to appreciate what our masters have done for us. No great event ever sprung, or ever will spring, from a little cause; and this, the greatest of all discov eries, had a cause fully equal to the effect produced. The cause of the discovery of the law of gravitation was not the fall of the apple, nor was it any thing that occurred in the external world. The cause of the discovery of Newton was the mind of Newton himself. purpose, which is merely to indicate the course his mind actually took. His object was to discover some law, that is, rise to some higher truth respecting gravity than was previously known. Observe how he went to work. He sat still where he was, and he thought. He did not get up to make experiments concerning gravitation, nor did he go home to consult observations which others had made, or to collate tables of observations: he did not even continue to watch the external world, but he sat, like a man entranced and enraptured, feeding on his own mind, and evolving idea after idea. He thought that if the apple had been on a higher tree, if it had been on the highest known The next instance I will mention of tree, it would have equally fallen. Thus the successful employment of the à prifar, there was no reason to think that the ori, or deductive method, concerns the power which made the apple fall was sus- mineral kingdom. If you take a crystalceptible of diminution; and if it were not lized substance as it is usually found in nasusceptible of diminution, why should it ture, nothing can at first sight appear be susceptible of limit? If it were unlim- more irregular and capricious. Even in ited and undiminished, it would extend its simplest form, the shape is so various above the earth; it would reach the moon as to be perplexing; but natural crystals and keep her in her orbit. If the power are generally met with, not in primary which made the apple fall was actually forms, but in secondary ones, in which they able to control the moon, why should it have a singularly confused and uncouth asstop there? Why should not the planets pect. These strange-looking bodies had also be controlled, and why should not long excited the attention of philosophers, they be forced to run their course by the who, after the approved inductive fashion, necessity of gravitating towards the sun, subjected them to all sorts of experiments; just as the moon gravitated towards the divided them, broke them up, measured earth? His mind thus advancing from them, weighed them, analyzed them, thrust idea to idea, he was carried by imagina- them into crucibles, brought chemical tion into the realms of space, and still agents to bear upon them, and did every sitting, neither experimenting nor observ- thing they could think of to worm out the ing, but heedless of the operations of na- secret of these crystals, and get at their ture, he completed the most sublime and mystery. Still, the mystery was not remajestic speculation that it ever entered vealed to them. At length, late in the into the heart of man to conceive. Ow- eighteenth century, a Frenchman named ing to an inaccurate measurement of the Haüy, one of the most remarkable men of diameter of the earth, the details which a remarkable age, made the discovery, verified this stupendous conception were and ascertained that these native crystals, not completed till twenty years later, irregular as they appear, are in truth perwhen Newton, still pursuing the same fectly regular, and that their secondary process, made a deductive application of forms deviate from their primary forms the laws of Kepler: so that both in the by a regular process of diminution; that beginning and in the end, the greatest is, by what he termed laws of decrement discovery of the greatest natural philoso--the principles of decrease being as unpher the world has yet seen, was the fruit of the deductive method. See how small a part the senses played in that discovery! It was the triumph of the idea! It was the audacity of genius! It was the outbreak of a mind so daring, and yet so subtle, that we have only Shakspeare's with which to compare it. To pretend, therefore, as many have done, that the erring as those of increase. Now, I beg that you will particularly notice how this striking discovery was made. Haüy was essentially a poet; and his great delight was to wander in the Jardin du Roi, observing nature, not as a physical philosopher, but as a poet. Though his understanding was strong, his imagination was stronger; and it was for the purpose of filling his mind with ideas of beauty that | Those among you who are interested in he directed his attention at first to the botany, are aware that the highest morvegetable kingdom, with its graceful forms phological generalization we possess reand various hues. His poetic tempera- specting plants, is the great law of metament luxuriating in such images of beauty, morphosis, according to which the stamens, his mind became saturated with ideas of pistils, corollas, bracts, petals, and so forth, symmetry, and Cuvier assures us that it of every plant, are simply modified leaves. was in consequence of those ideas that he It is now known that these various parts, began to believe that the apparently ir- different in shape, different in color, and regular forms of native crystals were in different in function, are successive stages reality regular; in other words, that in of the leaf-epochs, as it were, of its histhem, too, there was a beauty-a hidden tory. The question naturally arises, who beauty-though the senses were unable to made this discovery? Was it some indiscern it. As soon as this idea was firm- ductive investigator, who had spent years ly implanted in his mind, at least half the in experiments and minute observations discovery was made; for he had got the of plants, and who, with indefatigable key to it, and was on the right road, which industry, had collected them, classified others had missed because, while they ap- them, given them hard names, dried them, proached minerals experimentally on the laid them up in his herbarium that he side of the senses, he approached them might at leisure study their structure speculatively on the side of the idea. This and rise to their laws? Not so. is not a mere fanciful assertion of mine, discovery was made by Gothe, the greatsince Hauy himself tells us, in his great est poet Germany has produced, and one work on Mineralogy, that he took, as his of the greatest the world has ever seen. starting point, ideas of the symmetry of And he made it, not in spite of being a form; and that from those ideas he poet, but because he was a poet. It was worked down deductively to his subject. his brilliant imagination, his passion for It was in this way, and of course after a beauty, and his exquisite conception of long series of subsequent labors, that he form, which supplied him with ideas, from read the riddle which had baffled his able which, reasoning deductively, he arrived but unimaginative predecessors. And at conclusions by descent, not by ascent. there are two circumstances worthy of He stood on an eminence, and looking note, as confirming what I have said re- down from the heights generalized the specting the real history of this discovery. law. Then he descended into the plains, The first is, that although Haüy is univers- and verified the idea. When the discovally admitted to be the founder of the ery was announced by Göthe, the botanists science, his means of observation were so not only rejected it, but were filled with rude that subsequent crystallographers wrath at the notion of a poet invading declare that hardly any of his measure- their territory. What! a man who made ments of angles are correct; as indeed is verses and wrote plays, a mere man of not surprising, inasmuch as the goniome- imagination, a poor creature who knew ter which he employed was a very imper- nothing of facts, who had not even used fect instrument; and that of Wollaston, the microscope, who had made no great which acts by reflection, was not then experiments on the growth of plants, was invented. The other circumstance is, he to enter the sacred precincts of physithat the little mathematics he once knew cal science, and give himself out as a phihe had forgotten amid his poetic and losopher? It was too absurd. But imaginative pursuits; so that, in working Göthe, who had thrown his idea upon the out the details of his own science, he world, could afford to wait and bide his was obliged, like a schoolboy, to learn the time. You know the result. The men of elements of geometry before he could facts at length succumbed before the man prove to the world what he had already of ideas; the philosophers, even on their proved to himself, and could bring the own ground, were beaten by the poet; laws of the science of form to bear upon and this great discovery is now received the structure of the mineral kingdom. and eagerly welcomed by those very persons who, if they had lived fifty years ago, would have treated it with scorn, and who even now still go on in their old routine, telling us, in defiance of the his To these cases of the application of what may be termed the ideal method to the inorganic world, I will add another from the organic department of nature. |