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APPEND. A. OF THE PLATONIC THEORY OF IDEAS 403 B. ON PLATO'S SURVEY OF THE SCIENCES 417 BB. ON PLATO'S NOTION OF DIALECTIC 429 C. OF THE INTELLECTUAL POWERS ACCORDING TO PLATO 440 D. CRITICISM OF ARISTOTLE'S ACCOUNT OF INDUCTION 449 E. ON THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY 462 F. REMARKS ON A REVIEW OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES 482 G. ON THE TRANSFORMATION OF HYPOTHESES IN THE HISTORY OF SCIENCE 492 H. ON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA 504 Appendix to the Memoir on Hegel's Criticism of Newton's Principia 513 K. DEMONSTRATION THAT ALL MATTER IS HEAVY 522

ON THE PHILOSOPHY OF DISCOVERY.

W?r' nicht das Auge sonnenhaft Wie k?nnten wir das Licht erblicken? Lebt' nicht in uns des Gottes eigne Kraft Wie k?nnte uns das G?ttliche entz?cken? GOETHE.

Were nothing sunlike in the Eye How could we Light itself descry? Were nothing godlike in the Mind How could we God in Nature find?

INTRODUCTION.

I am far from undertaking, or wishing, to review the whole series of opinions which thus come under our notice; and I do not even attempt to examine all the principal authors who have written on such subjects. I merely wish to select some of the most considerable forms which, such opinions have assumed, and to point out in some measure the progress of truth from age to age. In doing this, I can only endeavour to seize some of the most prominent features of each time and of each step, and I must pass rapidly from classical antiquity to those which we have called the dark ages, and from them to modern times. At each of these periods the modifications of opinion, and the speculations with which they were connected, formed a vast and tangled maze, the byways of which our plan does not allow us to enter. We shall esteem ourselves but too fortunate, if we can discover the single track by which ancient led to modern philosophy.

I must also repeat that my survey of philosophical writers is here confined to this one point,--their opinions on the nature of knowledge and the method of science. I with some effort avoid entering upon other parts of the philosophy of those authors of whom I speak; I knowingly pass by those portions of their speculations which are in many cases the most interesting and celebrated;--their opinions concerning the human soul, the Divine Governor of the world, the foundations or leading doctrines of politics, religion, and general philosophy. I am desirous that my reader should bear this in mind, since he must otherwise be offended with the scanty and partial view which I give in this place of the philosophers whom I enumerate.

PLATO.

There would be small advantage in beginning our examination earlier than the period of the Socratic School at Athens; for although the spirit of inquiry on such subjects had awakened in Greece at an earlier period, and although the peculiar aptitude of the Grecian mind for such researches had shown itself repeatedly in subtle distinctions and acute reasonings, all the positive results of these early efforts were contained in a more definite form in the reasonings of the Platonic age. Before that time, the Greeks did not possess plain and familiar examples of exact knowledge, such as the truths of Arithmetic, Geometry, Astronomy and Optics became in the school of Plato; nor were the antitheses of which we spoke above, so distinctly and fully unfolded as we find them in Plato's works.

It would seem that what the author here describes as the most perfect form of exposition, is that which refers each object to its place in a classification containing a complete series of subordinations, and which gives a definition of each class. We have repeatedly remarked that, in sciences of classification, each new definition which gives a tenable and distinct separation of classes is an important advance in our knowledge; but that such definitions are rather the last than the first step in each advance. In the progress of real knowledge, these definitions are always the results of a laborious study of individual cases, and are never arrived at by a pure effort of thought, which is what Plato appears to have imagined as the true mode of philosophizing. And still less do the advances of other sciences consist in seizing at once upon the highest generality, and filling in afterwards all the intermediate steps between that and the special instances. On the contrary, as we have seen, the ascents from particular to general are all successive; and each step of this ascent requires time, and labour, and a patient examination of actual facts and objects.

It would, of course, be absurd to blame Plato for having inadequate views of the nature of progressive knowledge, at the time when knowledge could hardly be said to have begun its progress. But we already find in his speculations, as appears in the passages just quoted from his writings, several points brought into view which will require our continued attention as we proceed. In overlooking the necessity of a gradual and successive advance from the less general to the more general truths, Plato shared in a dimness of vision which prevailed among philosophers to the time of Francis Bacon. In thinking too slightly of the study of actual nature, he manifested a bias from which the human intellect freed itself in the vigorous struggles which terminated the dark ages. In pointing out that all knowledge implies a unity of what we observe as manifold, which unity is given by the mind, Plato taught a lesson which has of late been too obscurely acknowledged, the recoil by which men repaired their long neglect of facts having carried them for a while so far as to think that facts were the whole of our knowledge. And in analysing this principle of Unity, by which we thus connect sensible things, into various Ideas, such as Number, Magnitude, Position, Motion, he made a highly important step, which it has been the business of philosophers in succeeding times to complete and to follow out.

But the efficacy of Plato's speculations in their bearing upon physical science, and upon theory in general, was much weakened by the confusion of practical with theoretical knowledge, which arose from the ethical propensities of the Socratic school. In the Platonic Dialogues, Art and Science are constantly spoken of indiscriminately. The skill possessed by the Painter, the Architect, the Shoemaker, is considered as a just example of human science, no less than the knowledge which the geometer or the astronomer possesses of the theoretical truths with which he is conversant. Not only so; but traditionary and mythological tales, mystical imaginations and fantastical etymologies, are mixed up, as no less choice ingredients, with the most acute logical analyses, and the most exact conduct of metaphysical controversies. There is no distinction made between the knowledge possessed by the theoretical psychologist and the physician, the philosophical teacher of morals and the legislator or the administrator of law. This, indeed, is the less to be wondered at, since even in our own time the same confusion is very commonly made by persons not otherwise ignorant or uncultured.

FOOTNOTES:

ADDITIONAL REMARKS ON PLATO.

The leading points in Plato's writings which bear upon the philosophy of discovery are these:

So far the Doctrine of Ideas answers its primary purpose, and is a reply to a question still agitated among philosophers: What is the ground of geometrical truth?

But Plato seems, in many of his writings, to extend this doctrine much further; and to assume, not only Ideas of Space and its properties, from which geometrical truths are derived; but of Relations, as the Relations of Like and Unlike, Greater and Less; and of mere material objects, as Tables and Chairs. Now to assume Ideas of such things as these solves no difficulty and is supported by no argument. In this respect the Ideal theory is of no value in Science.

How far the caution in forming hypotheses which Bacon's writings urge upon us is more severe than suits the present prospects of science, we may hereafter consider; but it is plainly very conceivable that a boldness in the invention and application of hypotheses which was propitious to science in its infancy, may be one of the greatest dangers of its more mature period: and further, that the happy effect of such a temper depended entirely upon the candour, skill and labour with which the hypotheses were compared with the observed phenomena.

FOOTNOTES:

ARISTOTLE.

The views of Aristotle with regard to the foundations of human knowledge are very different from those of his tutor Plato, and are even by himself put in opposition to them. He dissents altogether from the Platonic doctrine that Ideas are the true materials of our knowledge; and after giving, respecting the origin of this doctrine, the account which we quoted in the last chapter, he goes on to reason against it. "Thus," he says, "they devised Ideas of all things which are spoken of as universals: much as if any one having to count a number of objects, should think that he could not do it while they were few, and should expect to count them by making them more numerous. For the kinds of things are almost more numerous than the special sensible objects, by seeking the causes of which they were led to their Ideas." He then goes on to urge several other reasons against the assumption of Ideas and the use of them in philosophical researches.

Yet Aristotle was so far consistent with his own doctrine of the derivation of knowledge from experience, that he made in almost every province of human knowledge, a vast collection of such special facts as the experience of his time supplied. These collections are almost unrivalled, even to the present day, especially in Natural History; in other departments, when to the facts we must add the right Inductive Idea, in order to obtain truth, we find little of value in the Aristotelic works. But in those parts which refer to Natural History, we find not only an immense and varied collection of facts and observations, but a sagacity and acuteness in classification which it is impossible not to admire. This indeed appears to have been the most eminent faculty in Aristotle's mind.

The influence of Aristotle in succeeding ages will come under our notice shortly.

FOOTNOTES:

ADDITIONAL REMARKS ON ARISTOTLE.

Elephant, horse, mule, &c. are long-lived. Elephant, horse, mule, &c. are all gall-less.

If we might convert this proposition, and say

All gall-less animals are as elephant, horse, mule, &c.:

All gall-less animals are long-lived.

And though we cannot infer this syllogistically, we infer it by Induction, when we have a sufficient amount of instances.

To Aristotle's argument that Ideas cannot be the Causes or Principles of Things, we should reply, that though they cannot be this, they may nevertheless be, and must be, the Conditions and Principles of our Knowledge, which is what we want them to be.

FOOTNOTES:

THE LATER GREEKS.

Thus while Plato was disposed to seek the essence of our knowledge in Ideas alone, Aristotle, slighting this source of truth, looked to Experience as the beginning of Science; and he attempted to obtain, by division and deduction, all that Experience did not immediately supply. And thus, with these two great names, began that struggle of opposite opinions which has ever since that time agitated the speculative world, as men have urged the claims of Ideas or of Experience to our respect, and as alternately each of these elements of knowledge has been elevated above its due place, while the other has been unduly depressed. We shall see the successive turns of this balanced struggle in the remaining portions of this review.

"What," he asks, "is the method of finding the Elements of bodies? There can, in my opinion, be no other than that which was introduced by Hippocrates; namely, we must inquire whether there be only one element, everywhere the same in kind, or whether there are more than one, various and unlike each other. And if the Element be not one only, but several, various and dissimilar, we must inquire in the second place, how many elements there are, and what, and of what kind they are, and how related in their association.

"Now that the First Element is not one only of which both our bodies and those of all other creatures were produced, Hippocrates shows from these considerations. And it is better first to put down his own expressions and then to expound them. 'I assert that if man consisted of one element only he could not fall sick; for there would be nothing which could derange his health, if he were all of one Element.'"

The doctrine of One Element did not prevail much after the time of Hippocrates: the doctrine of Four Elements continued, as I have said, long to hold possession of the Schools, but does not appear as an important part of the doctrine of Hippocrates. The doctrine of the Four Humours is more peculiarly his, and long retained its place as a principle of physiological Science.

But we are here not so much concerned with his discoveries in medicine as with his views respecting the method of acquiring sound knowledge, and in this respect, as has been said, he recommends by his practice a prudent limitation of the field of inquiry, a rejection of wide, ambitious, general assertions, and a practical study of his proper field.

In ascribing these merits to Hippocrates's medical speculations as to the ethical speculations of his contemporary Socrates, we assign considerable philosophical value to Hippocrates, no less than to Socrates. These merits were at that time the great virtues of physical as well as of ethical philosophy. But, as Mr. Grote well observes, the community of character which then subsisted between the physical and ethical speculations prevailing at that time, ceased to obtain in later times. Indeed, it ceased to exist just at that time, in consequence of the establishment of scientific astronomy by the exertions of Plato and his contemporaries. From that time the Common Sense of a man like Socrates, though it might be a good guide in ethics, was not a good guide in physics. I have shown elsewhere how the Common Sense of Socrates was worthless in matters of astronomy. From that time one of the great intellectual lessons was, that in order to understand the external world, we must indeed observe carefully, but we must also guess boldly. Discovery here required an inventive mind like Plato's to deal with and arrange new and varied facts. But in ethics all the facts were old and familiar, and the generalizations of language by which they were grouped as Virtues and Vices, and the like, were common and well-known words. Here was no room for invention; and thus in the ethical speculations of Socrates or of any other moral teacher, we are not to look for any contributions to the Philosophy of Discovery.

Nor do I find anything on this subject among later Greek writers, beyond the commendation of such intellectual virtues as Hippocrates and Galen, and other medical writers, schooled by the practice of their art, enjoined and praised. But before we quit the ancients I will point out some peculiarities which may be noticed in the Roman disciples of the Greek philosophy.

FOOTNOTES:

THE ROMANS.

The Romans had no philosophy but that which they borrowed from the Greeks; and what they thus received, they hardly made entirely their own. The vast and profound question of which we have been speaking, the relation between Existence and our Knowledge of what exists, they never appear to have fathomed, even so far as to discern how wide and deep it is. In the development of the ideas by which nature is to be understood, they went no further than their Greek masters had gone, nor indeed was more to be looked for. And in the practical habit of accumulating observed facts as materials for knowledge, they were much less discriminating and more credulous than their Greek predecessors. The descent from Aristotle to Pliny, in the judiciousness of the authors and the value of their collections of facts, is immense.

Since the Romans were thus servile followers of their Greek teachers, and little acquainted with any example of new truths collected from the world around them, it was not to be expected that they could have any just conception of that long and magnificent ascent from one set of truths to others of higher order and wider compass, which the history of science began to exhibit when the human mind recovered its progressive habits. Yet some dim presentiment of the splendid career thus destined for the intellect of man appears from time to time to have arisen in their minds. Perhaps the circumstance which most powerfully contributed to suggest this vision, was the vast intellectual progress which they were themselves conscious of having made, through the introduction of the Greek philosophy; and to this may be added, perhaps, some other features of national character. Their temper was too stubborn to acquiesce in the absolute authority of the Greek philosophy, although their minds were not inventive enough to establish a rival by its side. And the wonderful progress of their political power had given them a hope in the progress of man which the Greeks never possessed. The Roman, as he believed the fortune of his State to be destined for eternity, believed also in the immortal destiny and endless advance of that Intellectual Republic of which he had been admitted a denizen.

It is easy to find examples of such feelings as I have endeavoured to describe. The enthusiasm with which Lucretius and Virgil speak of physical knowledge, manifestly arises in a great measure from the delight which they had felt in becoming acquainted with the Greek theories.

Me vero primum dulces ante omnia Musae Quarum sacra fero ingenti perculsus amore Accipiant, coelique vias et sidera monstrent, Defectus Solis varios, Lunaeque labores!... Felix qui potuit rerum cognoscere causas!

Ye sacred Muses, with whose beauty fir'd, My soul is ravisht and my brain inspir'd: Whose Priest I am, whose holy fillets wear, Would you your Poet's first petition hear, Give me the ways of wand'ring stars to know, The depth of Heaven above and Earth below; Teach me the various labours of the Moon, And whence proceed th' eclipses of the Sun; Why flowing Tides prevail upon the main, And in what dark abyss they shrink again; What shakes the solid Earth; what cause delays The Summer Nights; and shortens Winter Days.... Happy the man who, studying Nature's Laws, Through known effects can trace the secret cause!

Ovid expresses a similar feeling.

Felices animos quibus haec cognoscere primis Inque domos superas scandere cura fuit!... Admovere oculis distantia sidera nostris AEtheraque ingenio supposuere suo. Sic petitur coelum: non ut ferat Ossam Olympus Summaque Peliacus sidera tanget apex.

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