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The great source of error and also the beginning of truth to them was reasoning from analogy; they could see resemblances, but not differences; and they were incapable of distinguishing illustration from argument. Analogy in modern times only points the way, and is immediately verified by experiment. The dreams and visions, which pass through the philosopher's mind, of resemblances between different classes of substances, or between the animal and vegetable world, are put into the refiner's fire, and the dross and other elements which adhere to them are purged away. But the contemporary of Plato and Socrates was incapable of resisting the power of any analogy which occurred to him, and was drawn into any consequences which seemed to follow. He had no methods of difference or of concomitant variations, by the use of which he could distinguish the accidental from the essential. He could not isolate phenomena, and he was helpless against the influence of any word which had an equivocal or double sense.

Yet without this crude use of analogy the ancient physical philosopher would have stood still; he could not have made even 'one guess among many' without comparison. The course of natural phenomena would have passed unheeded before his eyes, like fair sights or musical sounds before the eyes and ears of an animal. Even the fetichism of the savage is the beginning of reasoning; the assumption of the most fanciful of causes indicates a higher mental state than the absence of all enquiry about them. The tendency to argue from the higher to the lower, from man to the world, has led to many errors, but has also had an elevating influence on philosophy. The conception of the world as a whole, a person, an animal, has been the source of hasty generalizations; yet this general grasp of nature led also to a spirit of comprehensiveness in early philosophy, which has not increased, but rather diminished, as the fields of knowledge have become more divided. The modern physicist confines himself to one or perhaps two branches of science. But he comparatively seldom rises above his own department, and often falls under the narrowing influence which any single branch, when pursued to the exclusion of every other, has over the mind. Language, two, exercised a spell over the beginnings of physical philosophy, leading to error and sometimes to truth; for many thoughts were suggested by the double meanings of words (Greek), and the accidental distinctions of words sometimes led the ancient philosopher to make corresponding differences in things (Greek). 'If they are the same, why have they different names; or if they are different, why have they the same name?'—is an argument not easily answered in the infancy of knowledge. The modern philosopher has always been taught the lesson which he still imperfectly learns, that he must disengage himself from the influence of words. Nor are there wanting in Plato, who was himself too often the victim of them, impressive admonitions that we should regard not words but things (States.). But upon the whole, the ancients, though not entirely dominated by them, were much more subject to the influence of words than the moderns. They had no clear divisions of colours or substances; even the four elements were undefined; the fields of knowledge were not parted off. They were bringing order out of disorder, having a small grain of experience mingled in a confused heap of a priori notions. And yet, probably, their first impressions, the illusions and mirages of their fancy, created a greater intellectual activity and made a nearer approach to the truth than any patient investigation of isolated facts, for which the time had not yet come, could have accomplished.

There was one more illusion to which the ancient philosophers were subject, and against which Plato in his later dialogues seems to be struggling—the tendency to mere abstractions; not perceiving that pure abstraction is only negation, they thought that the greater the abstraction the greater the truth. Behind any pair of ideas a new idea which comprehended them—the (Greek), as it was technically termed—began at once to appear. Two are truer than three, one than two. The words 'being,' or 'unity,' or essence,' or 'good,' became sacred to them. They did not see that they had a word only, and in one sense the most unmeaning of words. They did not understand that the content of notions is in inverse proportion to their universality—the element which is the most widely diffused is also the thinnest; or, in the language of the common logic, the greater the extension the less the comprehension. But this vacant idea of a whole without parts, of a subject without predicates, a rest without motion, has been also the most fruitful of all ideas. It is the beginning of a priori thought, and indeed of thinking at all. Men were led to conceive it, not by a love of hasty generalization, but by a divine instinct, a dialectical enthusiasm, in which the human faculties seemed to yearn for enlargement. We know that 'being' is only the verb of existence, the copula, the most general symbol of relation, the first and most meagre of abstractions; but to some of the ancient philosophers this little word appeared to attain divine proportions, and to comprehend all truth. Being or essence, and similar words, represented to them a supreme or divine being, in which they thought that they found the containing and continuing principle of the universe. In a few years the human mind was peopled with abstractions; a new world was called into existence to give law and order to the old. But between them there was still a gulf, and no one could pass from the one to the other.

Number and figure were the greatest instruments of thought which were possessed by the Greek philosopher; having the same power over the mind which was exerted by abstract ideas, they were also capable of practical application. Many curious and, to the early thinker, mysterious properties of them came to light when they were compared with one another. They admitted of infinite multiplication and construction; in Pythagorean triangles or in proportions of 1:2:4:8 and 1:3:9:27, or compounds of them, the laws of the world seemed to be more than half revealed. They were also capable of infinite subdivision—a wonder and also a puzzle to the ancient thinker (Rep.). They were not, like being or essence, mere vacant abstractions, but admitted of progress and growth, while at the same time they confirmed a higher sentiment of the mind, that there was order in the universe. And so there began to be a real sympathy between the world within and the world without. The numbers and figures which were present to the mind's eye became visible to the eye of sense; the truth of nature was mathematics; the other properties of objects seemed to reappear only in the light of number. Law and morality also found a natural expression in number and figure. Instruments of such power and elasticity could not fail to be 'a most gracious assistance' to the first efforts of human intelligence.

There was another reason why numbers had so great an influence over the minds of early thinkers—they were verified by experience. Every use of them, even the most trivial, assured men of their truth; they were everywhere to be found, in the least things and the greatest alike. One, two, three, counted on the fingers was a 'trivial matter (Rep.), a little instrument out of which to create a world; but from these and by the help of these all our knowledge of nature has been developed. They were the measure of all things, and seemed to give law to all things; nature was rescued from chaos and confusion by their power; the notes of music, the motions of the stars, the forms of atoms, the evolution and recurrence of days, months, years, the military divisions of an army, the civil divisions of a state, seemed to afford a 'present witness' of them—what would have become of man or of the world if deprived of number (Rep.)? The mystery of number and the mystery of music were akin. There was a music of rhythm and of harmonious motion everywhere; and to the real connexion which existed between music and number, a fanciful or imaginary relation was superadded. There was a music of the spheres as well as of the notes of the lyre. If in all things seen there was number and figure, why should they not also pervade the unseen world, with which by their wonderful and unchangeable nature they seemed to hold communion?