Nature in the aspect which she presented to a Greek philosopher of the fourth century before Christ is not easily reproduced to modern eyes.  The associations of mythology and poetry have to be added, and the unconscious influence of science has to be subtracted, before we can behold the heavens or the earth as they appeared to the Greek.  The philosopher himself was a child and also a man ­a child in the range of his attainments, but also a great intelligence having an insight into nature, and often anticipations of the truth.  He was full of original thoughts, and yet liable to be imposed upon by the most obvious fallacies.  He occasionally confused numbers with ideas, and atoms with numbers; his a priori notions were out of all proportion to his experience.  He was ready to explain the phenomena of the heavens by the most trivial analogies of earth.  The experiments which nature worked for him he sometimes accepted, but he never tried experiments for himself which would either prove or disprove his theories.  His knowledge was unequal; while in some branches, such as medicine and astronomy, he had made considerable proficiency, there were others, such as chemistry, electricity, mechanics, of which the very names were unknown to him.  He was the natural enemy of mythology, and yet mythological ideas still retained their hold over him.  He was endeavouring to form a conception of principles, but these principles or ideas were regarded by him as real powers or entities, to which the world had been subjected.  He was always tending to argue from what was near to what was remote, from what was known to what was unknown, from man to the universe, and back again from the universe to man.  While he was arranging the world, he was arranging the forms of thought in his own mind; and the light from within and the light from without often crossed and helped to confuse one another.  He might be compared to a builder engaged in some great design, who could only dig with his hands because he was unprovided with common tools; or to some poet or musician, like Tynnichus (Ion), obliged to accommodate his lyric raptures to the limits of the tetrachord or of the flute.

The Hesiodic and Orphic cosmogonies were a phase of thought intermediate between mythology and philosophy and had a great influence on the beginnings of knowledge.  There was nothing behind them; they were to physical science what the poems of Homer were to early Greek history.  They made men think of the world as a whole; they carried the mind back into the infinity of past time; they suggested the first observation of the effects of fire and water on the earth’s surface.  To the ancient physics they stood much in the same relation which geology does to modern science.  But the Greek was not, like the enquirer of the last generation, confined to a period of six thousand years; he was able to speculate freely on the effects of infinite ages in the production of physical phenomena.  He could imagine cities which had existed time out of mind (States.; Laws), laws or forms of art and music which had lasted, ‘not in word only, but in very truth, for ten thousand years’ (Laws); he was aware that natural phenomena like the Delta of the Nile might have slowly accumulated in long periods of time (Hdt.).  But he seems to have supposed that the course of events was recurring rather than progressive.  To this he was probably led by the fixedness of Egyptian customs and the general observation that there were other civilisations in the world more ancient than that of Hellas.

The ancient philosophers found in mythology many ideas which, if not originally derived from nature, were easily transferred to her ­such, for example, as love or hate, corresponding to attraction or repulsion; or the conception of necessity allied both to the regularity and irregularity of nature; or of chance, the nameless or unknown cause; or of justice, symbolizing the law of compensation; are of the Fates and Furies, typifying the fixed order or the extraordinary convulsions of nature.  Their own interpretations of Homer and the poets were supposed by them to be the original meaning.  Musing in themselves on the phenomena of nature, they were relieved at being able to utter the thoughts of their hearts in figures of speech which to them were not figures, and were already consecrated by tradition.  Hesiod and the Orphic poets moved in a region of half-personification in which the meaning or principle appeared through the person.  In their vaster conceptions of Chaos, Erebus, Aether, Night, and the like, the first rude attempts at generalization are dimly seen.  The Gods themselves, especially the greater Gods, such as Zeus, Poseidon, Apollo, Athene, are universals as well as individuals.  They were gradually becoming lost in a common conception of mind or God.  They continued to exist for the purposes of ritual or of art; but from the sixth century onwards or even earlier there arose and gained strength in the minds of men the notion of ’one God, greatest among Gods and men, who was all sight, all hearing, all knowing’ (Xenophanes).

Under the influence of such ideas, perhaps also deriving from the traditions of their own or of other nations scraps of medicine and astronomy, men came to the observation of nature.  The Greek philosopher looked at the blue circle of the heavens and it flashed upon him that all things were one; the tumult of sense abated, and the mind found repose in the thought which former generations had been striving to realize.  The first expression of this was some element, rarefied by degrees into a pure abstraction, and purged from any tincture of sense.  Soon an inner world of ideas began to be unfolded, more absorbing, more overpowering, more abiding than the brightest of visible objects, which to the eye of the philosopher looking inward, seemed to pale before them, retaining only a faint and precarious existence.  At the same time, the minds of men parted into the two great divisions of those who saw only a principle of motion, and of those who saw only a principle of rest, in nature and in themselves; there were born Heracliteans or Eleatics, as there have been in later ages born Aristotelians or Platonists.  Like some philosophers in modern times, who are accused of making a theory first and finding their facts afterwards, the advocates of either opinion never thought of applying either to themselves or to their adversaries the criterion of fact.  They were mastered by their ideas and not masters of them.  Like the Heraclitean fanatics whom Plato has ridiculed in the Theaetetus, they were incapable of giving a reason of the faith that was in them, and had all the animosities of a religious sect.  Yet, doubtless, there was some first impression derived from external nature, which, as in mythology, so also in philosophy, worked upon the minds of the first thinkers.  Though incapable of induction or generalization in the modern sense, they caught an inspiration from the external world.  The most general facts or appearances of nature, the circle of the universe, the nutritive power of water, the air which is the breath of life, the destructive force of fire, the seeming regularity of the greater part of nature and the irregularity of a remnant, the recurrence of day and night and of the seasons, the solid earth and the impalpable aether, were always present to them.

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?

Two other points strike us in the use which the ancient philosophers made of numbers.  First, they applied to external nature the relations of them which they found in their own minds; and where nature seemed to be at variance with number, as for example in the case of fractions, they protested against her (Rep.; Arist.  Metaph.).  Having long meditated on the properties of 1:2:4:8, or 1:3:9:27, or of 3, 4, 5, they discovered in them many curious correspondences and were disposed to find in them the secret of the universe.  Secondly, they applied number and figure equally to those parts of physics, such as astronomy or mechanics, in which the modern philosopher expects to find them, and to those in which he would never think of looking for them, such as physiology and psychology.  For the sciences were not yet divided, and there was nothing really irrational in arguing that the same laws which regulated the heavenly bodies were partially applied to the erring limbs or brain of man.  Astrology was the form which the lively fancy of ancient thinkers almost necessarily gave to astronomy.  The observation that the lower principle, e.g. mechanics, is always seen in the higher, e.g. in the phenomena of life, further tended to perplex them.  Plato’s doctrine of the same and the other ruling the courses of the heavens and of the human body is not a mere vagary, but is a natural result of the state of knowledge and thought at which he had arrived.

When in modern times we contemplate the heavens, a certain amount of scientific truth imperceptibly blends, even with the cursory glance of an unscientific person.  He knows that the earth is revolving round the sun, and not the sun around the earth.  He does not imagine the earth to be the centre of the universe, and he has some conception of chemistry and the cognate sciences.  A very different aspect of nature would have been present to the mind of the early Greek philosopher.  He would have beheld the earth a surface only, not mirrored, however faintly, in the glass of science, but indissolubly connected with some theory of one, two, or more elements.  He would have seen the world pervaded by number and figure, animated by a principle of motion, immanent in a principle of rest.  He would have tried to construct the universe on a quantitative principle, seeming to find in endless combinations of geometrical figures or in the infinite variety of their sizes a sufficient account of the multiplicity of phenomena.  To these a priori speculations he would add a rude conception of matter and his own immediate experience of health and disease.  His cosmos would necessarily be imperfect and unequal, being the first attempt to impress form and order on the primaeval chaos of human knowledge.  He would see all things as in a dream.

The ancient physical philosophers have been charged by Dr. Whewell and others with wasting their fine intelligences in wrong methods of enquiry; and their progress in moral and political philosophy has been sometimes contrasted with their supposed failure in physical investigations.  ‘They had plenty of ideas,’ says Dr. Whewell, ’and plenty of facts; but their ideas did not accurately represent the facts with which they were acquainted.’  This is a very crude and misleading way of describing ancient science.  It is the mistake of an uneducated person ­uneducated, that is, in the higher sense of the word ­who imagines every one else to be like himself and explains every other age by his own.  No doubt the ancients often fell into strange and fanciful errors:  the time had not yet arrived for the slower and surer path of the modern inductive philosophy.  But it remains to be shown that they could have done more in their age and country; or that the contributions which they made to the sciences with which they were acquainted are not as great upon the whole as those made by their successors.  There is no single step in astronomy as great as that of the nameless Pythagorean who first conceived the world to be a body moving round the sun in space:  there is no truer or more comprehensive principle than the application of mathematics alike to the heavenly bodies, and to the particles of matter.  The ancients had not the instruments which would have enabled them to correct or verify their anticipations, and their opportunities of observation were limited.  Plato probably did more for physical science by asserting the supremacy of mathematics than Aristotle or his disciples by their collections of facts.  When the thinkers of modern times, following Bacon, undervalue or disparage the speculations of ancient philosophers, they seem wholly to forget the conditions of the world and of the human mind, under which they carried on their investigations.  When we accuse them of being under the influence of words, do we suppose that we are altogether free from this illusion?  When we remark that Greek physics soon became stationary or extinct, may we not observe also that there have been and may be again periods in the history of modern philosophy which have been barren and unproductive?  We might as well maintain that Greek art was not real or great, because it had nihil simile aut secundum, as say that Greek physics were a failure because they admire no subsequent progress.

The charge of premature generalization which is often urged against ancient philosophers is really an anachronism.  For they can hardly be said to have generalized at all.  They may be said more truly to have cleared up and defined by the help of experience ideas which they already possessed.  The beginnings of thought about nature must always have this character.  A true method is the result of many ages of experiment and observation, and is ever going on and enlarging with the progress of science and knowledge.  At first men personify nature, then they form impressions of nature, at last they conceive ‘measure’ or laws of nature.  They pass out of mythology into philosophy.  Early science is not a process of discovery in the modern sense; but rather a process of correcting by observation, and to a certain extent only, the first impressions of nature, which mankind, when they began to think, had received from poetry or language or unintelligent sense.  Of all scientific truths the greatest and simplest is the uniformity of nature; this was expressed by the ancients in many ways, as fate, or necessity, or measure, or limit.  Unexpected events, of which the cause was unknown to them, they attributed to chance (Thucyd.).  But their conception of nature was never that of law interrupted by exceptions, ­a somewhat unfortunate metaphysical invention of modern times, which is at variance with facts and has failed to satisfy the requirements of thought.