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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.
Plato's account of the soul is partly mythical or figurative, and partly literal. Not that either he or we can draw a line between them, or say, 'This is poetry, this is philosophy'; for the transition from the one to the other is imperceptible. Neither must we expect to find in him absolute consistency. He is apt to pass from one level or stage of thought to another without always making it apparent that he is changing his ground. In such passages we have to interpret his meaning by the general spirit of his writings. To reconcile his inconsistencies would be contrary to the first principles of criticism and fatal to any true understanding of him.
