All science is really based upon a combination of two methods, called respectively inductive and deductive reasoning. The first of these consists in gathering together the results of observation and experiment, and, having put them all together, in the formulation of universal laws. Having, for example, long observed that all heavy things tended to go towards the centre of the earth, we might conclude that, since the stars remain up in the sky, they can have no weight. The conclusion would be wrong in this case, not because the method is wrong, but because it is wrongly applied. It is true that all heavy things tend to go to the centre of the earth, but if they are being whirled round like a stone in a sling the centrifugal force will counteract this tendency. The first part of the reasoning would be inductive, the second51 deductive. All this reasoning consists, therefore, in forming as complete an idea as possible respecting the nature of a thing, and then concluding from that idea what the thing will do or what its other properties will be. In fact, you form correct ideas, or “concepts,” as they are called, and reason from them.
But the danger arises when you begin to reason before you are sure of the nature of your concepts, and this has been the great source of error, and it was this error that all men of science so commonly fell into all through ancient and modern times up to the seventeenth century.
Of course, if it were possible by mere observation to derive a complete knowledge of any objects, it would be the simplest method. All that would be necessary to do would be to reason correctly from this knowledge. Unfortunately, however, it is not possible to obtain knowledge of this kind in any branch of science.
The ancient method resembled the action of one who should contend that by observing and talking to a man you could acquire such a knowledge of his character as would infallibly enable you to understand and predict all his actions, and to take little trouble to see whether what he did verified your predictions.
The only difference between the old methods and the new is that in modern times men have learned52 to give far more care to the formation of correct ideas to start with, are much more cautious in arguing from them, and keep testing them again and again on every possible opportunity.
The constant insistence on the formation of clear ideas and the practice of, as Lord Bacon called it, “putting nature to the torture,” is the main cause of the advance of physical science in modern times, and the want of application of these principles explains why so little progress is being made in the so-called “humanitarian” studies, such as philosophy, ethics, and politics.
The works of Aristotle are full of the fallacious method of the old system. In his work on the heavens he repeatedly argues that the heavenly bodies must move in circles, because the circle is the most perfect figure. He affects a perplexity as to how a circle can at the same time be convex and also its opposite, concave, and repeatedly entangles his readers in similar mere word confusion.
Regarded as a man of science, he must be placed, I think, in spite of his great genius, below Archimedes, Hipparchus, and several other ancient astronomers and physicists.
His errors lived after him and dominated the thought of the middle ages, and for a long time delayed the progress of science.
The other great writer on astronomy of ancient times was Ptolemy of Alexandria.
53His work was called the “Great Collection,” and was what we should now term a compendium of astronomy. Although based on a fundamental error, it is a thoroughly scientific work. There is none of the false philosophy in it that so much disfigures the work of Aristotle. The reasons for believing that the earth is at rest are interesting. Ptolemy argues that if the earth were moving round on its axis once in twenty-four hours a bird that flew up from it would be left behind. At first sight this argument seems very convincing, for it appears impossible to conceive a body spinning at the rate at which the earth is alleged to move, and yet not leaving behind any bodies that become detached from it.
On the other hand, the system which taught that the sun and planets moved round the earth, and which had been adopted largely on account of its supposed simplicity, proved, on further examination, to be exceedingly complicated. Each planet, instead of moving simply and uniformly round the earth in a circle, had to be supposed to move uniformly in a circle round another point that moved round the earth in a circle. This secondary circle, in which the planet moved, was called an epicycle. And even this more complicated view failed to explain the facts.
A system which, like that of Aristotle and Ptolemy, was based on deductions from concepts,54 and which consisted rather of drawing conclusions than of examining premises, was very well adapted to mediæval thought, and formed the foundation of astronomy and geography as taught by the schoolmen.