These methods, however, when applied in politics, still represent a difficult and uncertain art rather than a science producing its effects with mechanical accuracy.

When the great thinkers of Greece laid down rules for valid reasoning, they had, it is true, the needs of politics specially in their minds.  After the prisoners in Plato’s cave of illusion should be unbound by true philosophy it was to the service of the State that they were to devote themselves, and their first triumph was to be the control of passion by reason in the sphere of government.  Yet if Plato could visit us now, he would learn that while our glass-makers proceed by rigorous and confident processes to exact results, our statesmen, like the glass-makers of ancient Athens, still trust to empirical maxims and personal skill.  Why is it, he would ask us, that valid reasoning has proved to be so much more difficult in politics than in the physical sciences?

Our first answer might be found in the character of the material with which political reasoning has to deal.  The universe which presents itself to our reason is the same as that which presents itself to our feelings and impulses—­an unending stream of sensations and memories, every one of which is different from every other, and before which, unless we can select and recognise and simplify, we must stand helpless and unable either to act or think.  Man has therefore to create entities that shall be the material of his reasoning, just as he creates entities to be the objects of his emotions and the stimulus of his instinctive inferences.

Exact reasoning requires exact comparison, and in the desert or the forest there were few things which our ancestors could compare exactly.  The heavenly bodies seem, indeed, to have been the first objects of consciously exact reasoning, because they were so distant that nothing could be known of them except position and movement, and their position and movement could be exactly compared from night to night.

In the same way the foundation of the terrestrial sciences came from two discoveries, first, that it was possible to abstract single qualities, such as position and movement, in all things however unlike, from the other qualities of those things and to compare them exactly; and secondly, that it was possible artificially to create actual uniformities for the purpose of comparison, to make, that is to say, out of unlike things, things so like that valid inferences could be drawn as to their behaviour under like circumstances.  Geometry, for instance, came into the service of man when it was consciously realised that all units of land and water were exactly alike in so far as they were extended surfaces.  Metallurgy, on the other hand, only became a science when men could actually take two pieces of copper ore, unlike in shape and appearance and chemical constitution, and extract from them two pieces of copper so nearly alike that they would give the same results when treated in the same way.