The apparent ease with which children learn is their ruin.  You fail to see that this very facility proves that they are not learning.  Their shining, polished brain reflects, as in a mirror, the things you show them, but nothing sinks in.  The child remembers the words and the ideas are reflected back; his hearers understand them, but to him they are meaningless.

Although memory and reason are wholly different faculties, the one does not really develop apart from the other.  Before the age of reason the child receives images, not ideas; and there is this difference between them:  images are merely the pictures of external objects, while ideas are notions about those objects determined by their relations.  An image when it is recalled may exist by itself in the mind, but every idea implies other ideas.  When we image we merely perceive, when we reason we compare.  Our sensations are merely passive, our notions or ideas spring from an active principle which judges.  The proof of this will be given later.

I maintain, therefore, that as children are incapable of judging, they have no true memory.  They retain sounds, form, sensation, but rarely ideas, and still more rarely relations.  You tell me they acquire some rudiments of geometry, and you think you prove your case; not so, it is mine you prove; you show that far from being able to reason themselves, children are unable to retain the reasoning of others; for if you follow the method of these little geometricians you will see they only retain the exact impression of the figure and the terms of the demonstration.  They cannot meet the slightest new objection; if the figure is reversed they can do nothing.  All their knowledge is on the sensation-level, nothing has penetrated to their understanding.  Their memory is little better than their other powers, for they always have to learn over again, when they are grown up, what they learnt as children.

I am far from thinking, however, that children have no sort of reason. [Footnote:  I have noticed again and again that it is impossible in writing a lengthy work to use the same words always in the same sense.  There is no language rich enough to supply terms and expressions sufficient for the modifications of our ideas.  The method of defining every term and constantly substituting the definition for the term defined looks well, but it is impracticable.  For how can we escape from our vicious circle?  Definitions would be all very well if we did not use words in the making of them.  In spite of this I am convinced that even in our poor language we can make our meaning clear, not by always using words in the same sense, but by taking care hat every time we use a word the sense in which we use it is sufficiently indicated by the sense of the context, so that each sentence in which the word occurs acts as a sort of definition.  Sometimes I say children are incapable of reasoning.  Sometimes I say they reason cleverly.