At the commencement of the sixth book, Plato anticipated his explanation of the relation of the philosopher to the world in an allegory, in this, as in other passages, following the order which he prescribes in education, and proceeding from the concrete to the abstract. At the commencement of Book VII, under the figure of a cave having an opening towards a fire and a way upwards to the true light, he returns to view the divisions of knowledge, exhibiting familiarly, as in a picture, the result which had been hardly won by a great effort of thought in the previous discussion; at the same time casting a glance onward at the dialectical process, which is represented by the way leading from darkness to light. The shadows, the images, the reflection of the sun and stars in the water, the stars and sun themselves, severally correspond,--the first, to the realm of fancy and poetry,--the second, to the world of sense,--the third, to the abstractions or universals of sense, of which the mathematical sciences furnish the type,--the fourth and last to the same abstractions, when seen in the unity of the idea, from which they derive a new meaning and power. The true dialectical process begins with the contemplation of the real stars, and not mere reflections of them, {cix} and ends with the recognition of the sun, or idea of good, as the parent not only of light but of warmth and growth. To the divisions of knowledge the stages of education partly answer:--first, there is the early education of childhood and youth in the fancies of the poets, and in the laws and customs of the State;--then there is the training of the body to be a warrior athlete, and a good servant of the mind;--and thirdly, after an interval follows the education of later life, which begins with mathematics and proceeds to philosophy in general.