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There is a difficulty in understanding what Plato meant by 'the

longer way': he seems to intimate some metaphysic of the future

which will not be satisfied with arguing from the principle of

contradiction. In the sixth and seventh books (compare Sophist

and Parmenides) he has given us a sketch of such a metaphysic;

but when Glaucon asks for the final revelation of the idea of

good, he is put off with the declaration that he has not yet

studied the preliminary sciences. How he would have filled up the

sketch, or argued about such questions from a higher point of

view, we can only conjecture. Perhaps he hoped to find some a

priori method of developing the parts out of the whole; or he

might have asked which of the ideas contains the other ideas, and

possibly have stumbled on the Hegelian identity of the 'ego' and

the 'universal.' Or he may have imagined that ideas might be

constructed in some manner analogous to the construction of

figures and numbers in the mathematical sciences.