The first action of the mind is aroused by the attempt to set in order this chaos, and the reason is required to frame distinct conceptions under which the confused impressions of sense may be arranged.

Hence arises the question, 'What is great, what is small ?' and thus begins the distinction of the visible and the intelligible.
The second difficulty relates to Plato's conception of harmonics.
Three classes of harmonists are distinguished by him:--first, the Pythagoreans, whom he proposes to consult as in the previous discussion on music he was to consult Damon--they are acknowledged to be masters in the art, but are altogether deficient in the knowledge of its higher import and relation to the good; secondly, the mere empirics, whom Glaucon appears to confuse with them, and whom both he and Socrates ludicrously describe as experimenting by mere auscultation on the intervals of sounds.

Both of these fall short in different degrees of the Platonic idea of harmony, which must be studied in a purely abstract way, first by the method of problems, and secondly as a part of universal knowledge in relation to the idea of good.
The allegory has a political as well as a philosophical meaning.

The den or cave represents the narrow sphere of politics or law (compare the description of the philosopher and lawyer in the Theaetetus), and the light of the eternal ideas is supposed to exercise a disturbing influence on the minds of those who return to this lower world.

In other words, their principles are too wide for practical application; they are looking far away into the past and future, when their business is with the present.