§ 161. There is, then, a "true order of going," and an order that leads from one to many, from thence to forms, from thence to morality, and from thence to the general objects of thought or _the ideas_. In the "Republic," where the proper education of the philosopher is in question, it is proposed that he shall study arithmetic, geometry, astronomy, and dialectic. Thus in each case mathematics is the first advance in knowledge, and dialectic the nearest to perfection. Most of Plato's examples are drawn from mathematics. This science replaces the variety and vagueness of the forms of experience with _clear_, _unitary_, _definite_, and _eternal_ natures, such as the number and the geometrical figure. Thus certain individual things are approximately triangular, but subject to alteration, and indefinitely many. On the other hand the triangle as defined by geometry is the fixed and unequivocal nature or idea which such experiences suggest; and the philosophical mind will at once pass to it from these. But the mathematical objects are themselves not thoroughly understood when understood only in mathematical terms, for the foundations of mathematics are arbitrary. And the same is true of all the so-called special sciences. Even the scientists themselves, says Plato, "only dream about being, but never can behold the waking reality so long as they leave the hypotheses they use unexamined, and are unable to give an account of them. For when a man knows not his own first principle, and when the conclusion and intermediate steps are also constructed out of he knows not what, how can he imagine that such a conventional statement will ever become science?"[330:9] Within the science of dialectics we are to understand the connections and sequences of ideas themselves, in the hope of eliminating every arbitrariness and conventionality within a system of truth that is pure and self-luminous rationality. To this science, which is the great interest of his later years, Plato contributes only incomplete studies and experiments. We must be satisfied with the playful answer with which, in the "Republic," he replies to Glaucon's entreaty that "he proceed at once from the prelude or preamble to the chief strain, and describe that in like manner": "Dear Glaucon, you will not be able to follow me here, though I would do my best."