While trudging through the landscape of his rambles, Coleridge filled his notebooks with reference to and drawings of geometric figures. The question arises: Given his fascination with the uncultivated, irregular wild hills and rivers of his rambles, why would he utilize the fixed, abstracted geometric idiom removed from time? This chapter addresses this seeming contradiction by suggesting that his attraction to the geometric figure in his landscape descriptions is neither perplexing nor inconsistent but rather an expression of his immersion in an environment that nurtured a geometric frame of mind and believed in a mathematical ordering of the entire universe. Beginning with his mathematical training both at Christ’s Hospital School and at the University of Cambridge, Coleridge inherited a cultural conviction that one should take Euclid seriously. Furthermore, this training sharpened his powers of attention, abstraction, and an a priori intuition. Ultimately, his attachment to a geometric perspective did not distract him from his attraction to the sensuous movements, sounds, and colors of his natural surroundings. He intertwined them both and in so doing tempered his contemporaries’ way of thinking that separated the two modes of perception.

Part 4 addresses some questions arising. (1) Elsewhere (and, we assume, in the Republic) Plato recognizes a ‘good-making’ good – that without which all other goods lack value – which he identifies with wisdom. How does the ‘good-maker’ relate to the sun-like form? (2) The Republic recognizes a form of the good in which all good things participate. This entity cannot be straightforwardly identical with the sun-like form since the latter is interrogative whereas the former answers to the predicate of a true declarative sentence saying that something is good. How are these ‘two’ entities related? Discussion shows that the sun-like one is metaphysically prior to the participand. (3) What is the purpose of the rulers’ mathematical education? The Republic is explicit that it constitutes their induction into rationality. It neither says nor implies (so the present argument) that their ethical expertise will be couched in mathematical language, or that dialectic is responsible for a programme of grounding mathematics on ultimate metaphysical principles. (4) What is the role of the form of the good in the divine crafting of the cosmos? Does the interrogative interpretation apply here too? And is the sun-like form of the good actually a god itself?