The Greek word analogia divides into two roots: the prefix ana, meaning “upward”, and logos, meaning “ratio”. An analogia is the application of a ratio derived from something well-known in order to point toward some feature of a less known pair. A analogy has four terms and two ratios. The missing feature may be (1) a unexpected similarity of relation or a (2) undefined term. Let me explain them in turn:
(1) An example of analogy revealing a ratio is Wallace Stevens’ claim that “A poet looks at the world the way a man looks at a woman.” Put in analogy form, the analogy is
All four terms are known, but the surprising point seems to be in the equivalence of ratio, that the relation between poet and world should take the same form as the well known man-toward-woman relation. The analogy communicates Wallace Stevens’ experience of being a poet, which is otherwise invisible to untutored eyes. We can point to features of external experience, but must rely on ratio — which is invariant to perspective (*see below) — and analogy to communicate inner experience. The philosophical importance of analogy should be obvious, since philosophy wants to point out features that are subjective but non-arbitrary. The form of Stevens’ philosophical vocation is an inner-something to which he conforms (subjective) but which he lives into without being its creator (non-arbitrary.) This protreptic pointing can really only happen through analogy.
(*Let me give an example of the perspectival invariance of ratio. Imagine looking a person from a distance of 50′ and then again at 100′. From the former perspective, the person will look taller and the latter shorter. Now imagine that the person is holding the same 12″ ruler in both cases. Although visually the two perspective differ in size, the ratio of length of ruler (e.g. 12″) to height of person (e.g. 72″) will be invariant in both cases. This is how measurement works, to allow the invariance made possible by ratio (logos).)
(2) Every analogy has four terms. If three are known and the ratios asserted to be equivalent, we can use an analogy to solve for the fourth term. The Divided Line is an analogy that guides the search for the fourth segment, e.g. noesis. The first two segments establish its guiding invariant ratio the difference between an image and that of which it is an image. We are then to apply this ratio to the third segment in order to find the fourth term. The Divided Line communicates a beginning point (the third segment, doxa-as-hypothesis) and a direction of search (an image calling forth its original, defined both by the first two segments and by the large division of the line as a whole) as a guide to understand noetic reality. It is protreptic, “forward-reaching”, since it frames an aspiration more than giving an answer. Noesis is what would be known if we are successful in following the guidance of the Divided Line analogy. The communication of noetic truth (immanent subjective criteria that are non-arbitrary) for someone who does not yet recognize it can happen no other way. Let me summarize my point with an analogy:
pointing : objects-in-the-world : : analogy : objects-of-inner-experience
The Divided Line is an invitation to look where Plato is pointing. It is less a conclusion than a task. It’s goal is the illumination of noetic experience for the willing seeker.