The four segments of the Divided Line

This is the beginning of a series of posts on the Divided Line Analogy, which can be found at the end of Republic, Book VI (509d-511e). I maintain that the Divided Line Analogy is is the hermeneutic key to understanding the purpose of the Republic as a whole, and the proper proportions of everything else in the Republic are revealed by it. The Analogy is so compact that it will take some development to convey its structure and meaning. Perhaps the best way to begin is not with the geometrical construction of the line (as the dialogue does) but to begin where Plato ends, by labeling its four segments:

EIKASIA — translated variously as “imaging” or “imagination.” My preferred definition of eikasia is Jacob Klein’s: “the power to see an image as an image.” Eikasia is a grasp that mere appearance is defective, that the image is not the original, thatthe shadow, sign or reflection is not the thing. Eikasia is the basis of all cognitive achievement, both perceptual and intellectual. All power of thinking with signs is based on a prior power of eikasia. It is a power particularly prominent when perception is ambiguous, such as when a change in distance creates a change in size or when a stick placed in the water appears broken. Eikasia is disturbed by the instability of appearance and initiates a search for an objective resolution to its subjective dissatisfaction. Eikasia adds a question mark to the data of appearance.

PISTIS — translated variously as “trust” or “belief.”Pistis is an opinion that resolves the unstable defects of mere appearance. It is the satisfaction of the dissatisfaction opened up by eikasia. I see the stick broken in water; I trust in the basic integrity of the stick. I see a person growing smaller when she walks away from me; I trust that the size is as stable as the tangible object. Whereas appearances can be contradictory, one cannot act in opposite directions at once. Pistis resolves the ambiguity; it is the resolution that makes action stable and fixed, to keep one from chasing the tail of shifting appearances. One good example comes from a previous stint that I had as a pilot. These are a variety of sensory illusions that can be inflicted upon a pilot, particularly in the absence of a visible horizon when flying in clouds. One of these is a condition called “the leans,” in which cues from one’s inner ear can make it seem like one is flying other than at level, even when everything is level. “Trust your instruments!” — this was the constant refrain in flight school. If the gyro says you are level, you are level, even if your sense of balance screams otherwise. Pistis is a resolute trust in an opinion that has proven reliable against the ambiguity and inconstancy of perception. We would be paralyzed without this power. One glaring downside though is that pistis, by steeling itself against shifting perception, makes itself immune to counter-evidence. As a result, pistis is never self-critical of its own commitments.

DIANOIA — translated variously as “thinking” or “thought” or “thinking-things-through.” Dianoia is hypothetical, calculative thinking. Just as eikasia is “the power to see an image as an image,” so dianoia is “the power to think an opinion as an opinion.”  Dianoia can be thought of as a higher-type of eikasia applied to pistis itself (Jacob Klein’s idea). It is the recognition in opinion of the defect inherent in mere opinion. Both pistis and dianoia are based in opinion. In fact, the same opinion can be taken up in the manner of either pistis or dianoia. (This identity of opinion is perhaps the reason that the two segments on the line necessarily have the same length at the end of the geometric construction.) Whereas pistis contrasts itself favorably with the hesitancies and dissatisfactions created by eikasia, dianoia reintroduces dissatisfaction with its own defects by comparing itself to noesis. Dianoia is an intermediate between pistis and noesis. Whereas pistis lacks self-criticism and is content with the seeming-true of its settled opinion, dianoia is essentially self-critical — particularly in exposing the biases that can make the false seem true and the true seem false. It attempts to replace seeming with measurement, i.e. the application of intelligible ratios. Dianoia is alert to counter-evidence.  Both eikasia and dianoia reach outside themselves toward the completion/perfection provided by pistis and noesis, respectively. Dianoia remains wedded to hypotheses and its progress is always step-wise and temporal, always aiming toward the “unhypothetical first principle of everything.” (Rep. 511b)

NOESIS — translated variously as “insight” or “understanding” or “intellection.” Noesis is both the immanent light of anticipated wholeness within dianoia and a transcendent desideratum outside of dianoia. Noesis is the unknown ‘X’ of form/eidos toward which dianoia extends. Noesis is the place of settled knoweldge. The Divided Line is itself a dianoietic image of dianoietic extension toward noesis, reaching from within dianoia outward toward noetic wholeness. The line assumes a known ratio (the relation of image to original) and applies it to a known basis (opinion) in order to direct a search toward what is an as yet unknown noetic consummation. We are told that (pure) noesis is not at all hypothetical, but begins, moves through and ends with forms. (Rep. 511b) Whereas dianoia reaches toward the whole by considering the parts and their relations, noesis is a grasps of the whole in its undivided integrity. Noesis is similar to pistis in that it provides a resolution to the unsettled questioning of its lower power (eikasia:pistis::dianoia:noesis). But whereas pistis achieves it resolution by closing itself off to higher questions, remaining content with the seeming-true, noesis is the originating source of higher-order questions and is the contentment in the really-true. Noesis is the implicit perfected understanding that makes the imperfect questionable. Noesis is an immediate grasp of truth, without the step-wise stepping from hypothesis to hypothesis that is characteristic of dianoia. Noesis is a flash of active insight that comprehends at once the answer that had been the goal of dianoia’s questioning. Noetic understanding is the goal of the Republic, but sits outside its essentially hypothetical structure. Noesis is a truth that cannot be stated directly; it is insight that cannot be communicated without a corresponding insight in the other. No string of words will ever suffice to replace it — communication of noesis must be indirect and protreptic.

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