The Four Levels of Plato’s Divided Line
Plato’s Divided Line is divided into four parts of different lengths reflecting lesser or greater epistemic clarity. The shorter the less grasp on reality. For those in the back, the longer, the greater the grasp on reality.
The line is divided into two with a 1:2 ratio, and then both sections are further divided by the same 1:2 ratio. This leads to the relative lengths of 1:2:2:4. This is what we would expect by using the shortest level of intelligence in creating this analogy.
The following extract goes into more detail.
This is where I draw the line
The various ratios supplied by Socrates for the sections of the line lead to the conclusion, not made explicit in the discussion, that the two central sections (visible things per se and visible things in the service of thinking) are of the same length. It would follow that ‘conviction’ and ‘intention’ have the same epistemic clarity, since epistemic clarity is what the lengths are said to represent. If, however, the geometer, for example, uses a visible circle to represent an intelligized geometrical abstract circle (as Socrates indicates that he does), his ‘intended’ circle must have more epistemic clarity than the merely visible circle. If so, the section representing ‘intention’ should be longer than that representing ‘conviction.’
Extract from Chapter 6, ‘The Digression’, in Ivor Ludlam (2014), Plato’s Republic as a Philosophical Drama on Doing Well, pp. 190–191.
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