The Divided Line
February 28, 2026 – 6:30 pmPlato’s analogy in Republic 509d-511e can be summarised as follows.
| Line segments | A | B | C | D |
| Realm | Intelligible (νοητος) (509d) | Visible (ορατος) (509d) | ||
| Objects | Forms (511c) – considered in their relationship to the Good. The First Principle of things. (511a, b) The unassumed. |
Forms – NOT considered in their relationship to the Good
Assumptions, mathematical postulates. (510c-511b) |
Living beings, plants, artificial things. (510a, e) Models, drawings of geometrical figures (510d, e) |
‘Images’ of objects in C. Shadows, reflections, etc. (510a) |
| Operations | a. Derive First Principle from conclusions in B (511a, b)
b. From First Principle, draw conclusions for objects in B |
a. Draw conclusions from assumptions (to be applied to objects of C?)
b. Assumptions are taken for granted c. Appeals made to sensibilia (in C) |
||
| Operators | Philosophers | Mathematicians and other masters of τεχναι | [Scientists] | Sophists, poets, artists |
| Mental States | Intelligence (νοησις/νους) (Intelligence) (511a, b) |
Thinking (διανοια) (Reason) (511a, b, d) |
Perceptual Assurance (πιστις) (Belief) (511d, e) |
Conjecture (εικασια) (Illusion) (511d, e) |
| Status | Knowledge (επιστημη) | Opinion (δοξα) | ||
Just as the Line Segments are related A:B::C:D::A+B:C+D wrt length,
so are the associated Objects related wrt ‘genuineness’/’reality’ (αληθεια)
and the Mental States (παθηματα) wrt ‘clarity’ (σαφηνεια)
Note that whereas the construction Plato gives actually forces B=C, he makes no reference to that and we must assume that it is irrelevant to the analogy.
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