Divided Line

The sensible world: things and their reflections — mere opinions.

Man lives amidst shadows. He creates opinions about things that he is not even sure if they exist. And even these things are not entirely real. The scientist can transcend the flawed world of the senses — of the things as they appear to us — and elaborate hypotheses about reality. But only the philosopher comes to see the light and, from it, he can see things as they really are. This is the Platonic theory about the world, a fascinating blend of theory of knowledge and metaphysics.


When Plato writes “The Republic” (ca. 380 B.C.), Socrates has already been dead for about twenty years. But the loss of his master only ascertains what Plato already knew since before the Peloponnesian War ended and Athenian shame began: democracy is a farce, and must be replaced.

This is, in short words, the historical-political context of “The Republic”, but Plato’s seminal dialogue is much more than a political critique. Yes, his text proposes a new form of government — that of the “philosophers-kings” — but in it Plato exposes a whole new theory of knowledge, as well as a new metaphysical understanding of the universe. Both are necessary for one of the projects inherent in his work: an educational reform.

What kind of education should the future philosopher-kings receive? Certainly not the one contained in the Homeric myths, where the gods are even more vile than men. Plato favors mathematics and its sister in the arts — music — but regardless of the method to be used, man must learn to distinguish the nature of each object that he sees, as well as to which attitude of the soul it relates. This is why he develops in Book VI  the “analogy of the divided line” and in Book VII the even more famous “allegory of the cave”, the latter a more dramatic way of exposing the former.

Socrates, the character, twice divides the line into two segments, thus forming four segments in total. But since the line correlates states of mind with their corresponding objects (making clear the intrinsic connection of epistemology and metaphysics), it is also worth imagining it dividing the vertical plane into two longitudinal sections, one on each side of the line. The left side (taking the line vertically) is the side of epistemology; the right, of metaphysics.

The lower section comprising two segments is the world of appearances, the sensible world, where all we have is an opinion (δόξα) about things. Within it is all that we apprehend with our senses (πίστις) — lakes and mountains, for example — as well as the distorted images we make of things (εικασία) — the reflection of the mountain on the surface of the lake. But Plato refers not only to physical things and the ideas we make of them, but to all kinds of opinions. Thus, if we see goodness in our parents, at least we are making the right judgment of what is being presented to us (πίστις). But when we allow ourselves to be convinced by the apparent goodness of a charlatan, then we see only shadows, distorted reflections of things as they appear; we are on the lower level of perception, that of mere conjectures, false opinions, illusions (εικασία).

The upper section is the world of things-in-themselves, of reality itself, the intelligible world. Apprehension of this world produces true knowledge (έπιστήμη) and not mere opinion. But even knowledge is divided into two levels. The lower segment corresponds to hypotheses formulated from the images of the sensible world. Plato seems to equate the objects of this segment with mathematical abstractions. Such hypotheses allow man to come to conclusions about the world, but not to the first principles that govern it. Thus, these conclusions are partial, temporary, mere understanding (διάνοια) about things. With the use of dialectics operating on these hypotheses, the philosopher manages to pass “from ideas, through ideas” until he reaches the “first principle of the whole”. Only then, retracing his way down, is he able to turn his hypotheses into final conclusions, into intelligence (νόησις). He has seen the light, and now he can illuminate his intellectual world.

Light is metaphorically seen as the Sun, but for Plato it is the very Idea of ​​the Good, the “good” being understood together as the beautiful, the good, and the true.

Good or God?

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