Episode 05: The Divided Line

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Socrates, from "The School of Athens" by Raphael

Socrates, from "The School of Athens" by Raphael

Now Plato goes for a more “left-brain” approach. Some may find it helpful to have a graphic representation of the divided line, and examples abound. But it can also be instructive not to look at a drawing, but to treat the description as an exercise of the “intelligible” rather than the “sensible.” For one, it avoids pointless questions like whether the line is vertical or horizontal, or left or right. Also, to do so is an example of using what Plato describes as “that other sort of knowledge which reason herself attains by the power of dialectic, using the hypotheses not as first principles, but only as hypotheses….” If you need to “see” in order to “believe,” you are stuck in the sensible end of the line, and will never be able to see light as opposed to things in the light.  (That said, this is arguably the most difficult of the three descriptions, and a diagram can be helpful.)

Socrates: You have to imagine, then, that there are two ruling powers, and that one of them is set over the intellectual world, the other over the visible. I do not say heaven, lest you should fancy that I am playing upon the name (ovpavos, opatos)¹. May I suppose that you have this distinction of the visible and intelligible fixed in your mind?
I have.
Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion, and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness, and you will find that the first section in the sphere of the visible consists of images. And by images I mean, in the first place, shadows, and in the second place, reflections in water and in solid, smooth and polished bodies and the like: Do you understand?
Yes, I understand.
Imagine, now, the other section, of which this is only the resemblance, to include the animals which we see, and everything that grows or is made.
Very good.
Would you not admit that both the sections of this division have different degrees of truth, and that the copy is to the original as the sphere of opinion is to the sphere of knowledge?
Most undoubtedly.
Next proceed to consider the manner in which the sphere of the intellectual is to be divided.
In what manner?
Thus: There are two subdivisions, in the lower of which the soul uses the figures given by the former division as images; the inquiry can only be hypothetical, and instead of going upward to a principle descends to the other end; in the higher of the two, the soul passes out of hypotheses, and goes up to a principle which is above hypotheses, making no use of images as in the former case, but proceeding only in and through the ideas themselves.
I do not quite understand your meaning, he said.
Then I will try again; you will understand me better when I have made some preliminary remarks. You are aware that students of geometry, arithmetic, and the kindred sciences assume the odd, and the even, and the figures, and three kinds of angles, and the like, in their several branches of science; these are their hypotheses, which they and everybody are supposed to know, and therefore they do not deign to give any account of them either to themselves or others; but they begin with them, and go on until they arrive at last, and in a consistent manner, at their conclusion?
Yes, he said, I know.
And do you not know also that although they make use of the visible forms and reason about them, they are thinking not of these, but of the ideals which they resemble; not of the figures which they draw, but of the absolute square and the absolute diameter, and so on–the forms which they draw or make, and which have shadows and reflections in water of their own, are converted by them into images, but they are really seeking to behold the things themselves, which can only be seen with the eye of the mind?
That is true
And of this kind I spoke as the intelligible, although in the search after it the soul is compelled to use hypotheses; not ascending to a first principle, because she is unable to rise above the region of hypothesis, but employing the objects of which the shadows below are resemblances in their turn as images, they having in relation to the shadows and reflections of them a greater distinctness, and therefore a higher value.
I understand, he said, that you are speaking of the province of geometry and the sister arts.
And when I speak of the other division of the intelligible, you will understand me to speak of that other sort of knowledge which reason herself attains by the power of dialectic, using the hypotheses not as first principles, but only as hypotheses– that is to say, as steps and points of departure into a world which is above hypotheses, in order that she may soar beyond them to the first principle of the whole; and clinging to this and then to that which depends on this, by successive steps she descends again without the aid of any sensible object, from ideas, through ideas, and in ideas she ends.
I understand you, he replied; not perfectly, for you seem to me to be describing a task which is really tremendous; but, at any rate, I understand you to say that knowledge and being, which the science of dialectic contemplates, are clearer than the notions of the arts, as they are termed, which proceed from hypotheses only: these are also contemplated by the understanding, and not by the senses: yet, because they start from hypotheses and do not ascend to a principle, those who contemplate them appear to you not to exercise the higher reason upon them, although when a first principle is added to them they are cognizable by the higher reason. And the habit which is concerned with geometry and the cognate sciences I suppose that you would term understanding, and not reason, as being intermediate between opinion and reason.
You have quite conceived my meaning, I said; and now, corresponding to these four divisions, let there be four faculties in the soul–reason (noesis) answering to the highest, understanding (dianoia) to the second, faith (or conviction) (pistis) to the third, and perception of shadows (eikaisia) to the last–and let there be a scale of them, and let us suppose that the several faculties have clearness in the same degree that their objects have truth.
I understand, he replied, and give my assent, and accept your arrangement. ²

So score another one for Socratic irony: Glaucon has just heard something that could have blown the top off his head, that is, the soul has the capacity for contemplation through the faculty of reason which is beyond the understanding. But he contents himself with saying, “I understand…assent…accept.” Plato is anticipating the reaction of those who would reduce this teaching to a system that can be “understood” by the critical mind, and then compared and contrasted with other systems. Glaucon is stuck with the hypotheses as ends in themselves, and cannot “soar beyond them to the first principle of the whole….” The term noesis, translated by Jowett as reason, is not the same as reasoning, which is more the realm of dianoia, the discursive mind. Noesis has the meaning of intuitive, a priori, knowledge―higher even than hypotheses. It is the realm of the Ideal, of contemplation, where the very machinery of the discursive mind can be observed.

An objection is sometimes raised that by using the term “divided,” that Plato is creating or perpetuating a duality–intelligible vs. visible.  But again, I think this is a product of a dualistic mind, like Glaucon’s.  Another apt analogy would be that of an electrical grid: there are the generators, transmission lines, wires running throughout the house, and finally the appliances.  One can divide this grid up into different parts for convenience sake, but we should not forget that it is all the physical apparatus of the invisible electrical current, whose nature is the same regardless of where on the grid it is located.  If the grid here is analogous to the Intelligible realm, we are like intellectual appliances in the visible, and we go along happily thinking we are separate, self-controlling toasters or lamps or microwaves.  Until one day our plug gets pulled.

So I believe Plato intends the divided line not as a mere philosophical diagram, but as a description of our true nature, and an aid in ascending the line to reach the noesis. In the Symposium, he describes, through Diotima, how someone who wished to see the form of beauty itself should begin by looking as much as possible on beautiful things, and proceed from there to an appreciation of the beauty of the mind and contemplate the beauty of laws and institutions and the sciences– “the vast sea of beauty.”

Diotima says, “And the true order of going, or being led by another, to the things of love, is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these as steps only, and from one going on to two, and from two to all fair forms, and from fair forms to fair practices, and from fair practices to fair notions, until from fair notions he arrives at the notion of absolute beauty, and at last knows what the essence of beauty is. …But what if man had eyes to see the true beauty ― the divine beauty, I mean, pure and clear and unalloyed, not clogged with the pollutions of mortality and all the colours and vanities of human life ― thither looking, and holding converse with the true beauty simple and divine? Remember how in that communion only, beholding beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities (for he has hold not of an image but of a reality), and bringing forth and nourishing true virtue to become the friend of God and be immortal, if mortal man may. Would that be an ignoble life?” ³

Finally, describing this journey in another way, Plato uses the famous analogy of the Cave.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.  Translation of Plato by Benjamin Jowett.  Graphics are not copyrighted, and are believed to be in the public domain.  Music courtesy of Stefan Hagel, and used by permission.  Special thanks to Richard G. Geldard.

¹ A play on the words for “heaven” and  “to see.”

²,³ Again, these selections are available at The Classics Archive.

Also available, a complete reading of The Republic (Desmond Lee translation) by someone who actually has a nice voice, Patrick Horgan.