Plato the divided line essay

Only realities can be known. But why is that so? The material that is object to this inquiry includes Plato's discussion of true Philosophy dd , the analogy of the divided line ce and the allegory of the cave ab. They all answer question A and B , but we will focus on Plato's discussion of true Philosophy for A and on the other two for B. Concerning A : From Plato's ideal city Kallipolis to his claim that rulers should be philosophers and vice versa.

In the beginning of book 5, Plato wonders how to achieve a good city in practice and states three points: He claims that women should be equal to men, that the rulers should love their city above all and that philosophers should be rulers or rulers should be philosophers. The first two statements refer to the books and are for this essay of minor importance.

The third statement however is very controversial. It was — and still is — considered an anti-democratic statement, furthermore, philosophers were considered of no practical use for society. In defending his controversial statement, Plato comes to our first object of interest: the discussion about what true philosophers are. The reason for this would be that philosophers have the means to find out about the truth — and that is where Plato starts with his first part of the message. He state that there is a fundamental difference between 'appearance' and 'reality'.

Answering A : What is 'appearance', what is 'reality' and why is there a difference between them? First, let us define the terms. Apart form the example of beauty, and apart from who can see the reality and also apart from the assignment of belief to appearance and knowledge to reality that is discussed later — we can draw one conclusion here: Appearance is ambiguous, changing and manifold, whereas reality is absolute, unchanging and clearly distinguishable.

So, now Plato gave us the definitions for the terms appearance and reality and an idea of how appearance is organized — namely in chaos. But how is the reality organized? The answer lies in the next big part of Plato's argumentation, the definition of 'forms'. All the different appearances of — let's say beauty — can be abstracted to one common ground, as the designation of various songs as music is also an abstraction. Music, movies, paintings, interesting articles, and every beautiful thing can, following that, be abstracted to a form — here the form of beauty.

Plato calls the process of doing so reasoning. Reasoning allows us to abstract what our senses allow us to see, hear, smell, etc. These things are then abstracted and concluded in forms, that can be thought of as containers in which we throw everything that has a common basis. People who think that there are many forms of beauty, for example do not — according to Plato — realize that there exists only one form.

Plato's explanation uses pure logic: beauty and ugliness, being opposites, are two separate things because opposites cannot be the same thing and in being separate things, they are each one thing a. So now we defined what appearance and reality are and what the difference between them is. By now, one can probably already guess why there can be no true knowledge of appearances and why those concerned with appearances can have no true knowledge: because appearances are too quickly changing, too ambiguous and too chaotically organized to form lasting knowledge about them.

For Plato's explanation, let us nevertheless have a brief look on the analogy of the divided line and elaborating the conclusions of this analogy, the allegory of the cave. Concerning B : Why can there be no true knowledge of appearances? Bringing things together. Plato only claims that philosophers should be kings because he says that this would be the right way to achieve the social good. But what is the good? Or in Plato's terms — what is the form of the good?

Plato says that knowledge is the good b; we should keep in mind Plato's claim that only true philosophers are capable of knowing! But why should we then call it good and not simply leave it at knowledge? Without knowing the form of the good, knowing every other form is worthless a , because individuals can not know if their deepest desires are contained by the form of the good. So, in order to have complete knowledge of the reality, one must know the nature — or the form — of the good. Socrates can plausibly be supposed to have provided Glaucon with a couple of examples of the contents of EB -- the square itself and the diagonal itself D Examples of the contents of AD presumably include the shadows and reflections mentioned at EA3.

Plato’s Allegory of the Cave - Alex Gendler

The contents of DC presumably include perceptible things around us: flora, fauna, and artifacts A But what about the contents of CE? Unfortunately, this language obscures more than it clarifies. Visible forms are the originals of which shadows and reflections in water are images EA1.

That is to say, they are perceptible, and as such they belong in DC, not in CE. Plato makes it very clear that one and the same thing a visible triangle can serve both as an original when compared to the shadows and reflections that are the contents of AD and as an image when compared to the triangle itself, which is among the contents of EB. The fact is that Glaucon is given no clear sense of the contents of CE.

Here again it is possible that he is speaking elliptically: the objects of dialectic i. But in the next several lines C6-D5 , Plato ignores the supposed differences between the objects of dialectic and those of the various branches of expertise, and focuses entirely on the difference in method and attitude between the dialectician and the mathematician. He even insists that nous i. The division between the two sections is not made by reference to their respective contents or objects; here again Plato's interest is in the attitudes and methods characteristic of the intelligible subsections.

If Plato thought that for each epistemic state there was a unique ontological correlate, why would lengthy arguments be needed to articulate this? If he thought this, it would be easy to say so; but Plato is careful to say nothing more than what he has already said at D6-E4.

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None of the Platonic passages I have noted suggests that for each term in the epistemological proportion there is a corresponding term in the ontological proportion. My second reason for not reading Plato in this way requires a look at the sorts of proportions Plato gives us. I suggested earlier that Plato is aware of this fact.


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So his first proportion is of the sort Greek mathematicians called "continuous. Nicomachean Ethics ab2. Plato's point is made with a line, not with a pair of numerical ratios. But this is what we should expect given the predominantly geometrical i.

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See Elements V, passim. The two segments nicely express the desired proportion. At the beginning of the divided line passage D , immediately before drawing the ontological proportion, Plato in effect places two such segments end to end, thus:. In Plato's account AC is the visible section and CB the intelligible, each of which comprises two subsections; by putting the two sections end to end Plato can make two points with a single illustration, namely that the ratio between the visible and the intelligible sections AC : CB is equal to that between the first and second subsections of the visible AD : DC and to that between the first and second subsections of the intelligible CE : EB.


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  5. Nevertheless, Plato suggests later that in CE the mind "uses as likenesses those very things which themselves are the originals of a lower order of likenesses" A In CE the mind uses the same things; but they are now -- in the intelligible section of the line, or from the point of view of their intelligibility -- used as likenesses cf. The same things are treated as visible models in DC and as intelligible likenesses in CE. Notice that this proportion cannot properly be thought of as equivalent to or isomorphic with the first, since unlike the first its middle terms are different.

    Consider the two ratios 2 : 4 and 5 : 10, i. The equality of these two ratios can be expressed as a proportion; we need only place the segments in Figure 4 end to end, thus:. A non-continuous proportion like that in Figure 5 behaves quite differently than a continuous proportion like that in Figure 3, and some of the points one can make with a continuous proportion cannot be made with a non-continuous proportion.

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    It is true, e. Plato returns to the epistemological proportion in Book VII, in a passage that looks back at the sun, the line, and the cave, and the psychological and educational points they were enlisted to illustrate:. When the mind's eye is literally buried deep in mud, far from home, dialectic gently extracts it and guides it upwards, and for this reorientation it draws on the assistance of those areas of expertise we discussed [the mathematical sciences, described at DD6]. It's true that we've often called them branches of knowledge in the past, but that's only a habit and they really need a different word, which implies a higher degree of clarity than belief has, and a higher degree of opacity than knowledge has.

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    Earlier [at D4] we used the word "thought" [ dianoia ]. But I don't suppose we'll quarrel about terminology when we're faced with matters as important as the ones we're looking into at the moment So the terms we used earlier will do As being is to becoming, so intellect stands to belief; and as intellect stands to belief, so knowledge stands to confidence and thought to conjecture.

    However, we'd better pass over the proportionate relationships between the objects of intellect and belief, Glaucon, and the twofold division of each of the two realms -- the domain of belief and the domain of intellect -- if we want to avoid getting entangled in an argument which would be many times as long as the ones our discussion has already thrown up.

    Ignoring for the moment ousia and genesis , Plato's claim here is that with respect to clarity and unclarity. So the proportion drawn at A reiterates that drawn earlier at D6-E4. Notice that nothing is said about the relationship of dianoia and pistis to each other -- which is just to emphasize the fact that the proportion is non-continuous. Hence the epistemological proportion must be distinguished from the ontological proportion. Here, then, is another reason to reject the idea that for each term in the epistemological proportion there must be a corresponding term in the ontological proportion.

    There are three different terms in the first proportion, and four in the second. Plato is now making a different point, using a different kind of proportion. My third reason for rejecting the idea of a unique ontological correlate for each item in the epistemological proportion is this. As we have seen, Plato suggests that the same things can be treated or used as originals or as likenesses, depending on one's purpose or point of view. Perceptible things around us are treated as originals at A; but the mind can also use them as likenesses in order to grasp something intelligible B, EA1, A The same things, then, can be objects of more than one of the epistemic states Plato distinguishes.

    Likewise, at D, in the course of developing the second proportion, Glaucon suggests that on Socrates' view geometers and mathematicians can have nous of the objects of their crafts, if they proceed from a genuine starting-point. Socrates goes along with this. More generally, I see no need to take Plato to be committed to the view that ta doxasta simply cannot be known or understood, that perceptible things are inherently beyond knowledge or understanding. I suggest that what he is claiming here -- and in similar-sounding passages at Rp EA12 and AD4, and Phaedo 74A2-E4 -- is that unless one understands that it is intelligible forms that constitute perceptible things, and unless one is able to grasp these forms in those things, one cannot understand those things.