The Sun, Line, and Cave

Foreword

This is the second tutorial written for Philosophy 430: History of Ancient Philosophy. It tackles Plato's Republic VI-VII, specifically the famous allegory of the cave. As with all tutorials, the first large portion is guided long answer questions, followed by some opinion-based ideas. We start by discussing the ideas Plato presented, and the parallels between his analogies. I finally end with some criticism of the ideas presented.

Body

We can draw parallels between Plato’s divided line and the cave allegory. The line can be interpreted as either physical or mental, I will describe the comparison in terms of the mental (Plato, Republic VI, 511d). The visible and intelligible sections are comparable to being inside and outside the cave respectively. Inside the cave, the artifact shadows are compared to guesswork, the artifacts themselves to belief. Outside the cave, images of things are comparable to thinking, and the things themselves to understanding.

One may feel prompted to instead, group things themselves and the images of things in the thinking subsection, and the sun with understanding, as that is how it seems Socrates intends to verbally group them (Plato, Republic VII, 516a). I find this to be disanalogous. It seems that in the allegory, the things outside are meant to be the Forms, and the sun the form of the Good. But, as the divided line initially made clear with its physical interpretation, the Forms themselves are grouped with the understanding, not the form of the Good. Rather, the form of the Good, and the sun can be placed on the top of both lines, completing the comparison.

Plato differentiates the philosophers and the laymen. The laymen are the prisoners in the cave, unable and unwilling to shift their perspective from the shadows in front of them. This is similar to the lovers of sight and sound, non-philosophers are only concerned with what is immediately apparent to them, and spend no time concerning themselves with gaining true knowledge. Meanwhile, the philosopher is constantly engaging with what is, theorizing and arguing. They go through the Socratic method to deduce things about reality. These are the skills that are necessary to advance from the visible to the intelligible, and from the inside of the cave to the outside.

The geometer is brought up when discussing thought. The geometer, like many other disciplines, searches for conclusions based on a set of axioms (Plato, Republic VI, 510c). In geometry, they still rely on the visible existence of shapes, such as squares, to make their deductions, regardless of whether or not their proofs use a particular shape. The dialectician, on the other hand, attempts to deduce those axioms, as opposed to assuming them. If they can find these axioms, anything deduced from them is a fundamental truth about the world that requires no visual understanding. The “unhypothetical first principle” is emblematic of the Good. This is the main form that Plato is interested in, as he argues that all other forms are offsprings of the form of the Good. To help find out this principle, philosophers can extensively utilize the geometer's methodology. Plato states that mathematical reasoning makes people “become generally sharper than they were” (Plato, Republic VI, 526b). He thinks that the deductive skills gained from geometry give people the ability to critically engage with what is, and allow them to be better dialecticians.

Meno would be at the second level of ascension. He seems to be unable to engage with any ideas that Socrates puts forward, nor provide any useful or original thoughts to the conversation, going as far as to quote other people’s definitions. However, it seems like he does have an understanding of what virtue is beyond what is immediately clear. Despite his inability to come up with his own definition, he can still distinguish between whether a specific act is virtuous or not. However, he seems content with not delving into why or why not that is the case, and rather more interested in staying in with what is generally considered virtue.

Someone who gives a “safe” answer would rest in the intelligible, but someone who gives an unsafe answer would be claiming that something is beautiful because of the colors or shape. This again seems to reflect the idea of belief. The person needs to understand enough simple concepts of beauty to be able to address some new item as being beautiful, yet has no curiosity to discover anything beyond their assumptions.

Socrates is an interesting case. Despite him clearly being more wise and self-aware than any other people in the belief subsection, he still claims that he has no knowledge, which is reasonably true. When he interrogates someone, he exposes them for having no knowledge on a topic despite claiming to. Yet, Socrates is also unable to provide any counterpoint, indicating that he doesn’t possess that knowledge himself. Despite this, he is clearly able to engage in dialectical reasoning, which is above those in the belief category, but he cannot claim that he has any understanding, thus he must live in the thought subsection.

The sun, line, and cave can be interpreted in multiple fashions, but the point that Plato is trying to get across is creating an allegory for the Forms, their necessity for the world, and how to proceed once we possess knowledge about the Forms. This is probably most clearly understood in comparison to the cave. The Sun is the form of the good, the things are the forms themselves, and the images of the things are rudimentary understandings of those forms, the artifacts are the particulars, and the shadows of the artifacts are poor understandings of the particulars. He argues that essentially everyone lives in a world of a lack of knowledge of the Forms, and rather we focus on all the rudimentary particulars in front of us. Plato pushes this entire allegory to show us how the layman is blind to what truly is, and to help us understand the benefit of understanding the Forms, specifically the Good. Plato directly says that the Good is to be thought of as the Sun. The line helps us have an understanding of where we are on the enlightenment scale and helps us visualize what the actual forms are.

Evaluating these dialogues, it seems like there is no strong argument for the necessary existence of the Forms. It irrefutably solves issues that these philosophers ran into, being what makes an object have F-ness, but that does not justify its necessary existence. A person could easily push another belief that solves the same problems. For example, a nihilist could argue that adjectives are just conventions and contain no intrinsic properties; we call something beautiful so it is easy to convey that we think it looks nice.

Furthermore, almost every argument presented is in the form of analogies. Some sort of argument through analogy could be phrased as:

1) X and Y are analogous in relevant respects

2) X has property Z because of the relevant characteristics

∴) Y has property Z

This argument could be made stronger but overall hinges on the idea that the analogy implies a deductive premise about the property Z. A refutation could be as easy as saying that X and Y are not analogous with respect to property Z, or the relevant characteristics don’t necessitate the existence of property Z. In our case, it is abundantly easy to claim that our worldly situation is not comparable to the situation in the allegory of the cave and that therefore the enlightened understanding of the forms does not exist. An analogy is only useful in assisting the understanding of well-formed arguments, not replacing them. In any case, it is on Plato to justify why it is necessary that our reality is like that of the cave.

Assuming the existence of the Forms, the analogies seem plausible. However, it is unclear why the Good itself is the parent of all other forms. Up until this point, Plato still is only arguing that the Forms are virtuous things, like justice, goodness, strength, etc., and not mundane things, like mud. In this case, the argument that all Forms come from the Good itself makes sense. However, it is not clear why some form of Mud or Injustice cannot exist. Were these to exist, it seems like they cannot be offspring of the Good itself, which would likely dismantle the analogies.

Plato argues that philosophers have found the true meaning of good and that therefore they ought to rule the city (Plato, Republic VII, 520c). Which, assuming is true, is not an absurd conclusion. However, I refute the idea that philosophers, especially during Plato’s time, had discovered such things. Even if we accept that the Forms are entirely true and that the Good itself is the parent of all forms, it is entirely unclear that Plato or any other philosophers have interacted with this form of the Good. They may inquire about it, or discuss the existence of these other forms. But just because they discuss it does not mean that they have found it. Consider the allegory, but instead of leaving the cave, they are simply discussing the idea of leaving the cave and thinking about all the ways they could leave the cave, and how good leaving the cave would be. It sounds useful, but it seems like they have no greater knowledge about the outside than the laymen.