Although Plato’s famous allegory of the cave is subject to many interpretations, many philosophers believe that it was designed to encapsulate and support his theory of Forms.
To a certain extent it does, however it is essential that in order to determine whether it does, we must first grasp what the complex theory of the Forms really meant to Plato, and then one may begin to put the allegory into context of his theory of Forms.
Plato believed that there were two distinct worlds, and those worlds provide the framework from which his theory of Forms is built. Plato, in his allegory of the cave uses the cave itself and everything inside the cave as a metaphor to provide persuasive support for the material, illusionistic world or senses. Plato believed that the material world is subject to a constant state of flux making it is impossible to know the truth of reality. Plato states that it is ‘ourselves’  who live in this material world. Our world, Plato likens to a cave, and we in the allegory are presented as the prisoners chained inside, who live in a material world of illusion which we think is real and important. The cave represents our own imperfect and changing experiences. The chains that constrain “us,” the prisoners, represent our false beliefs which obstruct our understanding of true reality. Thus, it is we who stare at our ‘own shadows, or the shadows of one another’  . In his allegory, everything outside the cave is portrayed as the eternal world, which possesses the object of knowledge and contains the true perfect world of the Forms.
Plato regards Forms as ideal, abstract objects which are perfect, eternal and unchanging. They are the perfect paradigm of each sort of object we see around us, and there is a Form for each characteristic or property and object could have. Plato also believes that there are forms for abstract objects and concepts such as beauty, numbers and goodness to name a few. Perhaps, most importantly Plato explains that the Forms are real, however the material objects are not. In the allegory of the cave, Plato portrays the shadows on the cave wall as a metaphor for material objects, in the hope of providing persuasive support for his theory of Forms. He reminds us that the shadows are all the prisoners would have seen and talked about, and the point he makes is that these shadows would be as close as the prisoners got to experiencing and seeing reality. Therefore they simply mistake them for reality, ‘the truth would be literally nothing but the shadows of the images’  . Socrates raises an important and efficacious question when he asks; ‘if they were able to converse with one another, would they not suppose that they were naming what was actually before them?’  Hence, for example, if one of the prisoners identified a shadow of what they learnt was a book in their language, and said “behold, a book;” Plato argues that the prisoner would be making the mistake of referring the word “book” to the shadow they see in front them. The real referent to the book however, is the object that cast the shadow; which the prisoner cannot see because it his behind him. Plato intends to support his theory of Forms in writing this because he wants to make the point that the general terms of our language are not the names of the physical objects that we see. Plato says that they are names of things that we can’t see, and believes they can only be grasped with our minds. Likewise, Plato argues that although we may obtain concepts by our perceptual experience of physical objects, we are sure to be mistaken if we think that the concepts we grasp are on the same level as the things we perceive.
Plato thinks that we can have only have genuine knowledge of things which are perfect and unchanging, and that although we can have knowledge about the forms, we cannot have knowledge about material objects. Plato believes we only have opinions or beliefs about the material world. In the allegory of the cave, Plato purposely creates a new analogy when Socrates asks Glaucon to ‘see what will naturally follow if the prisoners are released’  . This action is important because it essentially enables the prisoners to grasp the theory of Forms with their minds. After one prisoner is compelled to turn their head around, at first distressed by the fire he soon discovers that the shadows on the wall are imperfect representations of the real objects. It is clear to the prisoner that what he considered to be reality, is now ordinary shadows on the wall of the cave.
The ascent of a prisoner out of the cave from the material world and into the eternal world provides persuasive support for his theory of Forms, because it is intended to represent the process of recollecting our knowledge of the Forms. Socrates says that the prisoners eyes would be at first ‘dazzled by the light’  and then he would grow ‘accustomed to the upper world.’  This provides support for Plato’s theory of Forms, because it symbolically represents the move between the two worlds, the material world of senses to the eternal world of Forms. Once the prisoner has got used to the light, he is now able to see the truth and understand that what he and the other unenlightened prisoners saw in the cave, was actually an illusion. Plato explains that the prisoner, once he transcends beyond the cave, he will encounter real forms and not a mere approximation of the reality in the cave. He will also gain valid knowledge. The prisoner would recognise some of the shadows that he witnesses in the water, because he has seen them in the cave before. However, the reflections he would see in the water outside the cave would spark an advancement in his own knowledge, for what he once saw as dark fuzzy blurs would now be seen in precise detail of colour and lines. Plato intends this to support his theory of Forms because he wants to emphasise that the physical objects the prisoner sees represents the Forms of the physical objects. Plato also intends to represent the objects in the night sky, such as the moon and the stars, to what he believes are the Forms of abstractions. In the allegory, the prisoner is led to conclude that it is the sun that makes things visible, and it is the sun that causes the seasons of the year. The prisoner understands what the shadows are, and that the reflections differ from the objects in the visible world. The prisoner assumes that without the sun there would be no visible world. The sun is therefore a metaphor for the Form of the Good, and is the highest of all the Forms as it illuminates all the other Forms. It is the organising principle in which all the other Forms participate and is the ultimate object of knowledge.
Socrates proposes that that if the prisoner was to return to his ‘old habitation’  he would ‘felicitate himself on the change and pity’  of his fellow prisoners. However, in the harsh “reality” of the material world, Socrates says that the prisoners would ‘say of him that up he went and down he came without his eyes; and that it was better not even to think of ascending’ and ‘they would put him to death’  . Plato uses this allegory to suggest his belief that most of humanity are like the prisoners who are prepared to dwell in the the darkness of the material world. Plato believes that the “prisoners” who have been liberated from the “cave” have achieved the highest knowledge, however he believes they should not stay in the higher world of contemplation. Instead, Plato thinks that they must be made to come back down into the the material world, the “cave”, and like the philosopher educate the “prisoners” without knowledge.
In conclusion, I think that Plato’s allegory of the cave does provide persuasive support for his theory of forms. There are two worlds in the theory of Forms which Plato thinks exist, and this belief is supported in his allegory. Plato depicts the cave as a metaphor for the world of senses and depicts everything outside of the cave as the world of Forms. Plato pictures our world as a cave, and in the cave we are chained facing a wall. We are represented as the prisoners, who only see “shadows” of the true Forms. Inside the cave, although they can’t see it, the fire acts as the source of all the prisoner’s knowledge. Outside the cave, the sun is represented as the of Form knowledge itself. In order to discover the true Forms, Plato thinks we have to ascend to the world outside of the cave, and recollect our knowledge of the Forms. Plato, in his theory of Forms believes that in order to truly know something, you have to intelligibly capture the Form of that particular object. To understand the true meaning of a book, Plato states you have to go beyond the empirically given book and mentally contemplate ‘bookness.’ Plato’s point is that it is not possible to understand the meaning of book just by observing different “shadows,” which the prisoner do. By doing so, we are creating false beliefs that obstruct our understanding of true reality. Plato intends the chains to depict this. However, when the chains are released and we are able to adventure into the world of perfect Forms, once we have come across perfect Forms like the flowers and then the sun, only then have we gained knowledge. Plato’s point I believe is that like the remaining prisoners in the cave, people do not bother trying to capture bookness in itself. He claims that they are content in watching the shadows of books, and believing that they are the Forms of the books. ‘Would he not say with Homer, “Better to be the poor servant of a poor master”‘ and to endure anything, rather than think as they do and live after their manner?’ 
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