Plato’s allegory of the cave appears in Book VII of Plato’s most famous and longest dialog, The Republic. Plato’s dialogs frequently star Plato’s teacher Socrates as a character. The dialogs involved discussions and philosophical arguments between various characters, some of whom were based on real people. Plato particularly disliked the sophists who were professional rhetoricians and who seemed to care more about money and social success than truth. In fact, Plato accused them of teaching their students how to make the worse argument appear better – enabling their students to convict the innocent and set free the guilty.
Plato’s allegory of the cave posits four levels of reality. Plotinus called them the Physical, Psyche, Nous and the One. Another nomenclature would be the Physical, Mind, Soul and Spirit.
Among other things, Plato’s Cave is supposed to be a description of the structure of reality. Some regard it as a fairy tale. Interestingly, mathematicians tend to be realists about mathematics. They generally believe that mathematical truths are objectively true. They have always been true and will always be true. These truths are clearly not physical in nature. So where do they exist? They exist at a level of reality accessible by our minds but not created by our minds. We do not make these truths up. We discover them.
Plato called this level “The Forms,” or “Ideas.” The Greek word is “Eidos.” The Forms are eternal and perfect. The Forms are “universals” – concepts and categories of thought that allow us to identify any individual thing as the thing it is; as a “particular.” Plotinus, a second century Neo-Platonist called this level of reality, the Nous. The Nous is the Understanding and the Soul.