The elenchus or Socratic method essentially is a process in which a person repeatedly responds by asking questions. These questions are intended to refute the claims of the defender and make him/her realize that their original claim was contradictory. Socrates used this method to make people realize that they did not know what they claimed to know, but in fact their beliefs were tenuous, contradictory, and impermanent. Intended to make his students realize the heart of knowledge is to realize that you are ignorant and know nothing. Socrates rebuts arguments but he rarely gives his own opinions. 

Steps in elenchus

• Socrates asks interlocutor for a definition of some virtue, for example piety.
• The interlocutor gives the definition.
• Socrates responds with a series of other intensive questions that eventually show that the definition is inconsistent with other beliefs that the interlocutor holds.
• Interlocutor refines the definition, and the whole procedure begins again.

Socrates contends that knowledge is something that is permanent and true, whereas opinions are tenuous, malleable, and unstable. He believes that knowledge is something that is imparted to humans before they are born, when their souls are in contact with the Forms. He shows this by making a slave solve a geometry problem with no previous knowledge. Socrates thinks that true beliefs are useful so long as they stay with us, but most often they depart from our minds. Knowledge, however, is permanent. A person who has knowledge is able to back up his opinion by providing justification or an explanatory account.

Knowledge is something that can be explained by a particular method, it is stable and unchanging. Beliefs on the other hand, even true ones, can change and since they are not actually understood by the bearer, they are unreliable. Knowledge means understanding something from all viewpoints and not just memorizing things without being able to explain them.

Meno's paradox: If one has knowledge, you cannot inquire into it. If one does not have knowledge, you cannot inquire into it either because if you do not know what you are looking for in the first place, how will you recognize it when you come across the knowledge.

The Kallipolis is the ideal(perfectly good) city-state in Plato's opinion. It is ruled by a philosopher-king and is free from crime, poverty, or any other social issues that plague a democratic society like Athens at the time. The city is filled with people that have specific roles, and they fulfill those roles regardless of whether or not they like doing them. This means that the citizens of the Kallipolis do not have individual happiness but their individual actions promote the welfare and safety of the entire city. Freedom is sacrificed for the sake of universal peace in the city.

Comes from kalos meaning good and polis meaning city-state

The Form of the Good is the source of all knowledge. It gives truth to the objects of knowledge (the other Forms). It gives to the knowing mind the power to know. It is the cause of knowledge and truth. Just as the eye sees objects thanks only to the sun's supply of light, human reason can know the Forms only thanks to the intercessions of the Form of the Good. Just as the sun makes the existence of every living thing possible, the Form of the Good not only allows us to know the Forms but causes them to exist in the first place.

The Form of the Good allows us to fully comprehend the intelligible realm and use reason to understand the world instead of just our sight. It enables us to perceive through thought instead of belief. It expands our vision and enables us to think objectively about things without allowing past education, beliefs, or experiences dictate our understanding.

The paradox of inquiry is an idea that you cannot come to know something that you didn't already know. Basically, inquiry does not produce new knowledge but only reinforces what is already known. The three points of Meno's paradox are:

1. If you know what you’re looking for, inquiry is unnecessary.
2. If you don’t know what you’re looking for, inquiry is impossible.
3. Therefore, inquiry is either unnecessary or impossible.

Meno argues that one cannot look for something if one doesn't know what it is. Even if one finds it, they will not know that what they've found is what they were searching for in the beginning. 

Socrates responds with the Doctrine of Recollection. In the doctrine he states that the soul is immortal and is born often. Due to this there is nothing that the soul has not learned and recollecting the knowledge hidden within the soul is what men call learning. He proves this by asking a slave with no prior knowledge of geometry questions about finding the areas of squares. The slave arrives at the wrong answers at first but eventually succeeds as Socrates continues to question him.

Socrates argues that either the slave acquired the knowledge at some time or he always possessed it. If the slave acquired the knowledge at some time, it must have been acquired before his life when his soul was in contact with the forms. By finding the knowledge within himself, the slave was recollecting. If instead the slave always possessed the knowledge but forgot it at the beginning of the inquiry, he must find it again within himself. This argument solves the issue of the paradox of inquiry because if the knowledge is already hidden within us but we have forgotten it, we just have to recollect that knowledge and once we find it we will be able to recognize it because the knowledge was already there to begin with. Socrates says that once one sees the particulars of the Forms, it jogs their memory and they are able to recollect the knowledge that the soul possessed before they were born. Socrates acts as the connection between the Forms and the particulars and allows the slave to make the connection to the Forms after several attempts at trying to solve the geometry problem. He does not teach the slave anything but merely facilitates a way for the slave to recollect what he already knows but has forgotten.

Socrates' doctrine of recollection does provide a good defense to Meno's paradox when illustrated with the geometry discussion. Socrates does not tell the slave the answer but only leads him to discovering the answer for himself. However, it is very metaphysical and the argument can be made that if Socrates had not engaged in discussion with the slave at all, the slave would not have been able to solve the geometry problem and therefore it would disprove Socrates' theory that all knowledge is innately known, but has to be recollected. If instead someone who didn't know the answer himself were to converse with the slave, would the slave still have been able to arrive at the correct answer. Does this recollection process only work with empirical knowledge or does the soul also know the answers to theoretical questions as well.

The city of pigs is a city where the citizens only have the bare necessities to live. They have clothing to keep themselves warm, they have modest food to eat, and they only enjoy small pleasures like sex, but only as much as their resources allow. This city does not have luxuries because it only produces enough goods and has enough workers and merchants to meet the necessary needs of the city as a whole. The city of pigs arises because of this idea that no individual is entirely self-sufficient, but has many needs that he cannot satisfy on his own. Therefore a city is formed because of the different needs of all people. These needs are food, shelter, and clothes and other things. Due to these needs, a city needs people who can supply these different things, some have to be farmers, others have to be builders, weavers, and so on. In the city each person does what he is best suited for so that all necessary goods are plentiful. Enough goods should also be produced to satisfy the needs of people in other cities so that trade can occur.

Glaucon does pose that the people will need other luxuries such as the pleasure of reclining on proper couches, dine at tables, and have fine relishes and desserts. This makes Socrates stop discussing this city and he starts talking about the Kallipolis. But in order to do this, the city will require more workers like hunters, beauticians, bakers, prostitutes, and meat cooks in order to satisfy the additional desires of the people. These excess desires will spur the need for more doctors and more land to create extra food. This means that the city will require soldiers to capture land from others and thereby make the city bigger.

Socrates calls this new city a feverish city and this causes the discussion to move toward introducing roles that can accommodate the excess desires of the people. He believes the city is feverish because it wants excess things that a healthy city can live without and therefore it introduces the possibility of injustice and social problems. So the remaining part of the discussion focuses on how to accommodate the desires of the people, how to structure the social system, and how to educate society so that everyone does their own job well. Socrates introduces the concept of warfare and the guardian class, which serves to protect the people and capture other lands. This leads to a discussion about the education of the guardians. Socrates believes that the guardians require both musical and gymnastic training in order to develop both strong bodies and temperate minds. This is to ensure that they remain benevolent to their people but harsh to their enemies. Education of the guardians is paramount because they maintain order and purify the unhealthy, luxurious city. The education of the guardians means banning all poetry and books depicting the gods fighting or portraying death and the afterlife in a negative light. These new luxuries however bring up the issue of distribution of goods and happiness. The guardians could become unhappy because they are not allowed to own property like the craftsmen, but Socrates asserts that individual happiness is not important in this city if it is to function perfectly. 

Plato believes that the very same virtues found in the just city (wisdom, courage, temperance, and justice) must also be inside the just soul. He argues that these qualities exist in the just city because of the people living in them. For example the honor-loving natures of the Thracians and Spartans makes Thrace and Sparta spirited. Plato believes that the soul has 3 parts because the city is divided into 3 distinct classes, namely the merchants/craftsmen, auxiliaries, and the rulers. Since the souls of these different classes are composed of unique metals, either bronze, silver, or gold, each of the classes has a dominating element in their souls. Each soul has three parts because each person can be ruled by three elements that are predominant in the three different classes.

The three parts of the soul are the rationally calculating part, the spirited part, and the appetitive part. There are several ways in which the different parts of the soul can come into conflict. For instance, the appetitive part can push you to steal something but the spirited part can pull you away from that desire out of shame. The spirited part can also push you towards taking revenge on someone who wronged you, but the rational part can pull you away from anger by making you contemplate the consequences of resorting to violence. Any combination of the parts can come into conflict with one another, and the result will be one overpowering the other. 

Plato believes that this conflict can be best avoided if each part of the soul does its own job. The rationally calculating element should rule because it is truly wise and exercises foresight over the whole soul. The spirited element should follow the lead of the rational element and obey its instructions. The mixture of physical and musical training causes the spirited and rational elements to live harmoniously in the soul, which then allows both to watch over the largest element being the appetitive, which is most susceptible to excess, desire, and a love for money. The rational element allows one to deliberate and make sound decisions, while the spirited element gives one courage to fight and carry out the demands of the rational part. In order to avoid conflict, a person must not allow the elements in his soul to meddle with one another or do the job of another. Reason should allow neither spirit nor desire to make decisions on behalf of itself.

Glaucon's challenge is for Socrates to prove that justice is both good in itself and for its consequences. Glaucon draws an analogy to Gyges who was a shepherd in the service of the ruler of Lydia. An earthquake ripped open the ground and exposed a chasm in which Gyges descended and found a golden ring. After putting it on and turning the setting towards himself, Gyges realized that he could turn invisible. He used this power to secretly enter the palace, seduce the queen, and murder the king. Glaucon argues that if that same ring were to be worn by both a just and unjust person, both of them would not be able to resist taking other people's possessions, having sex with anyone they please, or killing his enemies. This is because there would be no repercussions to doing so, and therefore nothing to stop people from being unjust. Glaucon believes that justice is only good because it protects people from harm by others, and that life would be worse without it. However, if you could commit crime with impunity, there would be no good in justice.

Socrates challenges Glaucon by attempting to formulate the perfect city. This city consists of three different classes, the craftsmen, the auxiliaries, and the rulers/complete guardians. Each of these classes are responsible for performing specific jobs. The craftsmen and merchants create and sell the goods that the city and other cities require so that the people can be taken care of and trade can occur. The auxiliaries defend the city from invasion and engage in warfare to capture other lands. The rulers are to lead the city and take actions to keep it running properly. Socrates argues that an ideal city must have the virtues of wisdom, courage, temperance, and justice. He says that each of these virtues are embodied by the different social classes. Wisdom is best found in the rulers because they know the internal and external relations of the city and how to best rule it. Courage is predominantly embodied by the auxiliaries because they know how to preserve the laws. Temperance exists because all of the classes do the work they are best suited for and do not meddle with anything else - the citizens are happy to be who they are because they know they are doing what their natures are best suited towards. Socrates then finds the same virtues inside the soul and argues that justice is when the competing parts of the soul coexist in harmony as a result of the rational part mastering the spirited and appetitive part.

In a way Socrates did succeed in showing that justice is good in itself because when there is justice in the soul there is a natural harmony in the body that promotes good health, proper decision making, and living well. This allows the just soul to not only do what is right for himself but also for the good of the city as a whole. In this way justice is both good in itself and for its consequences. However, an argument can also be made that Socrates has not given any intrinsic good of justice but just says that justice in the soul means that the person will control his emotions and let reason rule, which in turn means that he will do the job that best benefits the city. So justice could still be interpreted as an instrumental good which is only favorable to bring about the best outcome for the city.