"Spirit" is in the sense of a "spirited" horse. Plato thinks that this is the energy that drives the soul and may be used to reason to keep desire in line. Temperance, or moderation, will mean the limitation of desires. The word "temperance" is now a little archaic, and it tends to suggest "temperance" as it came to mean abstention from alcohol, as was advocated in the early days of this century by Cary Nation and the Women's Christian Temperance Union, who brought about Prohibition.
The three parts of the soul also correspond to places in the body: reason to the head, spirit to the heart, and desire to the organs of desire, mostly in the abdomen. Plato simply made a good guess that reason had something to do with the brain. There wasn't a lot of evidence about this; and many people, including the Egyptians and Aristotle, thought that intelligence was centered in the heart. When the Egyptians mummified bodies, they actually used to throw the brain away, while the heart was carefully prepared and replaced in the body. Remember later in the course to compare Plato's parts of the soul and social classes with the doctrine of the gunas and the varnas later in Indian philosophy.
Now, Plato was originally looking for justice, but justice does not appear in the list of virtues.
The answer is that justice applies to them all in the sense of their organization. Reason (and the philosophers) should be in control, with the help of spirit (and the warriors). The philosophers and the warriors are thus the "Guardians" of Plato's ideal state. This does not seem like a familiar sort of definition for justice, but the result, Plato says, is that each interest is satisfied to the proper extent, or, in society, everyone has what is theirs.
The philosophers have the knowledge they want; the warriors have the honors they want; and the commoners have the goods and pleasures they want, in the proper moderation maintained by the philosophers and warriors.The root of all trouble, as far as Plato is concerned, is always unlimited desire.
Note:In his political writings, Justi stressed that a country could only be economically and commercially successful if it was run by a moderate government that recognised the inviolability of private property. By contrast, despotism necessarily led to the impoverishment and military weakening of a country. Under the influence of Montesquieu Justi extensively discussed the advantages and disadvantages of different forms of government, yet concluded that the only form of government that would be able to coordinate and implement wide-ranging economic reforms was a modernised monarchical regime.Johann Heinrich Gottlob Justi - Wikipedia, the free encyclopedia