Parmen was the product of a mass eugenics program on the planet Sahndara. He was bred for contemplation, self-reliance, and longevity. The number of individuals generated by the program was pared down to thirty-eight. Before the planet's star went nova, this group resettled on Earth where they were exposed to the Greek civilization. When this civilization died, they moved on to Platonius where they founded their republic.
Parmen was 120 years old when he married Philana and had the strongest command of the power among his people. Since each Platonian's own psionic ability apparently operated on a different incompatible frequency, combining their powers to challenge Parmen's was impossible and thus his authority was unassailable. He used his powers to amuse himself by torturing others and making them do his bidding.
In 2268, Parmen was the philosopher king. In that year, the USS Enterprise visited their planet Platonius. They found Parmen near death due to a leg wound that had become infected. Dr. McCoy was able to heal him and Parmen decided that his people needed a doctor, so he tried to force McCoy to remain on the planet. When McCoy refused, Parmen used his powers to torture Kirk, Spock, Uhura, and Chapel.
McCoy determined that the local food had a substance called kironide that caused the people to develop great mental powers. After injecting the Enterprise crew with the kironide, they too developed mental powers that helped them defend themselves from Parmen and his people. Before leaving, Kirk warned Parmen that if the United Federation of Planets found that Parmen and his people had fallen back to their old ways, "there will be trouble". (TOS: "Plato's Stepchildren")