Final answer:
Plato argues in the Republic that justice brings personal happiness and societal harmony, as each individual specializes in their role, leading to a well-ordered state and the common good.
Step-by-step explanation:
Plato's argument in the Republic for why we should be just even in the absence of external recognition essentially revolves around the belief that justice leads to personal happiness and a harmonious society. He conceived justice as a form of specialization where each individual only practices the things to which their nature is best suited, leading to a well-ordered state. Therefore, Plato suggests that justice is not dependent on social approval or subjectivity but is a virtue by itself that brings inner consistency and societal harmony.
In building the ideal city, Plato describes the roles of different social classes and the establishment of guardians whose courage and wisdom are pivotal for maintaining peace and order. He emphasizes the importance of communal living and the shared experiences that contribute to the unity and success of the city, ultimately implying that justice is integral to the well-being of citizens and the survival of a state.
Justice, according to Plato, is its own reward because it ensures that society functions optimally, with everyone fulfilling their duty for the common good, which in turn leads to individual contentment and overall societal prosperity.