Final answer:
Plato is the Greek philosopher known for explaining how each mode could be used for different reasons, building on the work of his teacher, Socrates, and influencing his student, Aristotle.
Step-by-step explanation:
The Greek philosopher that explained how each mode could be used for different reasons was Plato. As a student of Socrates, Plato carried forward his teacher's legacy, but he developed his own philosophical systems that included a theory of forms and the allegory of the cave, exploring the relationship between the abstract realm and physical reality. Aristotle, Plato's most famous student, went on to formalize logic and contributed significantly to metaphysics, but it is Plato who is renowned for his work on the modes and their use.