Final answer:
The figure in the image is Socrates, a central figure in Western philosophy whose teachings and methodology are captured in the works of his student, Plato. The correct option is a.
Step-by-step explanation:
The person depicted in the image from the lecture is Socrates, who is a foundational figure for Western philosophy and is known through the works of his students, primarily Plato.
Socrates is instrumental in the development of the philosophical process of thought, and although he never wrote anything himself, his ideologies and methodologies are preserved through Plato's dialogues.
Socrates's influences are so profound that they not only shaped his immediate disciples like Plato and Aristotle but also the broader scopes of Western thought, ethics, and philosophy. The correct option is a.