Aside from these sorts of questions related to your own interests, a good guide for a research topic is that you should pick one that is feasible to research. Remember that you are expected to independently read at least two sources, which will serve as the basis of your term paper. So you should ask yourself, what topic will you be able to look up and inform yourself about in this way? If you’re not sure what topic to pick, a good idea is to start doing some research just be reading broadly about relevant topics, to learn about what sorts of things other people have researched, and see if any of them might interest you. Consult the page on research tips for some resources to help with this.
Sample topics, which you can use or which might encourage some of your own thoughts:
What philosophical analysis can be made of other writings of ancient Greek literature, e.g. those of the Greek epics (Homer), tragedy (Aeschylus, Sophocles, or Euripides), comedy (Aristophanes), or history (Herodotus, Thucydides)?
Summarize the thought of one of the other Presocratic philosophers (e.g. Xenophanes, Parmenides, Zeno of Elea, Melissus of Samos, Empedocles, Anaxagoras, Leucippus, Democritus, Diogenes of Apollonia, the Pythagoreans, or the Stoics).
Discuss a famous theme from Plato (e.g. the allegory of the cave, the theory of love in Plato’s Symposium, or the death of Socrates).
Summarize or discuss a position from ancient philosophy of nature which we didn’t cover (e.g., Stoic physics or Epicurean physics).
Summarize or discuss a position from medieval philosophical anthropology, ethics, or political philosophy we didn’t cover (e.g., Augustine’s position on free will, Aquinas’ natural law theory, Ficino’s position on the immortality of the soul).
Summarize or discuss how a contemporary philosopher appropriates or develops ancient or medieval thought (e.g., Martha Nussbaum on Greek tragedy, Pierre Hadot on the Stoicism of Marcus Aurelius, Rosalind Hursthouse on Virtue Ethics, Alasdair MacIntyre on ancient and medieval ethics).
Discuss a connection between a theme in ancient or medieval philosophy and a theme in modern thought (e.g., Plato’s position on the mathematical foundations of nature and the development of modern physics in Galileo and onwards, Epictetus’ position on Stoic ethics and recent work applying it to psychotherapy).
Some more specific sample topics relating to ancient philosophy, in case thee above suggestions were too broad:
For Presocratic Philosophy:
Ancient Atomism: Democritus and Epicurus
Zeno’s Paradoxes and Eleatic Philosophy
Aristotle’s Response to Zeno’s Paradoxes
The Role of Pythagoreanism in Presocratic Philosophy
For Plato:
The Euthyphro Dilemma
The Death of Socrates
Mathematics or Physics in Plato’s Timaeus
Thrasymachus and Socrates on Justice in Plato’s Republic
For Aristotle:
Aristotle’s Poetics
Aristotle’s Theory of Rhetoric
Plato and Aristotle on Friendship
The Critique of Aristotelian Physics in the Scientific Revolution
For Hellenistic Philosophy:
Stoic Physics or Stoic Logic
Stoicism and Epicureanism on Free Will
Stoicism and Psychotherapy
Stoicism and Christianity.