1) Discuss how Parmenides determines, via logos, not mythos, that Being is the only reality. According to Melissos of Samos (and Sextus Empiricus), what are the four corollaries that follow from Parmenides's result? Demonstrate and/or discuss the derivations of as many of the corollaries as you can.
2) Explicate Zeno's Dichotomy Paradox (aka the Racecourse Paradox). Supplement any diagrammatic illustration with careful discussion. What are some of the salient metaphysical and/or epistemological implications of Zeno's paradoxical conclusion? Discuss and evaluate at least one prospective resolution (or dissolution) of the Dichotomy Paradox.
3) Discuss the concept of the One (to hen) in its various iterations from Anaximander, through Pythagoras, to Parmenides. If you wish, you may include relevant comparisons and contrasts with archaic and/or ancient Indian thought.
4) Discuss the how contrast between mythos and logos plays out in the development of ancient Greek literature and philosophy.