Conceptualism—the view that universals are mental entities without an external, independent, or substantial reality—has enjoyed popularity at various points throughout the history of philosophy. While Plato’s Theory of Forms is not a conceptualist theory of universals, we find at Parmenides 132b–c the startling conceptualist suggestion from a young Socrates that each Form might be a noēma, or a mental entity. This suggestion and Parmenides’ cryptic objections to it have been overshadowed by their placement directly after the notoriously difficult Third Man (...) Argument, and before the Likeness Regress. However, in the background of 132b–c, we find illuminating assumptions behind Parmenides’ arguments against the Theory of Forms in the first half of the dialogue. We also find in this text a set of implied criteria for Platonic concepthood. While in the Platonic corpus, Forms are explanantia for many of the phenomena explained by concepts in contemporary philosophy, concepts do seem to have an important epistemic role in Plato’s philosophy. An account of Platonic concepthood therefore opens the door for new ways of understanding the Platonic corpus as a whole. My focus in this paper is to uncover these assumptions and criteria through a close reading of Socrates’ conceptualist suggestion and Parmenides’ truncated objections to it at Parmenides 132b–c. (shrink)