In his Philosophical Investigations, Wittgenstein suggests that the logical atoms of his Tractatus Logico-Philosophicus are similar to the primary elements of Socrates’ Dream in Plato’s Theaetetus (P.I. §46). I explore the texts in detail and argue that there are two key similarities between the Tractatus and the Dream: they both propose the existence of a single type of logical ‘atom’ and they both reject the object-property distinction. I suggest that Plato’s Theaetetus and Sophist are effectively two parts of one larger dialogue which can be read as a critique of Tractatus-type theories – theories that have object-only ontologies. I argue that Plato demonstrates that any theory lacking the object-property distinction will be unable to explain how strings of words are transformed into meaningful propositions about the world. Such theories relegate all propositions and mathematics to the class of nonsense. Wittgenstein acknowledges that, strictly speaking, the propositions of the Tractatus are nonsense (TLP 6.54); I show that the inexpressibility problem that Wittgenstein references is the same problem that Plato shows is faced by Heraclitus in the Theaetetus (183b). At the time of writing the Tractatus, Wittgenstein did not realise that all propositions, not just those of philosophy, like those in the Tractatus, were reduced to nonsense by his theory. Plato, on the other hand, foresaw the issues that any Tractatus-type theory would inevitably face, and resolved them in the Sophist with the introduction of a second type of logical atom with a different (metaphorical) shape. Different shapes account for how logical atoms combine to create propositions with unity. I argue that the version of logical atomism that Plato presents in the Sophist looks more Fregean than Tractarian. I discuss Wittgenstein’s criticism of Frege, rejection of the idea of a second type of atom representing properties, and preference for necessarily featureless atoms. I conclude that this preference comes at too high a price.