Summary of the Dialogue of Theaetetus

Summary of the Dialogue
At the gates of the city of Megara in 369 BC, Eucleides and Terpsion hear a slave read out Eucleides' memoir of a philosophical discussion that took place in 399 BC, shortly before Socrates' trial and execution (142a-143c). In this, the young Theaetetus is introduced to Socrates by his mathematics tutor, Theodorus. Socrates questions Theaetetus about the nature of expertise, and this leads him to pose the key question of the dialogue: "What is knowledge?" (143d-145e). Theaetetus' first response (D0) is to give examples of knowledge such as geometry, astronomy, harmony, arithmetic (146a-c). Socrates objects that, for any x, examples of x are neither necessary nor sufficient for a definition of x (146d-147e). Theaetetus admits this, and contrasts the ease with which he and his classmates define mathematical terms with his inability to define of knowledge (147c-148e). Socrates offers to explain Theaetetus' bewilderment about the question "What is knowledge?" by comparing himself with a midwife: Theaetetus, he suggests, is in discomfort because he is in intellectual labour (148e-151d).
Thus prompted, Theaetetus states his first acceptable definition, which is the proposal (D1) that "Knowledge is perception" (151d-e). Socrates does not respond to this directly. Instead he claims that D1 entails two other theories (Protagoras' and Heracleitus'), which he expounds (151e-160e) and then criticises (160e-183c). Socrates eventually presents no fewer than eleven arguments, not all of which seem seriously intended, against the Protagorean and Heracleitean views. If any of these arguments hit its target, then by modus tollens D1 is also false. A more direct argument against D1 is eventually given at 184-7.
In 187a10-e4, Theaetetus proposes a second definition of knowledge: (D2) "Knowledge is true belief." D2 provokes Socrates to ask: how can there be any such thing as false belief? There follows a five-phase discussion which attempts to come up with an account of false belief. All five of these attempts fail, and that appears to be the end of the topic of false belief. Finally, at 200d6-201c7, Socrates returns to D2 itself. He dismisses D2 just by arguing that accidental true beliefs cannot be called knowledge, giving Athenian jurymen as an example of accidental true belief.
Theaetetus tries a third time. His final proposal (D3) defines knowledge as "true belief with an account (logos)" (201c-d). The ensuing discussion attempts to spell out what it might be like for D3 to be true, then makes three attempts to spell out what a logos is.
In 201d-202d, the famous passage known as The Dream of Socrates, a two-part ontology of elements and complexes is proposed. Parallel to this ontology runs a theory of explanation that claims that to explain, to offer a logos, is to analyse complexes into their elements, i.e., those parts which cannot be further analysed. Crucially, the Dream Theory says that knowledge of O is true belief about O plus an account of O's composition. If O is not composite, O cannot be known, but only "perceived" (202b6). When Socrates argues against the Dream Theory (202d8-206b11), it is this entailment that he focuses on.
Socrates then turns to consider, and reject, three attempts to spell out what a logos is—to give an account of "account." The first attempt takes logos just to mean "speech" or "statement" (206c-e). The second account (206e4-208b12) of "logos of O" takes it as "enumeration of the elements of O." The third and last proposal (208c1-210a9) is that to give the logos of O is to cite the sêmeion or diaphora of O, the "sign" or diagnostic feature wherein O differs from everything else.
All three attempts to give an account of "account" fail. The day's discussion, and the dialogue, end in aporia. Socrates leaves to face his enemies in the courtroom.