The first part of the paper (p. 10-21) tries to answer the first question of the title and describes a set of seven “knowledge-claims” made by Socrates: 1. There is a distinction between right opinion and knowledge. 2. Virtue is knowledge. 3. Nobody willingly does wrong. 4. To do injustice is the greatest evil for the wrongdoer himself. 5. An even greater evil is if the wrongdoer is not punished. 6. The just person is happy; the unjust person is unhappy. 7. The pleasant is not the good. These claims seem to be the “few” (oliga) (Men. 98 b3) but “very important” (kallista) (Grg. 472 c8) things that Socrates claims to know. The second part (p. 22-39) tries to answer the second question and defends the thesis that the supposed “knowledge” of Socrates is dianoetic, but not noetic. The main new idea of this paper is the comparison of the Socratic knowledge-claims with the upper states of the mind symbolized in the Divided Line, noesis and dianoia (cf. R. 511 d7-e1).