Socrates claims his own ignorance comprehensively. How, then, can we understand some passages where he claims some knowledge? How, moreover, can such a person be considered as a wise man and a good teacher? These questions are crucial for understanding his and/or early Plato's philosophy and should be treated in the context of the problem of ignorance claim, rather than of disavowal of knowledge. This paper analyzes Plato's Apology 20c-23c and argues as follows. First, his ignorance claim is, pace some interpreters, the claim that he knows (not just believes) his own ignorance. Second, concerning epistemological matters, he concentrates on the importance of the reflection of one's own cognition (i.e. process), rather than on the success of one's cognition (i.e. result). Third, in his epistemological scheme the second order knowledge has little difference from the second order true belief, while the first order knowledge has a huge difference from the first order true belief. Furthermore, the second order knowledge is set up as a necessary condition or an essential component of the first order knowledge. So his epistemological picture, setting up extremely high requirements for the first order knowledge, leaves no room for ignorance of knowledge. Fourth, thanks to that picture, he could conquer the dilemma about ignorance of knowledge which later afflicted Stoics. Fifth, although his philosophical project of knowledge of ignorance basically takes root deep into his own insights (e.g. the inseparability of knowledge and life/action and the view of philosophy as an on-going process), it also owes much to his predecessors' epistemological and psychological projects.