I am the reverse of a wise man.

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This phrase is an example of so-called Socratic irony. As a reader of Plato's work, you will discover that, despite Socrates' claim of ignorance, he is no dummy! This often leads a student to believe that Socrates is being dishonest and is merely laying intellectual traps for those with whom he converses. Try to think of it this way. If knowledge is defined as revisable claims that can be defended, then Socrates is being deceptive because he certainly has an understanding of such things. If, however, true knowledge is final and beyond revision, Socrates is being honest. He doesn't see himself as having reached that level of understanding. In either event, his professed ignorance challenges various self-proclaimed experts in the dialogue to join the process of discussion.