Socratic doubt, the knowledge that we know nothing, can help us become stronger and better people. The value of the Socratic doubt is that we are not living an unexamined life. For Socrates, ignorance is not bliss. He was a gadfly to ignorant society, constantly “stinging” people to examine what they take to know for certain. Socrates’ doubt and his endless questioning irritated his contemporaries. In this manner, Socrates’ doubt did not serve him well for he ended up being sentenced to death in order to silence him.

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However, Socratic doubt is valuable in our quest for improvement and knowledge.
In a way, this doubt makes us better and stronger people because we are constantly seeking to know rather than settling for status quo. It is a liberating doubt because Man is alleviated from his obligation to be certain. Man can be comfortable that although knowledge is not ours, we can always seek to understand our world better than we would without having doubt and without extensive examination. Socratic doubt, in a sense, gives Man the opportunity to be Man by acknowledging Man’s limited knowledge, but also detailing a method to overcome ignorance.

How might “knowledge of ignorance” about death inspire courage in the face of death (see central pages of the  Apology), or “separation” of soul from body (as described in the  Phaedo)?
It seems that Socrates is unafraid to drink the hemlock because he is indeed comforted by his ignorance. Socrates says that only the gods know about death, and again all he knows is that he does not know. Socrates finds courage that in facing the unknown it would not make sense for him to fear what he doesn’t know.
Socrates is so firm in his convictions that he does not allow any of his friends or family to try to save him. He doesn’t try to escape, and he doesn’t try to ask for another trial. He tells the Court that they are hurting themselves more than they are hurting him by sentencing him to death. Socrates’ doubt provided him the possibility that death could be an insightful experience. His doubt allowed him to approach death with the best coping mechanism possible.
However, one indication that Socrates was not as even-tempered about his death sentence is that Socrates does lash out a bit at Meletus. This is an out-of-character incident, and this is possibly the only evidence that Socrates may have been frightened. His words are chiding and intend to hurt Meletus (who deserves it!) but this is not of his character.
Whether Socrates was afraid or truly unafraid, he drank the Hemlock without hesitation.

What are the dangers of this kind of doubt?
The dangers of Socratic doubt are found at its logical extremes, a reductio ad absurtum. If we constantly question the truth of every matter, without at some point accepting that we know something, then it is impossible to advance ourselves with any knowledge. If we are constantly examining and re-examining our lives it is possible that the overly examined life is not lived.

The doubt also makes it seem like a pointless quest to ask questions. It does not seem that the doubt can be overcome because of our finite and unknowing existence. In one way the doubt encourages people to seek wisdom, but in another way, this doubt actually deters people from questing after knowledge because it simply cannot be had. Socratic doubt, in this manner, is like a carrot on a stick, and the horse is a human, the carrot is knowledge. The doubt will have us forever unable to reach the carrot, or to have any knowledge. After all, all we can know is that we know nothing, then how is it possible to know something?

Compare/contrast Socrates’ knowledge of ignorance with the radical doubt of Descartes in his  Meditations.
The radical doubt of Descartes embodies the dangers of Socratic doubt touched on above. Descartes decided that, like Socrates, he knew nothing. However, the difference between Descartes and Socrates in their approach is one of building up or breaking down. Socrates’ doubt would prompt question after question examining what is ignorantly taken for certain. Descartes’ doubt causes him to take nothing for certain or waste time questioning it, until he completely wipes away all faulty support for his beliefs. Descartes doubts the existence of everything that surrounds him, his office, his chair, the candle, the people walking outside. Descartes goes so far as to doubt himself, and this is where Descartes discovers a certitude on which to build the foundation for his philosophy. Descartes discovers that in order for him to doubt his own existence, there must be a “he” who is doubting. From doubt he extracts thought: cogito ergo sum.

For Socrates, he never doubts his own existence in the same manner that Descartes doubted, but he doubted the foundations and existence of knowledge. Socrates argues that all he knows is that he knows nothing.
In contrast to Socrates certainty that he is not certain, Descartes argues that because is uncertain he is certain. For Descartes, because he thinks he might be nothing, then he must be something, else there would be no thought one way or the other.