"On one hand, he denies having any kind of specialized knowledge, and on the other hand, he makes assertions"
The assumptions of rationality are not knowledge.
Rationality might assume "an unexamined life is not worth living" although we have no knowledge what "life" really is.
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"To prove Meletus wrong, Socrates undertakes to show that he must believe in gods of some sort."
He is ambiguous here. Can I assume that it points to Socrates? Is it indeed ambiguous?
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"Socrates is persists in saying "
The word "is" in the statement above should be removed. Reply to confirm.