Cleverly deceptive reasoning or argument.
Example:
The defendant's claim that he wasn't guilty of the crime because he didn't actually pull the trigger was dismissed as pure sophistry.
Our words sophist and sophistry come from the name of a group of Greek teachers of rhetoric and philosophy who were famous during the 5th century B.C. Originally, the Sophists represented a respectable school of philosophy and were involved in serious educational efforts. But in time they fell into disrepute and gained a reputation for their abilities to persuade more by means of clever and often misleading arguments than by the merits of their positions. It is not difficult to see the Sophists as the natural ancestors of many of today's politicians.