Intellectual dishonesty is the advocacy of a position known to be false. An argument which is misused to advance an agenda or to reinforce one's deeply held beliefs in the face of overwhelming evidence contrary.
The terms intellectually dishonest and intellectual dishonesty are often used as rhetorical devices in a debate; the label invariably frames an opponent in a negative light. It is a round about way to say "you're lying".
The statement that all hurricanes are caused by global warming is intellectually dishonest. Stating as fact that lung cancer is unrelated to cigarette smoking is intellectual dishonesty.