The Watchtower's position on logic and truth is basically that there are two logics (God's and man's) and two truths (God's and man's). This position makes knowledge impossible (especially knowledge of God) and allows the Society to contradict itself with impunity.
Read my letter to the Society:
http://watchingthetower.blogspot.com/2009/05/letter-to-christian-congregation-of.html
their reponse:
http://watchingthetower.blogspot.com/2009/09/response-from-society-ccjw.html
and my reply to that response:
http://watchingthetower.blogspot.com/2009/09/my-reply-to-ccjw-response.html