If you told the evil computer in the Star Trek episode The Wolf in the Fold, ‘Pinocchio says “My Nose Will Grow Now”‘, it would destroy it much like calculating to the last digit of Pi.
The Pinocchio paradox arises when Pinocchio says “My nose grows now” and is a version of the liar paradox. The liar paradox is defined in philosophy and logic as the statement “This sentence is false.” Any attempts to assign a classical binary truth value to this statement lead to a contradiction, or paradox.
The Haus of Dcaligari 