Consider the following statements:
- Ralph believes that Ortcutt is not a spy.
- Ralph believes that the man in the brown hat is a spy.
- The man in the brown hat is Ortcutt.
- Ralph believes of Ortcutt that he is not a spy.
- Ralph believes of Ortcutt that he is a spy.
This is apparently no problem, as long as Ralph does not believe "Ortcutt is a spy and Ortcutt is not a spy", which he does not. People with appropriate false beliefs or appropriate ignorance can believe (de re) contradictory things.
But now consider Hofstadter's Tortoise:
- The Tortoise affirms "My shell is green".
- The Tortoise affirms "My shell is not green".
- The Tortoise rejects "My shell is green and my shell is not green".
It seems to follow that:
- The Tortoise believes of his shell that it is green.
- The Tortoise believes of his shell that is is not green.
Must we accept that the Tortoise's beliefs are not contradictory de re, but only de dicto? The de re version seems exactly parallel to Ralph's de re beliefs. Yet Ralph is merely ignorant of a key point (viz. #3), whereas the Tortoise seems to be "logically insane".