Recently there was brought up the question whether duals of ccc's may have significance and it has been pointed out by P. Levy and P. Selinger that a good example is that of the Kleisli category for the continuation monad. In a sense the dual of the Kleisli category is much neater as it is cc. There is some ``odd'' structure there corresponding to some sort of ``classical disjunction''. It is precisely this ``odd'' structure which is used for constructing ``function spaces'' in the Kleisli category which, however, aren't exponentials. Actually, there can't exist proper function spaces for the following reason. If C and its dual are both cartesian closed then C is a bi-Heyting algebra as if C^op is cc then 1+(_) is a right adjoint and accordingly 1+1 ~= 1 form which it follows that C is posetal. This strengthens ``Joyal's Lemma'' saying that any c.c. with an involution is actually a Boolean algebra. Thomas S.