It seems that from the crocodile's viewpoint it doesn't matter if the mother speaks truly or falsely, for if she speaks truly the crocodile cannot return the child without destroying the truth of the mother's statement. Similarly, if the mother has spoken falsely, the crocodile still cannot return the child, because the mother has not fulfilled the agreement. From the mother's viewpoint it doesn't matter if she has spoken truly or falsely. If the mother has spoken truly, then by the terms of the agreement the crocodile must return the baby. Then, too, the mother can be said to have spoken falsely only after the child has been returned. Therefore, whether the mother speaks truly or falsely, the child must be returned.
To understand the logical inconsistencies buried in the mother's and the crocodile's arguments, it is helpful to sumarize their views.
The crocodile's argument can be expressed as follows:
If the mother accurately predicts what I will do, then I will return the baby. If I return the baby, then the mother has not accurately predicted what I will do. Therefore I will not return the baby.
The mother's view can be expressed as follows:
If I accurately predict what the crocodile will do, then my baby will be returned to me. If my baby is not returned (eaten), then I predicted accurately what the crocodile will do. Therefore the baby will be returned to me.
Consider the two premises of the crocodile's argument. As the crocodile states in the first premise, he returns the baby if and only if the mother accurately predicts what he will do. However, according to the second premise, if he does return the baby, then the mother's prediction is false. But how can this be, if based on the first premise the baby can be returned if and only if the mother predicts accurately? The point is that it can't be for as we have just demonstrated, assuming that the agreement can be kept leads to validly deduced contradictory conclusions. A similar analysis can be made of the mother's argument.