Who Stole the Tarts? Part IV

So, who stole the pepper? Well, the King's next suspects were the March Hare, the Mad Hatter, and the Dormouse. Soldiers were sent to their house, but no pepper was found. Still, they might be hiding it somewhere, so they were arrested on general principles.

At the trial the March Hare claimed that the Hatter was innocent and the Hatter claimed that the Dormouse was innocent. The Dormouse mumbled some statement in his sleep, but it was not recorded.

As it turned out, no innocent one made a false statement and (we recall) people who steal pepper never make true statements. Also, the pepper was stolen by only one creature. Which, if any of the three, is guilty?

(Source: Alice in Puzzle Land: A Carrollian Tale for Children Under Eighty by Raymond Smullyan)

There is a kind of transitivity to this problem. Consider the first statement, made by the March Hare, that the Mad Hatter is innocent. Suppose it false. If it is false, then the Mad Hatter was the one and only thief. But because the supposition is that the March Hare lied, then the March Hare is also the thief. But this is impossible because it was stipulated that there would be only one thief. It follows thereon that the March Hare is in fact honest and that the Mad Hatter is innocent and therefore truthful. Transitively, the Dormouse is also innocent and therefore truthful. This time, none of them are guilty.