Cat at the Duchess' house in her kitchen, and later on the branches of a tree, where it appears and disappears at will, and engages Alice in amusing but sometimes perplexing conversation. The cat sometimes raises philosophical points that annoy or baffle Alice; but appears to cheer her when it appears suddenly at the Queen of Hearts' croquet field; and when sentenced to death, baffles everyone by having made its head appear without its body, sparking a debate between the executioner and the King and Queen of Hearts about whether a disembodied head can indeed be beheaded. At one point, the cat disappears gradually until nothing is left but its grin, prompting Alice to remark that 'she has often seen a cat without a grin but never a grin without a cat'.[5]