Paradox

WITTGENSTEIN AND THE DEPTH OF A GRAMMATICAL JOKE 347infinitely large numbers. Wittgenstein thinks Cantorinvented the transfinite numbers while under the influenceof an alluring interpretation of “1, 2, 3, 4, . . . . ” He speculatesthat “The dots introduce a certain picture: of numbers trailingoff into the distance too far for one to see. And a great deal isachieved if we use a different sign. Suppose that instead ofdots we write , then ‘1, 2, 3, 4, ∆’ is less misleading.” (1976,170) Dr. Seuss’s On Beyond Zebra opens with a young boyproudly writing on a blackboard. Conrad Cornelius o’Donaldo’Dell, has demonstrated his exhaustive knowledge of thealphabet: A is for Ape, B is for Bear, . . . and Z is for Zebra. Anolder boy compliments Conrad. He breezily concedes toyoung Conrad that most people stop with Z. But his alphabetcontinues beyond Z. The extra letters let him spell newthings. The older boy thus introduces Conrad to an otherwiseinaccessible realm of exotic creatures. For instance, the Q-ishletter quan is for the vertically symmetric Quandary who liveson a shelf.In a hole in the ocean alone by himselfAnd he worries, each day, from the dawn’s early lightAnd he worries, just worries, far into the night.He just stands there and worries. He simply can’t stop . . .Is his top-side bottom? Or bottom-side top?The tour given to Conrad would put Wittgenstein in mind ofother never-never lands.Wittgenstein insists that he does not wish to replace onephilosophical theory with another. But he frequently doesjust that. He advances, albeit guardedly, the use theory ofmeaning, the avowal theory of pain, the doctrine of familyresemblance, etc. Despite poking fun at the philosopher’s