 Partitioning the universe into types accordingly exacted a high price for the ‘logicism’ that might result. It is not reassuring to learn that the logicist reconstruction on offer for one’s favorite mathematical structures is so generous as to be uniquely re-presented within each type. One would wish to capture their commonalities within some one structure. And that, as we have just seen, is what Russell was trying to do, even though it was doomed to failure from the start, on account of its being committed to the existence of a different series of the ‘same’ numbers within each type. 