  But historically-wrong and philosophically-hasty does not imply unproductive. There is no doubt that restricting attention to wellfounded sets (in the sense that it is them alone that one tries to axiomatise) concentrated the minds of 20th century mathematicians to great effect. ZF does seem to avoid the paradoxes, and the conception of set it formalises is one that apparently allows one to interpret the whole of mathematics. But how can an historically wrong and philosophically hasty story have such a happy ending? The answer is that, although it may be a mistake to think that all sets are wellfounded, it is not a mistake to think that the concept of wellfounded set is worth axiomatising.