“The strongest arguments for nominalism are questions like the following: Who set up these Platonic ideals? Why are they there? For the past several hundred years, scientists have made steady progress by eliminating metaphysical presuppositions. Why keep any such metaphysics in mathematics and in set theory? A nominalist would counter a Platonist's proof by saying that the mathematicans are not all isolated from each other. Before they entered their lonely writer's garret, they were all aware of the rules for being a good mathematician. They knew that if they were to write anything that would cause a contradiction, they would lose their status as a mathematician. They were not isolated because they knew the language beforehand.”