 There is here an instructive contrast with Peirce. Peirce, in the spirit of the 19th-century algebraists, was happy to explore a lush abundance of logical structures: his attitude was fundamentally pluralist. The logicists, working in the analytical tradition, were more concerned to discover what the integers actually are: their attitude was fundamentally monistic and reductionist. But in order to single out first-order logic as was done in the 1930s, two things were needed: an awareness that there were distinct logical systems, and an argument for preferring one to the other. Peirce had the pluralism: the logicists had the urge to find a “correct” system: but neither had both.