 Cook Wilson used his interpretation of Plato’s doctrine of Idea numbers as ἀσύμβλητοι ἀριθμοί as a basis for an attack on Russell and the logicist definition of numbers, Plato’s doctrine being understood (see section 2) as entailing that there cannot be a universal of the members of the ordered series of universals: 1-ness, 2-ness, 3-ness, etc. because they do not share an ‘intrinsic character’. Confusing this series with that of the natural numbers, he concluded that the logicist definition in terms of classes of classes, e.g., of the number 5 as the class of all classes equinumerous with a given quintuplet, is “a mere fantastic chimera” (SI, 352). In line with the argument about putting the universal ‘triangularity’ in the subject position (previous section), Cook Wilson reasoned for the case of natural numbers that there would be an alleged ‘universal of numberness’ and that this would lead straight to a contradiction: since all particulars of a universal are said to possess its quality, a group of 5 as a particular of ‘5-ness’ would thus possess the ‘universal of numberness’, thus contradicting his claim that a particular cannot be a universal (SI, 353). 