186 PHILOSOPHY 



and Many as the sum of the ones, makes part of the measure of that 

 primally real world which the world of minds alone can be. If the 

 contrast One and Many can pass the bounds of the merely phenome- 

 nal, by passing the temporal and the spatial; if it applies to universal 

 being, to the noumenal as well as to the phenomenal; then the abso- 

 lutely real world, so far as concerns this essential condition, can be 

 a world of genuine individuals, identifiable, free, abiding, responsible, 

 and there can be a real moral order; if not, then there can be no 

 such moral world, and the deeper thought-conceptions to which we 

 now approach must be regarded, at the best, as fair illusions, bare 

 ideals, which the serious devotee of truth must shun, except in such 

 moments of vacancy and leisure as he may venture to surrender, 

 at intervals, to purely hedonic uses. But if the One and the Many 

 are not dependent on Time and Space, their universal validity is 

 possible; and it has already been shown that they are not so de- 

 pendent, are not thus restricted. 



And now it remains to show their actual universality, by exhibiting 

 their place in the structure of the absolutely real; since nobody calls 

 in question their pertinence to the world of phenomena. But their 

 noumenal applicability follows from their essential implication with 

 all and every difference: no difference, no distinction, that does not 

 carry counting; and this is quite as true as that there can be no count- 

 ing without difference. The One and the Many thus root in Identity 

 and Difference, pass up into fuller expression in Universal and Par- 

 ticular, hold forward into Cause and Effect, attain their commanding 

 presentation in the Reciprocity of First Causes, and so keep record of 

 the contrast between Necessity and Contingency. In short, they are 

 founded in, and in their turn help (indispensably) to express, all the 

 categories, Quality, Quantity, Relation, Modality. Nor do they 

 suffer arrest there; they hold in the ideals, the True, the Beautiful, 

 the Good, and in the primary Ideas, the Self, the World, and God. 

 For all of these differ, however close their logical linkage may be; 

 and in so far as they differ, each of them is a counted unit, and so they 

 are many. And, most profoundly of all, One and Many take footing 

 in absolute reality so soon as we realize that nothing short of intelli- 

 gent being can be primordially real, underived, and truly causal, and 

 that intelligence is, by its idea, at once an /-thinking and a universal 

 recognizant outlook upon others that think I. 



Hence Number, so far from being the derivative of Time and Space, 

 founds, at the bottom, in the self-definition and social recognition of 

 intelligent beings, and so finds a priori a valid expression in Time and 

 in Space, as well as in every other primitive and spontaneous form in 

 which intelligence utters itself. The Pythagorean doctrine of the rank 

 of Number in the scale of realities is only one remove from the truth : 

 though the numbers are indeed not the Prime Beings, they do enter 



