652 PSYCHOLOGY. 



ultimate and had no farther predicates. In such a world 

 there would be as many kinds as there were separate things. 

 We could never subsume a new thing under an old kind ; 

 or if we could, no consequences would follow. Or, again, 

 this might be a world in which innumerable things were 

 of a kind, but in which no concrete thing remained of the 

 same kind long, but all objects were in a flux. Here again, 

 though we could subsume and infer, our logic would be of 

 no practical use to us, for the subjects of our propositions 

 would have changed whilst we were talking. In such worlds, 

 logical relations would obtain, and be known (doubtless) as 

 they are now, but tney would form a merely theoretic 

 scheme and be of no use for the conduct of life. But our 

 world is no such world. It is a very peculiar world, and 

 plays right into logic's hands. Some of the things, at least, 

 which it contains are of the same kind as other things ; sorne 

 of them remain always of the kind of which they once were ; 

 and some of the properties of them cohere indissolubly and 

 are always found together. Which things these latter things 

 are we learn by experience in the strict sense of the word, 

 and the results of the experience are embodied in 'empirical 

 propositions.' Whenever such a thing is met with by us 

 now, our sagacity notes it to be of a certain kind ; our 

 learning immediately recalls that kind's kind, and then that 

 kind's kind, and so on ; so that a moment's thinking may 

 make us aware that the thing is of a kind so remote that 

 we could never have directly perceived the connection. 

 The flight to this last kind over the heads of the intermedia- 

 ries is the essential feature of the intellectual operation here. 

 Evidently it is a pure outcome of our sense for apprehend- 

 ing serial increase ; and, unlike the several propositions 

 themselves which make up the series (and which may all 

 be empirical), it has nothing to do with the time- and space- 

 order in which the things have been experienced. 



MATHEMATICAL RELATIONS. 



So much for the a priori necessities called systematic 

 classification and logical inference. The other couplings 

 of data which pass for a priori necessities of thought are 

 the mathematical judgments, and certain metaphysical prop- 



