vi THE EMPIRICAL ORDER 105 



accurately defined and nicely correlated concepts have arisen 

 in arithmetic and geometry. Men have learnt what it is 

 to observe and describe accurately, and the distinction 

 between a vague generality and a strictly universal relation 

 can no longer be missed. On this side the growth of 

 science engenders discontent with the empirical order as 

 rendered by common sense. On another side, it threatens 

 the supernatural, with the demand for evidence and for 

 consistency. The old easy-going acceptance of tradition 

 is disturbed. The gods must give an account of them- 

 selves or vanish. With the consciousness of methods, 

 postulates and conditions of sound thinking, we have 

 passed the limits of unreflective development and entered 

 those of methodical construction. Let us carefully con- 

 sider the position at this stage, and the problem to be 

 solved. 



We first note the characteristics of the empirical order. 

 To begin with, as its name indicates, it has been built up 

 on the basis of experience, and the units of experience are 

 objects of perception. Without seeking for the moment to 

 analyse the phrase, we may point out that perception bears, 

 not only upon the events of the material world, the quali- 

 ties, motions and changes of material objects, but also on 

 the inner world of consciousness, and that by the analysis 

 and synthesis of perceptual data, by generalisation and 

 deduction, we arrive at the connective ideas which we have 

 treated as the essential tissue of the world of common 

 sense, and which embody and connect for us, knowledge 

 both of nature in the narrower sense of that term, and of 

 human nature. Given that we can observe, and by 

 analysis, synthesis and generalisation construct and apply 

 ideas and judgments dealing with our surroundings, we 

 have the simple foundations of common sense knowledge. 

 When experience is specified as the foundation of common 

 sense, it means experience worked up into an order of 

 ideas by the factors specified. The same factors suffice to 

 explain the power of calculation where even within the 

 world of common sense we seem to reason a priori rather 

 than empirically. For both the number and the space 

 concepts are derivable from the empirical order by analysis, 



