402 PHILOSOPHICAL THOUGHT. 



to start a train of reasoning, the results of which might 

 or might not be true, according to the verification or 

 otherwise afforded by experience and observation. 



Thus it has come about that what Kant, and before him 

 Hume, looked upon as exact knowledge, has in the eyes 

 of more recent thinkers acquired quite a different aspect 

 from that which it presented to them. Mathematical 

 and mechanical calculations are only a convenient 

 method of joining together various facts and phenomena 

 which surround us in time and space, a means by which 

 we can fix, define, and describe them, and arrive at 

 a knowledge of other facts and phenomena which, but 

 for these methods, would remain hidden and unknown 

 to us. The present aim of scientific knowledge is, to 

 describe the occurrences round about us in the simplest 

 form and as completely as possible. The object is on 

 the one side to attain to a greater simplicity and accord- 

 ingly to a more complete unification of knowledge, and 

 on the other side to make this more and more complete. 

 In order to do this, it has been found necessary to 

 supplement what we can see and observe by imaginary 

 pictures of that which we cannot see, either because it 

 is too remote, too far away in space and time, to come 

 within our horizon, or because it is too minute, and 

 accordingly escapes our notice. But unless we return 

 on these circuitous paths which lead us beyond our 

 horizon or underneath that which lies on the surface 

 into the limits of what we can see and observe, ending 

 up with the visible, the tangible, and the finite, all 

 those complicated theories, built up with so much ingen- 

 uity and elaborated with so much care, are of no use 



