i EXPERIENCE AND REALITY 239 



thought. This system moreover must be a single system, 

 and it must be possible to say certain things of it univer- 

 sally. These things must hold, however far the system 

 extends, but to assert them is not to enumerate the cases in 

 which they apply nor to define the extent of the system of 

 which they hold. The unity of the system again is not 

 that of a whole defined by limits, but that which consists 

 in the interconnectedness of all causal processes. No 

 knowledge of the ultimate beginning or end of such pro- 

 cesses is required. Thought, therefore, does not postulate 

 a closed system. On the other hand, if we ask, not what 

 thought necessitates, but what ideal it sets before us, it 

 would be true to say that it aims at completeness. Now a 

 complete system as ordinarily conceived is incompatible 

 with infinity. For a system must either, according to the 

 well-known argument, be finite. Then it must have boun- 

 daries, and there must be something that bounds it, so that 

 it is not the whole. Or it is infinite, and if so it is never 

 complete. Modern mathematical analysis advances a solu- 

 tion by conceiving the infinite as a whole, which differs 

 qualitatively from the finite whole in that it is similar to its 

 parts. Whether the definitions on which this conception 

 rests are free from all ambiguity, and, if so, whether the 

 conception can be fruitfully applied to the world of experi- 

 ence, are questions which I cannot here attempt to deter- 

 mine. But the conception of the infinite as differing 

 qualitatively from the finite emerges also from more 

 familiar mathematical considerations. These considera- 

 tions lead us to conceive of series which, as they proceed, 

 approximate to a point at which a certain change of 

 character ensues. This point is the limit of the series 

 which it may be conceived as reaching at infinity. Thus 

 the series .999..., which is a fraction, approaches more 

 and more nearly as we prolong it to the number i, 

 which is an integer. The arc of a circle, if we take 

 smaller and smaller segments or remove the centre 

 further and further away, approximates more and more 

 closely to the straight line drawn at a tangent. What is 

 common to these cases which run through the entire world 

 of quantity and are the foundation of the infinitesimal 



