

53 



the level of ideas, fell back upon tlie abstractions of 

 sense, and, by preference, upon those which were most 

 ready to hand, namely those of Mathematics. Plato's 

 ideas relapsed into a doctrine of numbers ; Mathematics 

 into Mysticism, into Neo-Platonism, and the like. And 

 so, through many long ages, through good report and 

 evil report. Mathematics have always held an unsought for 

 sway. It has happened to this Science, as to many other 

 subjects, that its warmest adherents have not always been 

 its best friends. Mathematics have often been brought 

 in to matters where their presence has been of doubtful 

 utility. If they have given precision to literary style, 

 that precision has sometimes been carried to- excess, as 

 in Spinoza and perhaps Descartes ; if they have tended 

 to clearness of expression in Philosophy, that very 

 clearness has sometimes given an appearance of finality 

 hot always true ; if they have contributed to definition in 

 theology, that definiteness has often been fictitious, and 

 has been attained at the cost of spiritual meaning. And, 

 coming to recent times, although we may admire the 

 ingenuity displayed in the logical machines of Earl 

 Stanhope and of Stanley Jevons, in the Formal Logic of 

 De Morgan, and in the calculus of Boole ; although 

 as mathematicians we may feel satisfaction that these 

 feats (the possibility of which was clear a priori) have 

 been actually accomplished ; yet we must bear in mind 

 that their application is really confined to cases where 

 the subject matter is perfectly uniform in character^ 

 and that beyond this range they are liable to encumber 

 rather than to assist thought. 



Not unconnected with this intimate association of 

 ideas and their expression is the fact that, which ever 

 may have been cause, which ever efiect, or wiiether both 

 may not in turn have acted as cause and efiect, the cul- 



