1 2 Locke s Mathematical Method. 



mathematics a constant advance upon previous 

 attainment, so that each new result is an original 

 addition to what went before, not, as in logic, a 

 mere explication of it. Every mathematical prop 

 osition, being the expression of a fresh insight, 

 of a brand-new perception of relations, by the 

 synthetic activity of the mind, has its voucher, 

 not in antecedent truths, but in the immediate 

 affirmation of that constructive intelligence by 

 which those truths in continuous regression to the 

 axioms have been evidenced and maintained. It 

 is not, therefore, as Locke supposed, merely a 

 lack of first principles from which ethics suffers 

 in comparison with mathematics. Ethics is fatally 

 handicapped in quite a different way. In the 

 spatial relations, e.g., with which geometry deals, 

 the mind has the power (prior to sense-experi 

 ence, too) of making intuitive discoveries, of con 

 structing, as it were, by its own native activity, a 

 genuine science (which is afterwards found valid 

 for the objects of perception). The geometer, 

 accordingly, knows a great deal more about the 

 relations of space than the rest of mankind do. 

 But the moralist can tell us nothing new about 

 morality. The sciences begun by Euclid and 

 Archimedes have been so extended in the course 

 of eighty generations that the most arduous study 



