Mental Discipline in Ktiiication. 409 



affairs. An exclusive mathematical discipline must, therefore, 

 be held as an actual disqualification for the work of life.* 



It is important to notice that, so far as the mode of ex- 

 ercising the mind is concerned, mathematical discipline 

 does not correct the defects of lingual discipline, but rather 

 confirms them. We hence see how it was that mathemat- 

 ics so perfectly harmonized with philology as to have been 

 early and naturally incorporated with it in the same scheme 

 of culture. Both begin with the unquestioning acceptance 

 of data axioms, definitions, rules ; both reason deduc- 

 tively from foregone assumptions, and therefore both ha- 

 bituate to the passive acceptance of authority the highest 

 mental desideratum in the theological ages and establish- 

 ments which gave origin to the traditional curriculum. 



To those familiar with the literature of this discussion, 

 the objections here presented will not be new ; but there 



* Dugald Stewart remarks : " How accurate soever the logical process 

 may be, if our first principles be rashly assumed, or if our terms be in- 

 definite and ambiguous, there is no absurdity so great that we may not be 

 brought to adopt it ; and it unfortunately happens that, while mathemat- 

 ical studies exercise the faculty of reasoning or deduction, they give no em- 

 ployment to the other powers of the understanding concerned in the inves- 

 tigation of truth. On the contrary, they are apt to produce a facility in 

 the admission of data, and a circumscription of the field of speculation by 

 partial and arbitrary definitions. ... I think I have observed a peculiar 

 proneness in mathematicians to avail themselves of principles sanctioned 

 by some imposing names, and to avoid ail discussion which might tend to 

 an examination of ultimate truths, or involve a rigorous analysis of their 

 ideas. ... In the course of my own experience I have not met with a 

 mere mathematician, who was not credulous to a fault ; credulous not 

 only with respect to human testimony, but credulous also in matters of 

 opinion ; and prone, on all subjects which he had not carefully studied, to 

 repose too much faith in illustrations and consecrated names." Pascal 

 also observes : " It is rare that mathematicians are observant, or that ob- 

 servant minds are mathematical, because mathematicians would treat mat- 

 ters of observation by rule of mathematic, and make themselves ridiculous 

 by attempting to commence by definitions, and by principles." 



