362 THE POPULAR SCIENCE MONTHLY 



science is ' ' absolutely pernicious as a mean of internal culture, ' ' ° that an 

 "excessive" study of the mathematical sciences "absolutely incapacitates the 

 mind, for those intellectual energies which philosophy and life require. We are 

 thus disqualified for observation either internal or external — for abstraction and 

 generalization — and for common reasoning ; and disposed to the alternative of 

 blind credulity or irrational scepticism. ' ' ' Further on Hamilton says that 

 mathematics can not ' ' conduce to ' logical habits ' at all. The art of reasoning 

 right is assuredly not to be taught by a process in which there is no reasoning 

 wrong. " * " But if the study of mathematics do not, as a logical discipline, 

 warn the reason against the fallacies of thought, does it not," inquires Hamil- 

 ton," "as an invigorating exercise of reason itself, fortify that faculty against 

 their influence ? ' ' 



To this, Hamilton says, "it is equally incompetent. ' ' '" He next observes 

 "that to minds of any talent, mathematics are only difficult because they are 

 too easy, ' ' " that ' ' in mathematics dullness is thus elevated into talent, and 

 talent degraded into incapacity. " " "Of Observation, Experiment, Induction, 

 Analogy, the mathematician knows nothing."^ "After all," says Hamilton,'* 

 ' ' we are afraid that D 'Alembert is right ; mathematics may distort, but can 

 never rectify, the mind." 



From these quotations it appears that Hamilton tried to prove that 

 the study of this science is positively injurious to the mind. If this be 

 true, then, of course, mathematics ought to be excluded entirely from 

 a scheme of liberal education, unless, as Bledsoe says,^^ the object of 

 such a scheme be to injure, and not to benefit, the mind of the student. 

 Had Hamilton adhered to the position which he first outlined, he could 

 have entrenched himself behind practically unconquerable breastworks. 

 But what has given notoriety to his paper, is the fact that most of the 

 time he really argues against mathematical study altogether by en- 

 deavoring to show that its effect upon the mind is injurious. For 

 sevent3'-five years Hamilton's article has been singled out as the most 

 powerful argument in existence against mathematics. 



To show the alleged pernicious effect of mathematics upon the mind 

 Hamilton's argument proceeds along two principal lines, the first of 

 which is the contention that mathematicians who have confined their 

 studies to mathematics alone are addicted to blind credulity or irra- 

 tional scepticism and, in general, lack good judgment in affairs of life. 



It is my opinion that Hamilton establishes this proposition. The 

 mere mathematician is a man of one-sided development. But how 

 about the metaphysician who confines his studies to metaphysics alone ? 



^ Loc. cit., p. 424. 



8 Loc. cit., p. 427. 



"Loc. cit., p. 428. 



^"Loc. cit., p. 428, 



" Loc. cit., p. 430. 



^ Loc. cit., p. 430. 



" Loc. cit., p. 433. 



" Loc. cit., p. 453. 



^^ Southern Eeview, Vol. 22, 1877, p. 261. 



