ATTACKS UPON THE STUDY OF MATHEMATICS 363 



Is he an all-round man? Is the caveling metaphysician, who disputes 

 all things, very far ahead of the credulous mathematician ? Had Hamil- 

 ton been disposed to attack the study of metaphysics, could he not have 

 made as strong a case against metaphysics as he did make against 

 mathematics? The mere metaphysician and the mere mathematician 

 are one-sided individuals. How about the mere philologist with 

 his roots and stems, the mere paleontologist with his old bones, the 

 mere physicist with his moment of inertia and latent heat, the mere 

 chemist with his pedantic formulae, the mere entomologist with his draw- 

 ings of beetles ? The truth is that the exclusive study of any branch of 

 knowledge is to be discouraged as undesirable for a liberal education. 

 Every one recognizes the dangers of premature and excessive speciali- 

 zation. But because a certain branch of study, taken by itself, fails to 

 accomplish fully all the ends of education, are we to draw the inference 

 that this branch of study is injurious? Because the human body can 

 not readily subsist upon a diet consisting exclusively of roast beef, are 

 we to conclude from this fact alone that roast beef is unhealthy and 

 ought to be banished from the dining table? Yet this is exactly the 

 mode of argument which Hamilton applies to mathematics. Plenty of 

 people are willing to testify that mathematics is not the sole and ex- 

 clusive intellectual diet that a growing boy should have. From testi- 

 mony of this sort Hamilton attempts to argue that " mathematics may 

 distort, but can never rectify, the mind."^^ In our humble opinion the 

 learned philosopher is guilty of a very unphilosophical argument, " un- 

 philosophical in its design, in its spirit, and in its execution."^'^ 



We said that Hamilton argues along two principal lines. His sec- 

 ond mode of attack is to show that many mathematicians, some of them 

 of great eminence, have found mathematics unsatisfactory as an exer- 

 cise of the mind, and have renounced it. I hardly know how to ap- 

 proach this part of Hamilton's argument. For lack of space I can not 

 demonstrate the conclusions we are about to state. Bledsoe's reply to 

 Hamilton covers sixty-nine pages, and for details we must refer you to 

 him and to the authorities quoted by Bledsoe and Hamilton. By his 

 extensive inquiry Bledsoe proves what some other writers before him 

 hinted at, or proved only in part, namely, that Hamilton was extremely 

 careless in the selection of his quotations. By means of partial extracts, 

 badly chosen, he made scientists say exactly the opposite of their real 

 sentiments. Bledsoe convicts Hamilton of this practise in his quota- 

 tions from D'Alembert, Pascal, Descartes and Dugald Stewart, who are 

 the most celebrated mathematical witnesses called by Hamilton. 



Take the case of Descartes. We quote from Hamilton the follow- 

 ing :^® 



" Loc. cit., p. 453. 



" Southern Review, Vol. 22, p. 282. 



" Loc. cit., p. 421. 



