Is he an all-round man? Is the caveling metaphysician, who disputes all things, very far ahead of the credulous mathematician? Had Hamilton 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 formulæ, the mere entomologist with his drawings 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 specialization. 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 exclusive intellectual diet that a growing boy should have. From testimony of this sort Hamilton attempts to argue that "mathematics may distort, but can never rectify, the mind."[1] In our humble opinion the learned philosopher is guilty of a very unphilosophical argument, "unphilosophical in its design, in its spirit, and in its execution."[2]
We said that Hamilton argues along two principal lines. His second mode of attack is to show that many mathematicians, some of them of great eminence, have found mathematics unsatisfactory as an exercise of the mind, and have renounced it. I hardly know how to approach 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 quotations 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 following:[3]
