science is "absolutely pernicious as a mean of internal culture,"[1] 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."[2] 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."[3] "But if the study of mathematics do not, as a logical discipline, warn the reason against the fallacies of thought, does it not," inquires Hamilton,[4] "as an invigorating exercise of reason itself, fortify that faculty against their influence?"
To this, Hamilton says, "it is equally incompetent."[5] He next observes "that to minds of any talent, mathematics are only difficult because they are too easy,"[6] that "in mathematics dullness is thus elevated into talent, and talent degraded into incapacity."[7] "Of Observation, Experiment, Induction, Analogy, the mathematician knows nothing."[8] "After all," says Hamilton,[9] "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,[10] 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 endeavoring to show that its effect upon the mind is injurious. For seventy-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 irrational 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?
