minds of its recipients. There is also considerable danger, from the very nature of the ideas with which this science is conversant, that it should foster a tendency to dreamy barren speculation, which I believe to be a prevalent intellectual vice of the inhabitants of this country: the remoteness and indistinctness of its images do not supply that healthy corrective which is needed for a people whose philosophy has much in it everywhere which is cognate to their old cosmical theory, explaining the stability of the earth by supposing it supported by an elephant, the elephant upon a tortoise, and the tortoise they know not upon what; and so considering the difficulty disposed of when removed two steps farther out of the reach of sense and observation.
"Now mathematics and natural philosophy, when rightly taught, are exactly and excellently well calculated to supply this defect.
"Through the hard, dry, incontestable truths of elementary arithmetic and geometry, founded upon our simplest conceptions of number and form, we are able to give good practical lessons in the art, if not in the science of logic: and this application of logical reasoning I believe to furnish a far better mental discipline than the formal science itself affords; and that there is an incalculable advantage in forcing the young student to perceive that there is such a thing as abstract truth, not in any way dependent upon the opinions and authority of his instructors, but derived from the very nature of the subject of his thoughts; and in accustoming him, when he has seized such truth, to follow it boldly and steadily into its remote consequences, as unassailable as the principles from which they are derived.
"Accordingly, a favorite reproach against mathematical studies by those who, it is charitable to think, have little knowledge of their nature, scope, and tendency, is that they make men too logical; that the habit of strict reasoning to which they become accustomed unfits them for balancing probabilities, and weighing one kind of evidence against another, expertness in which makes a shrewd practical man of business. I apprehend this to be an utter mistake; and the probability of its being so seems in some degree supported by the great number of distinguished mathematicians who have become acute lawyers, skilful physicians, and eminent statesmen. Besides, it is a complete misapprehension to suppose that the study of physics deals solely with certainties. Even in the purely mathematical branch we have the elegant and abstruse theory of probabilities, specially concerned with those propositions only of which we have only obscure and imperfect evidence; and
