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MATHEMATICS IN EDUCATION.
Goldsmith's opinion of mathematics and logic were shared by Warburton, Gray, and other eminent writers. Bishop Warburton, in the Introduction to his Discourse on "Julian," says:—
"Tho use of these boasted instruments of truth [Logic and Mathematics,] goes no further than to assist us, the one in the form of reasoning, the other in the method of discourse.
"Aristotle's invention of the categories was a surprising effort of human wit But, in practice, logic is more a trick than a science, formed rather to amuse than to instruct And, in some sort, we may apply to the art of syllogism what a man of wit says of rhetoric, that it only teacheth us to name those tools which nature had before put into our hands, and taught the use of. However, all its real virtue consists in the compendious detection of a fallacy. This is the utmost it can do for truth. In the service of chicane, indeed, it is a mere juggler's knot, now fast, now loose; and the schoolmen, who possessed it in a supreme degree, are full of its legerdemain. But its true value is now well known; and there is but little need to put it lower in the general estimation.
"However, what logic hath lost of its credit for this service, mathematics have gained. And geometry is now supposed to do wonders, as well in the^system of man asof matter. It must be owned, the real virtue it hath, it had acquired long since: for, by what is left us of antiquity, we see how elegantly it was then handled, and how sublimely it was pursued. But the truth is, all its use, for tho purpose in question, besides what hath been already mentioned, seems to be only habituating the mind to think long and closely: and it would be well if this advantage made amends for some inconveniences, as inseparable from it It may seem perhaps too much a paradox to say, that long habit in this science incapacitates the mind for reasoning at large, and especially in the search of moral truth. And yet, I believe, nothing is more certain. The object of geometry is demonstration, and its subject admits of it, and is almost the only one that doth. In this science, whatever is not demonstration, is nothing; or at least below the professor's regard. Probability, through its almost infinite degrees, from simple ignorance up to absolute certainty, is the terra incognita of the geometrician. And yet here it is that the great business of the human mind is carried on, the search and discovery of all the important truths which concern us as reasonable creatures. And here too it is that all its vigor is exerted: for to proportion the assent to the probability accompanying every varying degree of moral evidence requires the most enlarged and sovereign exercise of reason. But the harder the use of any thing, the more of habit is required to make us perfect in it. Is it then likely that the geometer, long confined to tho routino of demonstration, the easiest exercise of reason, where much less of the vigor than of the attention of mind is required to excel, should form a right judgment on subjects, whose truth or falsehood is to bo rated by the probabilities of moral evidence? I call mathematics the easiest exercise of reason, on the authority of Cicero, who observes, 'that scarce any man ever set himself upon this study, who did not make what progress in it he pleased.'* But besides acquired inability, prejudice renders the veteran mathematician still less capable of judging of moral evidence. He who hath been so long accustomed to lay together and compare ideas, and hath reaped th&itit'hcst fruits of speculative truth for his labor, regards all the lower degrees of evidence as in the train only of his mathematical principality: and he commonly disposes of them in so despotic a manner, that the ratio ultima mathematicorum is become almost as great a libel upon reason, as other sovereign decisions. I might appeal, for the truth of this, to those wonderful conclusions which geometers, when condescending to write on history, ethics, or theology, have made from their premises. But the thing is notorious: and it is now no secret that the oldest mathematician in England is the worst reasoner in it. But I would not be mistaken, as undervaluing the many useful discoveries made from time to time in moral matters by professed mathematicians. Nor will any one so mistake me, who does not first confound the genius and the geometer; and then conclude that what was the achievement of his wit, was the product of his theorems.
"Yet still it must be owned, that this discipline habituates the mind to think closely; and may help us to a good method of composition. In those most* unpromising ages, when the forms of the schools were as tedious and intricate, as the matter they treated, was absurd or trifling, it hath had force enough to break through the bondage of custom, and to clear away the thorns that then perplexed and overgrew the paths of learning. Thomas Bradwardin, a mathematician, and Archbishop of Canterbury, in the fourteenth century, in his famous book De causa Dei, hath treated his subject, not as it was wont to bo handled in the schools, but in the better method of the geometers. And in another instance, of more importance, he hath given the age he lived in an example to emancipate itself from the slavery of fashion, I mean in his attempt (as by his freedom with the fathers it seems to be) of reducing their extravagant authority to its just bounds. But yet, Bo true is tho preceding observation, that though mathematics, in good hands, could do this, it could do no more: all the opening it gave to truth could not secure Bradwardin from the dishonor of becoming advocate for the most absurd opinion that ever was, the Anti-Pelagian doctrine of St. Austin; in which the good archbishop was so much in earnest, that he calls the defense of it, the cause of God."
Gray, says his biographer Mitford, "would never allow that mathematical knowledge was necessary in order to form the mind to a habit of reasoning or attention." In a letter to a friend written during his residence at Cambridge, he asks: "must I pore upon mathematics? Alas! I can not see in too much light; I am no eagle. It is very possible that two and two make four, but I would not give four farthings to demonstrate this ever so clearly; and if these be the profits of life, give me the amusements of it. The people I behold all around me, it seems, know all this and more, and yet I do not know one of them who inspires me with any ambition of being like him."
%Quis iffnorat. ti. qui mathematiei vocanlur, quanta in nbseuhtate rerum. and quatn recondite in arte and multiplici cubtiiitate versenlur 1 quo tamen in gent-re ita mulli perfecti homines exiliterunt, ut nemo fere studuisse ei sciential vehementius videatur, quin, quod voluerit, leculua sit. De Oral. 1.1.
Chase's Adjustable School Dese Axd Seat. To meet the want, long felt, of a style of seat and desk, capable of being adapted to the exceptional cases in every school, viz., of persons, who are above, or below the maximum or minimum height provided for in a particular grade of school,—or who require from incipient deformity, or any other cause, a chair or desk with special reference to height or position, Mr. Amos Chase, of North Weare, New Hampshire, has constructed an Adjustable School Desk and Seat, which is represented in the following cut, and for which he has obtained two patents.
The seat is rigidly secured to the rod, a, which slides smoothly in the hollow cylinder, b, this cylinder being enlarged at its base and fastened firmly to the floor. The middle slat of the seat's back is lengthened downward and attached at its lower end to a projection from tho rod, a, which passes through a vertical slit made in the cylinder, b, for that purpose; this slit being of sufficient length to allow the arm to slide up and down with the rise and fall of the seat. The seat is secured in any desired position by a set-screw.
The desk is also made adjustable in height by a similar arrangement; the footrest being supported on an arm which is fastened to the sliding-rod, and passes through a slit in tho cylinder or stand.
Beside the facility of adjustment, the convenience of sweeping a room provided with these desks and seats is apparent
Further information in relation to tho matter may be obtained by addressing tho assignee, N. C. Page, at North Weare, N. II.