LH 2:2.67 i?4> ■ 0:^; BACCALAUREATE ADDRESS. /? , H&J^^ BACCALAUREATE ADDRESS: DELIVERED AT THE ANNUAL COMMENCEMENT GENEVA COLLEGE, ^CC AUGUST 4, 1841. BY BENJAMIN HALE, D. D., PKESIDENT. PUBLISHED BY REQUEST OF THE TRUSTEES GENEVA, N. Y.: PRINTED BY J, STOW, JR. & CO., MAIN STREET. I8T2. BACCALAUREATE ADDRESS. On the occasion of delivering my first Baccalau- reate Address, three years ago, I commenced what I designed should be a series of discourses on Edu- cation, "in its relation to the full and free develope- ment of the reason and the understanding," intend- ing to exhibit therein an extended view of the true scope and means of a liberal education, as demanded by a community in the full enjoyment of free insti- tutions. It is the common faith among us, that our free institutions rest ultimately on the knowledge and vir- tue of the people ; but, in interpreting this common faith, the right of private judgment is most freely exercised. Every one regards himself as at liberty, and few are so modest as not to believe themselves fully competent, to define the knowledge, which is necessary to the citizen of a free state. And what is the consequence I That which each understands, the bearing of which he can see, he sets down as necessary ; that on the other hand, which lies beyond his scope, or which appears to him to be conducive to the distinctioa- of its possessor, while its impor- tance to the whole community, however great, he does not understand, he regards as a matter in which the public has no concern. Narrow views are be- gotten, and the value of learning in itself is inade- quately estimated. Learning declines, and it is found too late, that common education, and the general intelligence of the people decline with it. Such seems to be, in brief, the course to which things are tending, upon this most important subject, in our country. The high estimate of learning for its own sake, and from enlarged views of the benefits of the highest provision for the nourishment of the intel- lect, which was once prevalent in some of the older parts of our land, seems to exist no longer in the same power and purity; and too generally that only is valued, the immediate application of which to the business of living, is apparent to the unlearned and unreflecting. There is among us a strong tendency to belieiie only what we can see. Men see not, and it is impossible that they should see the full value of the learning which they do not possess, and they cast it out of their creed. So far, however, as they see, they believe, and hence while comparatively little wisely directed effort has been made for the promotion of university education, it has become popular to expend vast sums for the support of common schools. Against such expenditure, I have nothing to ob- ject. There is no kind of internal improvement so important, or which will yield so large a revenue, as the improvement of the mind and heart of the peo- ple. I would only, that men should so value the streams and rivulets which carry fertihty to every door, as not to look upon the ocean, from whose bosom their waters have been drawn up in vapor, as a useless waste. I w ould, that they should have faith in something which they do not see, — if not in the opinions of those who are best qualified to judge in such matters, yet in the immortal and rational nature of man, as his highest glory, and the origin of all, that in human character and society is most excellent. Then would they believe, that in the high- est cultivation of the reason is to be found the means of carrying to higher and still higher elevation, his superiority. The soul of man is a mystery, and it might well be admitted that its nourishment, and its action even in things which most concern men, should have something in them which the w holly unlearned should not be able to expound. Had men such a measure of faith, is there any thing capable of being known which would be ridiculed as a subject of human enquiry] — anything too abstract, anything too recondite, any thing too apparently remote from human concerns to deserve attention 1 We know well, that we are sometimes compelled to go into abstractions J to find the principles on which the most important practical questions are to be settled, espe- cially w^hen these questions are out of the common course of events, and precedents and analogies fail us ; and the profounder the abstractions, if we reach them by accurate analysis, and reason from them exactly, the more valuable our deductions. We know too, that the recondite is not therefore useless. All that is true and good does not lie upon the sur- face. The richest treasures of the earth are deeply hidden within its bowels, and many of the great prin- ciples of physical science, w hich are so full of prac- tical applications to the uses of life, have but re- cently been brought to light, after a search of many generations. So, too, the 7 emote can never be too far removed to concern us, and to concern us nearly. The remote sun warms us, and the remote stars are our silent time-keepers. Nay, these distant orbs are the very guides of the sailor upon the trackless ocean, and he then only feels lost in his desert w ay, when " neither sun nor stars in many days appear." I suppose that the Danish astronomer, as he watched the stars from his island observatory, and, year after year, studied the distant heavens, may have been the standing jest of many a rude navigator of the Baltic, who little dreamed how great practical results, touch- ing the comfort and the safety of none more closely than of the sailor, w ere to come of this, as he thought it, idle star-gazing. Let human thought expand itself where it w ill, its earnest application can scarcely be without fruit. Let learning of any kind be pursued in a serious way, it cannot be without profit, and may lead to benefits, no one can say how great, or how widely diffused. Let it not be left, then, to men of unexpanded minds to decide what kind or extent of learning shall be thought worthy of public sup- port ; nor let it be supposed that what is expended for the education of a learned class, is lost to the community. If it come not back in some grand dis- covery, which blesses and enriches an age, it is certain to return, with interest, in the weekly instructions of the pulpit, in the labors of well-taught teachers, of thoroughly educated physicians, or lawyers or legis- lators. And let me add one remark more to this point. Let it not be thought that University Educa- tion, if supported at the public expense, ought there- fore to adapt itself to the popular taste, or popular notions of what is fitting, without farther question, or any serious and strenuous effort to give the popu- lar taste and popular notions a right direction. Let " learning made easy" be left to those who can nei- ther attain nor impart it in any higher shape, — but let our highest institutions be not only suffered, but sustained in their high duty of imparting mature learn- ing in a manly way, and of making scholars, whose well-disciplined minds and sound learning shall be ready for any of the higher services of the republic. The value of such a service can certainly be made apparent to an intelhgent people, and will be appre- ciated. In my last address upon a similar occasion,* I con- sidered the study of the Latin and Greek Languages as a part of liberal education, and I trust, sufficiently vindicated their claim to the place they have so long held, and the careful study of them as among the best means of intellectual discipline, and as performing a part in this important process, for which nothing else yet devised can be successfully substituted. In my present discourse, I shall say a few words * In 1839. The usual Address at the Commencement of 1840, was omitted on account of the imperfect health of the author. 8 on the study of Mathematics. The Languages, and the Mathematics, are properly regarded as the two fundamental parts of education. The discipline which they severally gave, is as different as that of any two studies can well be, while they seem to cover the whole ground of the elementary train- ing of the understanding. The one exhibits nfioral reasoning — the other, demonstration in its sim- plest form. I shall not be obliged on this subject, as on the former, to undertake a defence against popular prejudice and misjudgment. The use of Mathematical learning is too manifest, and exhib- its itself too clearly in the business and improve- ment of modern times to permit it to be over- looked. We keep and settle our accounts — we measure our land — we lay out our rail-roads and canals — we establish our weights and measures — we obtain our time — we find our place on the earth's surface, or our path upon the ocean, by the means of this science. Not that pure Mathematics contains all that is necessary for all these purposes, but it constitutes the language and the logic by which all reasoning upon number and quantity must be conducted. The language of moral sub- jects, that in which reasoning of the probable kind is conducted, is the ordinary language of men, the language which we begin to speak at our first lisping. We overlook its scientific dignity in its commonness, and, regarding it merely as a means of communication, not as an instrument of reasoning, we seem to ourselves to learn it sufiiciently by use, without making it an object of distinct and care- ful study. Not so with the language of number and quantity. It is learned at a maturer age, and under the impression of its scientific character. It is learned by all in its more elementary forms, be- cause the affairs of civilized life cannot be con- ducted without it ; and those who apply themselves to the attainment of a liberal education, are en- couraged to pursue it into its highest forms of rea- soning, and its profoundest abstractions, because it is perceived that more knowledge of it than is re- quired for the ordinary business of life, is necessary for the settlement of questions, and the conducting of affairs, which are of the highest moment to the peace and advancement of society. In the early days of our country, the study of the learned languages and of logic, constituted by far the most important part of university education. At that period the subjects which most interested and agitated men, were moral and political. Reli- gion was regarded as the highest object of learning ; and the sacred records of Christianity were written in one of the learned languages of antiquity, and the works of theologians principally in the other. In- deed, the language of the learned was the Latin, and those who wrote for Europe, rather than the partic- ular country in which they lived, wrote in the lan- guage of Cicero and the Caesars. The study of the languages and of logic, therefore, was demanded by the circumstances of the age, and suited its general current of thought and of speculation. At the pre- 10 sent day, we are not so much occupied with high and abstract questions of moral and rehgious, and I must be pardoned if I add pohtical rights and obligations, as with the outward machinery of living comfortably, and carrying forward the material progress of so- ciety. Railroads and canals, the settlement of boundaries, and the exact survey of our new terri- tory, and the marking it by lines which can be found again by the stars, should all terrestrial metes and boundaries be destroyed, are among the great ques- tions of the present day. Even politics deals more with mathematical than with moral reasoning, and takes the shape of Statistics or Economics, or of calculation in the less dignified form of the proba- bilities of elections ; and Religion itself, if I mistake not, has not escaped the influence of this " spirit of the age," though upon this topic I would here sim- ply suggest the enquiry, whether the profound and earnest search for the right has not been too much forgotten in the eagerness for the expedient, and calculation too much taken the place of an humble and reverent love of truth. Such a change in the character, objects and tendencies of the age, could not but show itself in our universities, and in the increased popularity of the physical sciences, and the sciences of calculation. It is a change from the moral to the mechanical, from a devotion to abstract truth in religion and politics, to a devotion to the outward improvement of our fortunes, and the de- velopement of the resources of our country. It has brought with it a change in the general current of 11 thought, and the necessity of a kind of learning, before Httle cultivated. This great change I do not speak of by way of censure ; it has taken place in the course of events, leading us on as a people to the fulfilment of our destinies. The former epoch naturally terminated with the war of the Revolution, when those great principles of civil liberty, which had been working in men's minds and formed the end and scope of so much of their study and meditation, were secured by the securing of our national independence, and by the same event we were put in possession of a country, to be governed by ourselves without re- straint — a country of vast resources, unknown but continually unfolding themselves to stimulate the energies of an enterprising people. The moral had had its result — the mechanical was to follow. The moral peopled the country originally, and estab- lished it as the home of liberty and a refuge for the oppressed of other lands, — the mechanical estab- lishes commerce and manufactures, constructs rail- roads and canals, and works out all the other visible means of national wealth. It is remarked by Mr. De Tocqueville, "that the " spirit of the Americans is averse to general ideas ; " and that it does not seek theoretical discoveries."* This remark applies to the present state of things in our country, and finds its explanation in the cause which I have just pointed out. That it is not ap- plicable to the earlier portion of our history, we * Democracy, vol. i, p. 296. 12 need no other authority to assure us than the same able writer. "In studying the laws," says he, " which were promulgated in the first era of the "American republics, it is impossible not to be " struck by the remarkable acquaintance with the "science of government and the advanced theory " of legislation which they display. The ideas there " formed of the duties of society towards its mem- " bers, are evidently much loftier and more compre- " hensive than those of European legislators at that " time.^" " The boldest theories of human reason " were put in practice by a community so humble, " that not a statesman condescended to attend to it."t Such a change as I have spoken of then has taken place. Within its just limits, it was important and necessary. Whether these limits have been trans- cended — whether in pushing forward the mechan- ical improvements of our age, we have not lost in too great a degree, the spirit of the former epoch, and whether this may not be precisely the ground of the greatest existing dangers to American liberty, let the reflecting decide. I am led to speak of it, in consequence of its influence on our systems of in- struction, producing a change in all ; but more deci- dedly apparent in those newer parts of our country, which are less influenced by the often salutary, but not often commended force of prescription, and venerable custom. Without the apparatus of our universities and schools, and just the direction of studies which for- * Democracy, vol. i, p. 23. f lb., p. 24. 13 merly existed, the past generation would not have been prepared to fulfil the part assigned it ; nor with- out the existence of means in much higher degree than they were enjoyed among us before the Revolu- tion, to train a competent number of young men in the mathematical sciences, would the present have been able to discharge its duties. The change on this point however, has in general been much too sweeping. It will easily be remembered by those who were educated at any of our Colleges twenty or thirty years ago, how meagre was the course of mathe- matical study, though even then the translation of La Place existed in the manuscripts of the self-edu- cated Bowditch. Geometry was studied, and in the application of Mathematics to the physical sciences, the geometrical method of proof alone was used. Analysis was almost unknown, except in some mea- gre treatises of Algebra, in which the science was taught synthetically. This form of Mathematics, although well fitted for the purpose of intellectual discipline, was but an imperfect instrument of re- search, and so long as it prevailed, improvement in all the sciences, involving mathematical reasoning, could not but be slow. For the introduction of the analytical Mathemat- ics into the universities and schools of this country, we are indebted principally to the Military Academy at West Point ; and if this valuable institution had rendered no other service to the country than this, it would have amply repaid its cost. Consider the 14 position of our country after the war of the Revo- lution, rich almost beyond example in the capabili- ties of wealth and power — possessed by a people sprung from the industrious and substantial classes of the most enlightened nation of Europe — already known for wisdom in council and courage in action, and ambitious of an honorable rank among the na- tions of the earth ; and how necessary to the devel- opement of these capacities, and to these proud hopes, and the wonderful changes by which they have since been vindicated, was the possession of mathe- matical and physical science in its highest form, and it will appear how large a debt we owe to this institution. There were engineers among us before West-Point furnished them, but they were few, and the greatly increased resources of civil engineering in our country, the perfection and cheapness with which important works are executed, and the wide diffusion of the knowledge of this important science, and that knowledge in a scientific form, are mainly attributable to that school. My purpose does not lead me to speak of it in other respects, but as a source of mathematical knowledge in our country, it seemed due from me, led to it as I am by my pre- sent subject, to speak of it with the highest acknow- ledgments. The practical value of the study of Mathematics, and its importance in relation to public improve- ments and the progress of the arts, are important considerations in vindicating its claim to a place in a system of liberal education. These considerations 15 merely however do not separate it from other studies, which are strictly professional, and could we urge no more than this, Mathematics might, like the law, be regarded as a professional study of the high- est importance to be pursued by surveyors, naviga- tors and engineers, but not entitled to demand of the general student a very careful study of its higher mysteries. Its claim to the important place, which it holds in a system of liberal education, is grounded on its peculiar fitness as a means of intellectual dis- cipline, and its necessity, in connexion with other means, for the full developement of the powers of the understanding in their just proportions. The study of Language is important as a means of disciplining the mind to moral reasoning, and fur- nishes examples of it in the shape most convenient, as it seems to me, for elementary instruction. The province of demonstration is occupied in a great measure by Mathematics, and it is unquestionably in this science that we find its simplest forms, and the means of training the mind most successfully to the exactness of demonstrative reasoning. Although a taste for mathematical reasoning may create a de- mand for it in cases, in which it is impracticable, and beget a sceptical dissatisfaction, in unbalanced minds, with other reasoning ; yet by exhibiting in the clearest manner and under the simplest forms, the true nature of demonstration, the study of this sci- ence may lead to the detection of the obstacles, which stand in the way of its extension to other prov- inces of human knowledge, and thus to their removal. 16 The very circumstances, which render Mathemat- ics capable of demonstrative reasoning, render it the best means of elementary instruction in reason- ing vs^ith absolute precision. Its subjects are all capable of being precisely stated, and its language is free from ambiguity. The slightest error in its processes is as palpable as the largest, and an ap- proximate result can never be mistaken for an abso- lute one. It is concerned wdth the simplest and most precise relations, and therefore is suited to elementary discipline in exact 'thinking. I do not in these remarks intend to imply that our w^hole discipline in reasoning can be entrusted to Mathe- matics. My conviction is far otherwise. Discipline in moral reasoning can be successfully conducted only by practice in moral reasoning. Mathematical studies may however, most successfully teach the young mind what exact reasoning is. An eminent jurist once said to me, "Before I studied Geom- etry, I never saw light ;" and it is said of another, that it was his habit, while holding his courts, to read over one or two of Euclid's demonstrations every morning. The difficulties of mathematical reasoninof, do not consist in the obscurity of the separate steps, but chiefly in their great number, and the brevity with which they are stated. A single theorem may con- tain more distinct steps, than a whole vokime of argumentation on politics or morals. The brief lan- guage of Mathematics expresses in a single symbol, what would require a page of ordinary language, 17 and its absolute precision renders long explanation unnecessary. A dull mind, which cannot master or distinctly retain the definitions and fundamental processes of mathematical reasoning, and the impa- tient one, which hurries over the thronging steps of a demonstration without clearly seeing their sequence, will find the difficulties of this science oppressive. There are few however so dull as not to be able, with proper pains at the outset, to attain a distinct apprehension of the elementary principles of math- ematics, and those who find difficulties in its study, from either their dullness or their impatience, may derive from it the most valuable discipline. No study will more clearly teach the necessity of precise and steady views of the elements of a science, in order to its successful prosecution, or the general truth that step by step is not only the surest, but the readiest way to exact conclusions. Such, then, is the great value of the Mathe- matics as an elementary part of a liberal educa- tion. It is a discipline of exactness, of circum- spectness, and of patience in the conduct of the understanding. It gives positive knowledge which no well educated man can be without, and imparts to the mind a new instrument of research. In considering the importance of Mathematics as a part of a liberal course of study, it would be im- proper not to notice its bearing upon the progress of general philosophy. In a former discourse, I spoke of language as the great instrument of anal- ysis, and in illustrating its analytical character, re- 18 ferred to Algebra, the language of which is the lan- guage of analysis in its most perfect form. " The principal cause," says Dugald Stewart, "of the over- " throw of the sect of the Nominalists, I am disposed " to think, was their want of some palpable exam- " pie, by means of which they might illustrate their " doctrine. It is by the use which algebraists make " of the letters of the alphabet in carrying on their " operations, that Leibnitz and Berkley have been " most successful in explaining the use of language " as an instrument of thought."^ In meditating upon this subject, it has seemed to me that all elementary study resolves itself into the study of language, or of the several instruments of analysis. Language is the immediate object of Logic, v^hich, as Abp. Whately states it, is merely " the art of employing language properly for the purpose of reasoning." It would be unsuitable to the occasion to pursue farther so abstract a subject, but if the remark be well founded, that the study of Mathematics is the study of one of the great instru- ments of analysis, and that the study of these instru- ments of analysis, as the means by which the mind must pursue its labors in investigation, and in the attainment of knowledge, is the most substantial ground-workof a thorough education ; it furnishes an irrefragable defence of the study of Mathematics, and deserves to be profoundly considered by all to whom education is entrusted. If such then as I have represented are the reasons • Phil, of the Hiunan Mind. vol. i. 164. 19 for the study of Mathematics in a course of liberal education, it is apparent that this study ought to be pursued in a manner at once the most exact and thoroughly analytical. If the pupil is to learn from it the nature of demonstration, and to habituate himself to exact reasoning, if he is to avail himself, in any measure, of its means for investigating the processes of the understanding, and detecting the helps which it employs, he must study it with the utmost exactness. It will be perceived upon the mere mention, that in the nature of the training given to the mind, Geometry or synthetical Mathematics, differs in some respects materially from analysis. In Ge- ometry, the proposition is first stated, the point to be proved must be kept steadily in view during the whole process of the demonstration, and the mind receives little aid except from the figure before the eye. It is thought by many to be superior even to analysis as a means of intellectual discipline. To train the mind, as in Geometrical reasoning to pro- pose to itself distinctly that which is to be proved, and to keep it unwaveringly in view during the pro- cess of the argument, is indeed a most important part of education ; but whatever advantage we may allow it in this respect. Geometry cannot carry the mind into these profound generalizations, which are perfectly easy by analysis, nor does it so reveal to it the aid, which it may derive from a w^ell contrived language, or so train it to research ^ The extent to which mathematical studies should 20 be pursued in a course of liberal education, will be differently estimated. Some would give them a pre- ponderance, others confine them within narrow lim- its. It should be the aim of such a course to devel- ope the powers of the mind in harmony, and to cul- tivate the habit of forming distinct conceptions, and reasoning accurately, not only upon mathematical and material subjects, but upon moral, on which exact reasoning is at once more difficult, and more important, inasmuch as "probability," to use the lan- guage of Bp. Butler, " is the very guide of life." An exclusively mathematical education then, notwith- standing the very important office we have assigned to Mathematics, as apart of a hberal course of study, would be a very defective one. I make this remark to meet an opinion, unfortunately too prevalent, which confounds practical with technical education, and assumes it as the business of education to teach the doing of some particular thing, rather than to evolve from the germ in which it is enfolded, the rational nature of man, in the fulness and perfect harmony of its proportions. But while some look upon Mathematics too ex- clusively as the source of intellectual discipline, and as the great object of practical knowledge ; others object to the study of it to any consider- able extent, as tending to produce rigidity, and a technical habit of mind. The exclusive study of Mathematics tends undoubtedly to such results, especially in minds of small capacity. But it is not peculiar to Mathematics to induce a rigidness 21 in intellectual habits. Any study remote from the common pursuits of men, and requiring severity of application and great exactness will, if devoured vv^ith more appetite than digestion, produce a simi- lar heaviness. To have one's intellect overborne — to be perpetually struggling with subjects too weighty for its power, is certainly not the way to cultivate vivacity of mind. If one of little strength desires to handle his thoughts with the show of ease and expertness, he must be cautious [that they be not too heavy for his handling. Let him deal with lighter studies — let him exercise himself with the ' graces,' but avoid the discus. If however he would attain a manly vigor, he must discipline his intel- lect with manly exercises, and as he becomes fa- miliar with them and his strength increases, he may acquire, if not flippancy, a manly ease and freedom. That mathematical studies do not necessarily pro- duce rigidity of mind, may be seen by the fact, that the most lively people of Europe have cultivated them most successfully, and few men, whom it has been my happiness to know, have surpassed in viva- city the most distinguished of American mathema- ticians, the translator and commentator of the Me- canique Celeste. One who saw Bowditch in his hours of business or recreation, would scarcely sus- pect that his mornings were spent in the abstrusest mathematical investigations ; and nothing shows more clearly the energy of his intellect, than that under such labors he should have uniformly retained the freshness and vivacity of manner and conversa- 22 tion, which always distinguished him. Labors which would have crushed another, were his recreation, and while devoting the regular hours of business with the greatest punctuality and energy to the duties of a highly responsible office, he accomplished in his hours of leisure a work, which gives him undeniably the first place among the men of science of this con- tinent. He was at once one of the most profound analysts, and one of the most delightful of compan- ions — remarkable for the symmetry and simplicity of his character, and as free from ever}^ thing false or indirect, as the most perfect calculation of his favorite science. But it is not my purpose to pronounce his eulogy, though in an academical discourse on mathematical science, the first of American mathematicians might fairly claim notice, especially one whose character was a beautiful commendation of his pursuits, and whose history, an exemplification of the success of ability and merit, without adventitious advantages. But it is time, young geMtlemen of the graduating class, that I address a few words more particularly to you. T have been speaking of the value of one of the studies, to which your attention has been di- rected, since you have resided among us, and in which you have been faithfully trained. I trust you do not leave us, without having reaped a good mea- sure of the advantages which flow from it, and that you will carry with you into the world the habits of exact thinking and careful study, in which it has 23 been our effort to train you. If you have formed such habits, preserve them — confirm them by con- stant exercise, and let me assure you that the longer you live, the more highly will you value them. Your highest duties in life, and your highest hopes, whe- ther of the present or the future, require of you not so much brilliancy and ingenuity, as pertinent and well-digested knowledge, and soundness of judg- ment. Seek earnestly, young gentlemen, to attain and to sustain " whatsoever things," in the beau- tiful enumeration of the Apostle, " are true, whatso- ever things are just, whatsoever things are lovely, and of good report." You leave our care, young gen- tlemen, but you carry with you our warmest wishes, and our prayers, that the blessing of Almighty God may be with you, both now and ever. LIBRARY OF C2,2lM 028 316 098 8