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On the Utility of the Mathematics.

1798 cause of its accidental association, in and infidel principles, are their most the case of a few individuals who study decided enemies; and the natural tenit, with principles hostile to Chris- | dency of the convictions they produce tianity, alas for many other sciences upon the human mind, is highly fabesides the Mathematics! History, vourable to the authority of the great for instance, harmless as it may ap- truths of revelation. Let Quinctilian pear to be, must be forthwith excom- be heard : quid quod se eadem geomemunicated ; for some of the most re- tria tollit ad rationem usque mundi? in markable historians of recent times qua cum siderum certos constitutosque have stood in the very foremost ranks cursus numeris docet, discimus nihil esse of infidelity, as Hume, Gibbon, Volney, inordinatum atque fortuitum.”* Sciand Voltaire, of whom the names are ences that inculcate such a lesson, denot at all associated with Mathemati- serve much better of the advocates for cal science; and Metaphysics must divine revelation, than to be accused take ilight along with it, for being of any alliance with the cause of infifound connected with the name of delity. And, in fact, unless the followHume. The truth is, all kinds of learning absurdity can be demonstrated, viz. ing are, in this respect, equally in dis- that they are at the same time friendly grace; or rather they are all clear of and hostile to the same cause the charge blame. They have suffered from being insinuated against them ought on this in bad company; but the guilt of that consideration to be abandoned. mischief which has been attributed to Should any one attempt to make out them, belonged solely to the pride and the charge against them, by citing wickedness of human nature, inde- examples of those who have been Mapendently of all accidental connec- thematicians and infidels at the same tions.

time; we might oppose example to But, to meet the question fairly ;- example. Take, for instance, the illusDoes the study of the Mathematics trious Sir I. Newton, who was at the necessarily induce any tendency to in- same time the greatest of Mathemafidelity ? In answer to this question, ticians, and a most devout and humble I would plead in behalf of these stu- Christian; who, though he was so dies, a claim to the privilege allowed deeply involved in his abstract investito criminals in a British court of ju- gations, as not to know whether or not dicature, viz. that until the validity of he had taken his dinner,t yet made the charge insinuated against them it his practice daily to read the Bible shall be established by sufficient evi- on his knees. I dence, they be considered to be inno- The sixth number of your own Macent. Let this be granted, and their gazine supplies another example on triumph against all the open or insi- the same side, from amongst those nuated slanders of their enemies is who are now living ;and there are perfectly secure. There are but two others very near at hand. The same ways of establishing the proof of their highly respectable individual, to whom guilt; the first is, by demonstrating this country is indebted for the best that, according to the nature of things, treatise in our language, on the subject infidelity and Mathematics are insepa- of Mechanics, and for other matherable, which would be positive evi- matical productions, is also the author dence against them; and the second of one of the most popular modern is, by shewing that they have, in fact, publications in defence of Christianity.ll seldom been far distant from each And another, who is justly celebrated other,-an evidence which, at the best, as the author of an excellent treatise could only be considered as presumptive. No one, certainly, would attempt * This same geometry extends its researches the former; the utmost any one could to the system of the universe, from which as do in that way would be, to express it shows that the motions of the heavenly bohis suspicion under the form of an

dies are uniformly according to certain laws, it opinion: and, in defence, the friends teaches us, that there is nothing in that universe of Mathematics would oppose opinion effect of chance.

that is not regular, or that could be merely the to opinion. They would appeal to

† Sce Life prefixed to his Principia, by Cotes. what I have already quoted as the sen

# See Simpson's Plea for Religion. timents of Dr. Barrow; and would Ś See Memoir of Mr. Exley. even shew that Mathematics, instead

|| D. O. Gregory. See his “ Letters on the of being confederated with sceptical Christian Religion.”

on the subject of Fluxions, is well destitute of all corporeal senses, and known to be the warm friend and ad- to pray that all connection between vocate of the Bible, and proves him our spirits and sensible matter might self to be at the same time a disciple of be eternally dissolved. The cases, in genuine science and of true religion. my judgment, are exactly parallel. In

There is indeed one way in which the the former case, it is mathematical study of the Mathematics may, like evidence that is required, where only any thing else that is good, be pervert- moral or historical evidence ought to ed to mischievous purposes, and be- be expected ; and in the latter, (as in come subservient to the cause of in- the example of Thomas,) the evidence fidelity. This happens, when the mind, of the senses is demanded, as a substifrom its habituation to mathematical | tute for faith. Let Mathematics and inquiries, learns to doubt of every thing our senses, then, either be retained towhich will not admit of mathematical gether, or together be expelled. They demonstration, and feels a disposition are both guilty of the same offencein consequence to reject all belief in both deserving of an equal punishthe truth and authority of Scripture. ment. I am not intending to give an opinion I feel great confidence, Sir, in the on the question, whether or not any of goodness of my cause, however inthe important truths revealed in it, are adequate my defence of it may be. I capable of such a demonstration ? but even su us enough to be certainly, whether capable or not, it lieve, that God himself has stamped the ought not to be insisted on. There is mathematical sciences with the seal of enough of evidence, to establish the His own approbation, as well in other claims of the Bible to the title of a respects, as by allowing some of the divine revelation ; and when the va- most important improvements in them lidity of that title is made good, the to occur contemporaneously with retruth of its contents will follow as an markable events tending to the spread inference of course.

of Christianity; by causing as it were, I do not know, however, nor do I a light from heaven to shine at the believe, that this perversion of the Ma- same time on the mathematical and thematics is very general ; but even the religious world. supposing that it is, we need not have It is no argument against this suprecourse to so desperate a remedy as position to affirm, that improvements their extinction, since it will be quite in the Mathematics have been commusufficient to remind the student of them, nicated to mankind through the methat he ought not to confound moral or dium of infidels and sceptics. It was historical evidence with mathemati- the stubbornness and ill-temper of cal; and that he must not expect the some of the Protestants, not less than latter, in cases where there is a suffi- their piety and zeal, that furthered the ciency of the former. Besides, the glorious Reformation on the continent; same objection which lies against the and the establishment of its principles study of the Mathematics, lies with in this country, was effected very equal force against the use of our cor- greatly through the caprice and wickedporeal senses. We are not more liable ness of one of the most dissolute and to confound mathematical with moral abandoned princes that ever swayed evidence, than we are to confound the the British sceptre. evidence of our senses with that of The fact is, true science is the handfaith, as may appear from the case of maid of religion. Satanic influence, Thomas, John XX. 24–28; and from and human pride, have indeed, often the frequent occurrence in Scripture, set them at variance with each other; of passages which remind us, that we and ignorance and superstition, have are to walk by faith, and not by in turns fomented the dissension. But sight.” And if Mathematics are to be they are beginning now to understand abandoned, because, by a perversion each other better; and the mischievous of their tendency, they may sometimes meddlers in the quarrel, to whose inmislead us, we ought, for a reason terference its continuance to the preequally as good, to wish ourselves sent period is principally to be attri

| Mr. Professor Dealtry.-See his Treatise buted, are retiring, ashamed and conon Fluxions, and its character, p. vol. 3. Dr. founded, back to their native dark. Hutton's Course ; and also his Defence of the ness. And as superstition gives way British and Foreign Bible Society.

on the one hand, and ignorance upon

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the other, we expect that“ pure and whence the quotation is takon, he conundefiled religion,” and real learning siders actions as proceeding immeof every kind, will blend their interests diately from the will of man, or from in one common cause, against their the will or decrees of God; without recommon enemies, and enter upon referring, at that time, to motives as terms of mutual and permanent recon- the occasions of willing, or as the inciliation. Divine truth and human struments by which the Divine purscience shall shine with mingled and poses are accomplished His object is unbeclouded lustre on the moral and to show that that doctrine which teaches mundane condition of society-con- us that the will is “bound,” is opposed tinue thus to shine so long as the sun to those first principles that are found and moon endure--suffer a momentary in every human being possessing comobscuration, at least to human vision, mon sense; and that these principles by the smoke and dust of the final con- are so closely interwoven with the meflagration-and then burst forth with a chanism of the human mind, that notglory, in which “ the spirits of just men withstanding there are persons who made perfect" shall find a source of persuade themselves into a partial beenjoyment, and a subject of contem- lief of opinions contrary to these plation, for ever and ever. J. C. “ genuine sentiments of nature,” yet, Frodsham, September 6th.

when both are brought to a fair practical test, the dictates of common sense

are generally found predominant. Reply to Observationson Buffier's

That man is free, Buffier considered Wager.

one of those important truths which [Inserted in No.7, col. 607.] nature teaches all men; and hence for MR. EDITOR,

a necessarian seriously to pretend to Whatever transformations the doc- him that he was not free, and yet not trine of Necessity may undergo in pass- consider his wager advantageous, he ing through such hands as the infidel inferred could only proceed“ from the Volney, the deist Hobbs, the socinian necessary and invincible opinion he Priestley, or the calvinist Toplady, it had of his being free.” Those who unloses nothing of its real nature. Whe- derstand the controversy on liberty and ther, with the pompous title philosophi- necessity, need not be informed that it cal, it connects human actions with is not an objection of yesterday against the laws of nature as their necessary the compulsive scheme, that it concauses ; or whether, with the more tradicts our consciousness; nor yet saered appellation decretive, it repre- that the pens of some of the ablest sents them as the results of the eternal necessarians have been employed to purpose and decrees of God, the con- elude the force of this objection. And sequences are the same. Ifit be true,an had N. R. attempted to prove that the uncontrollable destiny reigns through doctrine of necessity harmonizes with heaven, earth, and hell ; free-agency our consciousness, and that the docis annihilated; the distinction between trine of liberty clashes with it, his obvirtue and vice is confounded ; and the servations would have been more in equity of rewards and punishments en place than they now are; as my object, tirely lost. But notwithstanding that in the article which contains Buffier's in every form which it assumes it ex- wager, was merely to repeat this obculpates man from guilt, and fixes what jection. As his remarks are foreign to are called his crimes, either on na- the subject, I might very properly pass ture or on nature's God; it is fre-them over in silence. I shall, however, quently of importance to keep the dis- briefly notice some of his observations. tinction in view to which I have just At the commencement, this writer adverted. It was partly the forgetting informs us, that he “ is convinced in of this distinction, I presume, that led his judgment of the fact, that man is your correspondent N. R. to mistake free; but whether he has precisely the the object of that article on which he same idea of freedom with that corhas animadverted, No. 7, col. 607. respondent, he is not prepared to

By referring to No. 5, col. 414, it assert.” It is extremely probable, will be seen that Buffier uses the words that we do not both use the word free“necessarily decreed,” and conse- dom in precisely the same sense; espequently had a reference to decretive ne- cially if, in the meaning which he atcessity. In that part of his work from Itaches to it, nothing is included as No. 9.-Vol. I.

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the “

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trary to the import of the language ascribing to God an influence which he which he has put into the mouth of has not thought proper at all times to

poor fellow” whom he has hypo- exert: it consists in a feeling of the thetically introduced; namely, that heart. It is not the offspring of every

movement of” the “body” is mere opinion; it has a higher source ; previously ordained.” Such a free- and is possessed by all good men, by dom, I think, looks very much like whatever shades of sentiment they may compulsion ; and if it be true that be distinguished.

every movement of” the “body” be But, Sir, if this singular wager”

previously ordained,” then, for ought“ exhibits an erroneous view of the I see to the contrary, the murderer subject in dispute,” your corresponwho struggles beneath a gallows, de- dent N. R. endeavours to remove these serves no blame for the “

movements false impressions which it may have of” his “ body” that brought him to occasioned, by placing the subject on his unhappy end; nor does the writh its proper foundation. The true quesing martyr in the flames, deserve tion seems, in his estimation, to be this; praise for the piety and constancy with respect to the “movement of” the that led him to the stake. What I“ body," a man may do whatever he mean by freedom, is something very chooses (physical impediments of course different.

excepted,) but then he will choose to do By freedom, as it refers to actions nothing without a reason or motive. On morally good or morally evil, I mean, the first point, there can be no differthe absence both of compulsive causes ence between us; and to the second, I and invincible impediments. The unhesitatingly and unequivocally asprinciple of action itself, I call a sent. At first sight, one might almost power imparted to the mind, by Him | think that we might“ shake hands, and who formed it, either to act or forbear ever after live in peace ;” “but,” no, to act, when solicited by different de- | “it is vain to talk of peace: it must sirable objects. Without such a free- not be concealed, that this is not the dom and such a power, the judgment question.” day is to me an enigma that baflles my The real question goes deeper, and conceptions. It lies on those who ob- is this, Whether in every action that is ject to this, to prove, 1. That it is im- past, the volition which led to that acpossible for God to confer, or for a tion was absolutely controlled by the creature to possess, such a freedom. motive which it followed? or whether, 2. To show, that without it a man may prior to volition, it was not in the be justly accountable for his actions, power of the mind to have paused, and and be a proper subject for rewards to have collected and examined other and punishments. And when they motives, that would have presented a have done this, they will have accom- greater real or apparent good; and plished more than philosopher or di- consequently have led to another vovine has ever done before them.” lition and another action ? This I

“ But in their treatment of” this sub- maintain in the affirmative. That moject, “ let them be on especial guard tives do not compel the will, is obvious not to” lay too much stress on negative from the following considerations. 1. causality, nor to waste their time in They have no real existence separate the sillý” charge, that a belief in free from the mind; being nothing more agency proceeds from pride; “ because than perceptions of certain desirable such a" charge was never dreamt of qualities in things. 2. In choosing or by any” one, except he were an en- willing, it is the will that acts, and not thusiast or a bigot.” Such a belief the motives ; motives being passive, neither proceeds from, excites, nor im- like their causes. 3. It is impossible plies, a “haughty spirit.” The doctrine for that which is passive, to force that of liberty does not place man beyond which is active. Motives, therefore, the control of his Maker ; nor are its are merely the occasions, and not the advocates reluctant to acknowledge, efficient causes, of choosing ; the effithat they are wholly at the disposal of cient cause must be sought for in the that God whose creative power formed, mind itself. If, then, motives are pasand whose continued energy preserves sive, and it is the will itself that acts; them in being. Humility does not con- and if the mind has a power to pause sist in denying to man a power which before volition, and oppose motive to God has conferred upon him, nor in motive; we may very safely admit that

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Reply to Observations on Buffier's Wager.

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motive is essential to choice, without of all voluntary actions. Now, with subjecting our elections to absolute ne-out attempting to prove, that self-denial cessity.

can never be more agreeable than self“ The difficulties,” says a modern gratification ; and without adducing metaphysician, in which this subject a single fact from the page of history, has hitherto been involved, have to show that there have been men who arisen in great measure from the im- have sacrificed every thing dear to proper expressions used in treating themselves for the good of others; I it; most of which are, in their literal will suppose, that all men uniformly sense, applicable only to corporeal na- act upon the principle laid down by ture, which is passive, and therefore necessarians: and then I shall be glad suggest false conceptions when ap- to be informed, in what the difference plied to mind, which is essentially ac- consists between men and devils ? tive. Thus motives seem to imply Judging of them by the spring of their something active, whereas they are, in actions, I seriously affirm, that I can reality, passive, being the ends which conceive of no difference; as, the same the mind pursues, or may pursue. definition will suit both. A being uniThey are said to impel the mind to formly acting most agreeably to himself, action ; which again falsely denotes is a definition that will exactly answer activity, whereas the mind naturally to either saint, sinner, or devil, if mopursues them in proportion to the real tives determine the choice, and if the or apparent good they present. Thus end of all action is personal gratificaalso force and strength are improperly tion. A scheme which levels these applied to them.”. And again, speak- obvious distinctions of character, must ing of volition, he says, The efficient be false.--I have probably written too cause of the volition is the mind itself; much, and therefore hasten towards a the term motive is in some degree im- conclusion. proper, as it conveys the idea of ac- That there are questions of difficult tivity, whereas it is, in reality, passive, solution connected with the liberty of being the term towards which the mind the will, I am by no means disposed moves, or from which it recedes.” On to deny. But as we have the evidence the same subject, Dr. Watts observes, of consciousness for its truth; to deny * Some philosophers suppose nothing it, is only to imitate the absurdity of worthy of the name of agent or action, those, who, discrediting the testimony but the will and its exercises ; and of their senses, deny the existence they call all other beings, and their and motions of material beings, bepowers and operations, merely passive; cause consciousness is not added to but this, perhaps, is too great a vio- sense, to attest their existence. One lence offered to the common sense of of the writers already referred to, words, though there may be some ap- speaking of liberty, observes, It is pearance of reason for it in the nature needless to adduce any arguments in of things.” From the Dr.'s statement, proof of it, as the consciousness of the view that has been given of the our being ourselves, the active princiwill and its exercises, corresponds ples from which our determinations with the nature of things; it is only originate, and the remorse incident opposed to the common sense of words. to the abuse of this self-determining And when words suggest conceptions power, impress the fullest conviction contrary to the nature of those things of this important truth.” Having made which they represent, the meaning of these observations, I shall take a final those words must, of course, be ac- leave of Buflier's Wager. Whatever commodated to the nature of things, inadvertency I may attribute to N. R., and not the nature of things altered I by no means impute to him intento correspond with words.

tional misrepresentation; and with The will then determining the choice every proper feeling towards him, I itself, instead of being certainly deter- remain, Sír, your's respectfully, mined by the greatest, or always by the strongest motive; the only remaining topic claiming notice, is, “ that in all voluntary actions, a man will uniformly

Query on Elliptical Figures, do that which, upon the whole, is most MR. EDITOR, agreeable to himself.” Thus, it seems, By giving the following remarks to the that self-gratification is the only spring consideration of your readers, you will

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