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XLIII. The impartiat reader is intrealed to remarli throughout yourwhole pers mance how consident you a re in asserting and withal howmodest in proving or eXplaining et how frequent it is with you to emplo figures and tropes instead of reasons: how many dissiculties pro- posed in the Analyst are discreetly overtooked by you, and what strangemork you mahe with the rest: ho grosely you mistahe and miseepresent, and how littie yoia practi se the ad vice which you se liberalty bestois. Belleve me, sir, I had long and maturely considered the principies of the modern analysis, hesore I ventu red to publim my thoughis thereupon in the Analyst. An d sinco the publication thereos, I have myself Deelyconversed with mathematicians os ali ranks, and sonae of the ablest professors, as weli as made it my businest to be informed of the opinions ofothers, heing very destrous to hear what could be said to arils clearing my dissiculties or answering my objections. But though you are notastald or ama med, to represent the analysts as very clear and uniform in their conception of these matters, yet I do solemnly amrm' and severat of themselves know it to be true) that I sound no harmony or agreementamong them, hut the reverse thereos the greatest dissonance and evencontrariety of opinions, employed to explain What aster ali siemed inexplicabie. XLIV.
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XLIV. Some By to proportions belween nothings. Some reject quantities because infinitesimal. inhers allow only finite quantities, and reject them because inconsiderable. Others place the method of fluxion son a seot with that of exhaustio is, and admit nothing neWr therein . Somemaintain the clear conception of fluxions. Others hold they can demonstrate about things incomprehensi ble. Some would prove the algorism os fluxions by reductio ad absurdum ι others a priori. Some hold the evanescent increments to he real quantities, so me to be nothings, semeto be limits. Ag many men, so many minds: each di fiering one Domanother, and ait Dom Sir L ac Neiston. Some plead inaccurate ex prensons in the great author, where by they would draw him to speah their sense, not considering that is he meant as they do, he could not want words to expresis his mean ing. Others are magisteriai and positive, saythey a re satisfied, and that is ali, not considering that we, who deny Sir I ac M.tons authori ty, mali not submit to that of his discipies. Somein sis , that the conclusions are true, and there re the principies, not considering what hath been largely suid in the Analyst ' on that head. Last-ly severat and thoso notae of the meanest), frankly o ned the objectionsto be unan Merable. Alt whicli I mention by way of antidote to your false colours: and that the uni rejudiced inquirer aliter truth may see, itis not without foundation, that I cali on the celebrated mathematicians of the present age to clear up these obscure analytics, and concur in givingto the public seme consistent and intelligibie account of the principies of their great master: whicli is they do not, I belle ve the world will tali eit for granted that they cannot. XLV. Having gone through your delance of the Sriti b mathematicians, I find in the nexi place, that you attach me on a Potnt of metaphys cs, with what success the reader will determine. I had upon another. Sect. XIX, XX, &c. occasion
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2 IA Defence of Free Thinling, Uc. occasion many years ago wrote against abstract generat ideas . In opposition to which, you declare yourself to adhere to the vulgar opinion, that nei ther geometry nor any other generat science can subsist without generat ideas P. ). This impli es that Ι hold there a re no generali deas. But I hold the direct contrary, that there a re in deed generalideas, but not formed by abstraction in the manner siet forti, by Mr. Locle. To me it is plain, there is no consisterit idea, the likeness whereos may not reatly exist : what ever there re is sa id to be sonaewhat whichcannot exist, the idea thereos must be inconsistent. Mr. Locle aclinowledgem it doth require patiis and sh ill to form his generat idea os a trian-gle. He further expressty faith, it must be ne i ther oblique nor redi angular, net ther equi laterat, equior urat, nor scalenum; but ali and none of these at once. He also salth, it is an idea wherein sonae paris of severat different and incusistent ideas are put together l. All this looks very like a contradictiora. Eut to put the matter pati dispute, it must benoted, that he affirms it to be so mewhat impersect that cannot exist . consequently the idea thereos is impossibie or inconsistent. XLVI. I delire to know, whether it is not possit, te sor any thing to exist , whicli doth not include a contradiction : and is it is, whether me may not infer, that What cannot possibiy exiit, the sanae doth include a contradiction : I fur ther destre to know, whether the rea ter can frame adistinct idea of any thing that includes a contradiction t For my pari, ICann Ot, nor Consequently of the above mentioned triangle; though you who it Oenis know bet ter than myseis what I can do) are pleased toassure me of the contrary. Again, I ask whether that, whicli it is above the power of man to forin a complete idea os, may not be called incomprehensibiet And whether the reader can frame a complete idea of
Introduction to the Treati se concerning the Principies os Human Knowledge.' Lslay on Human Undcrstanding, b. iv. C. vii. b. ix.
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et a A Defenee of Tree-Thinling, Uc. this impersect impossibie triangle ' And is not, whether it doth not Llow that it is incomprehensi bie t It mould seem, that a distinct aggregate
of a sew consistent paris was nothing so dissiculi to conceive or impossi-ble to exist , and that, there re, your comment must he wide of the author'S mean ing. You give ino to understand P. 82 that this account of a generat triangle was a trap which Mr. Locle set to catin Bois. Who, is caught therein lut the re ader judge. XLVII. It is Mr. Locte's opinion, that every generat name stands sora generat abstruct idea, whicli prescinds from the species or individua is comprehended under it. Thus, for example, according to him, the generat nam e colour stands sor an idea, whicli is nei ther bllae, red, greeΠ, nora ny other particular colour, but semewhat distinct and abstracted Domthem all. To me it seems, the word colour is only a more generat name applicabie to ali and each of the particular colours; while the other specific names, as blue, red, green, and the like, are eaeli restra ined to amore limited signification. The same may be seid of the word triangle. Let the reader jud ge whether this be not the case ; and whether he can
species thereos, or os a triangle whicli mali an Mer Mr. Loiae's account,
prescinding and abstracting from ali the particular soris of triangles, in
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the idea, between words or expressions and the conceptions of the mind,
the issue of this dispute may be fairly put. This doctrine os abstraei generat ideas seemed to me a capital error, productive of numberlesi dissi- culties and disputes, that runs not only throughout Mr. Locles book butthrouo most paris of learning. Consequently, my animadversions there-upon were not an effect of heing inclined to carp or cavit at a single passage, as you Would wronglalty insinuate, but proceeded from a love os truth, and a desire to banish, so far as in me lay, false principies and wrong ways os thinhing, without respect of persens. And indeed, thoughyou and other Party-men are violently attached to your respective manters, yet I, Who Prosese myself only attached to truth, see no rea n whyl may not as Deely animadvert on Mr. Locle or Sir θ aac M.ton, as theywould on Arsoto or Descartes. Certain ly the more extensive the influence of any error, and the greater the author ity whicli supporis it, themore it deserves to be considered and detected by sincere inquirersaster knowledge. XLIX. In the close of your per rurance, you let me understanti, thalyour geat for truth and the reputation of your masters halli occasionedyour reprehending me Mith the ut most Deedom. And it must be orenedyou have mewn a singular talent therein. But I am com rted under the severi ty of your reprehensiong, when I consider the wealinesse of your arguments, whicli, were they as strong as your reproo , Could leave nodoubi in the mind of the reader concerning the matters in dispute be-
tween us. As it is, I leave him to reflect and examine by your light
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horu clear γ he is enabled to conceive a fluxion, or the suxion of a suxion, a pari infinitely smali subdivided into an infinity of paris, a nascentor evanescent increment, that whicli is nei ther semething nor nothing, attiangle sor med in a poliat, veloci ty without motion, and the rest of those arcana of the modern analysis. To conclude, Ι had some thoughts of advising you how to conduct yourseis for the future, in return for the advice you have so Deely imparted to me: but, as you think it becomes me rather to insorm myself than instruct others, I smali, sor my further insormation, take leave to propose a sew Queries to those learned gentie-men of Cambri e, Whom you associale with yourself, and represent as
L. I destre to know, whether those who can neither demonstrate nor conceive the principies of the modern analysis, and yet give into it, maynot be justly said to have Lith, and he styled heli evers of mysteries tWhether it is impossibie to find among the physicians, incchanical philo
sophers, mathematicians, and philomathematicians of the present age, me such belle vers, who yet deride christians for their belles os mysteriest Whether Mith lach mcn it is not a Dir, rea nable, and legitimate method to use the argumentum ad hominem ρ And being so, whether itought to surprisse ei ther christians or scholarsi Whether in an age whereinso many pretenders to science attach the christian religion, we may notbe allo ed to malae repri fais, in order to merit that the irreligion of thoi emen is nOt to be presumed an effect of deep and just thini ing t Whether an attempt to detest false reasonings, and remedy defecis in mathematics, ought to be ill received by mathematicians t Whether the introducing more easy methods and more intelligibie principies in any science ould be discounten anced Z Whether there may not be fair objectionsas weli as caviis' And whether to inquire diligently in to the mean ing oi termS and the proos of propositions, not excepting against any thingMithout assigning a reason, nor ali edting to mistat e the signification or
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ing the subject in ali lighis, sincerely en dea uouring to finit out any senseor mean ing what ever, candidly set ting sortii What sterias obscure and what fallaci ous, and calling upon those, who professe the knowledge ossuch matters, to expla in them, whether I say such a procee ling can belustly called cavillingi Whether there be an isse dixit erectedi And is se,
When, Where, by whom, and Dpon What authori tyi Whether even where authori ty was to talie place, orae might not hope the mathematios, atteast, would be exceptedi Whether the chi ef end, in mal ing mathematics se considerable a part of academicat education, be not to forna in theminiis of young studenis habits of just and exact rea ningi And whether the study of abstruse and subiit matters caia conduce to this e , uniosi they a re weli understood, examin ed, and fifted to the bottom tWhether, there re, the bringing geometrical demonstrations to the severest test os rea n should be rectioned a discouragement to the studies of any learned society t Whether to separate the clear paris of thingssrom the obscure, to distinguissa the real principies, whereon trullis rest, and whence they a re derived, and to proportion the just measu res of aD sent according to the various degrees of CVide iace, be an uselesi or unworia thy underi akingi Whether the mal ing more os an argument than it will bear, and placing it in an undue rank of eviden ce, be not the lihely wayto disparage it i Whether it may not be of se me use, to provol e and stirup the learned proselibrs to explain a part of mathematical learn in g, whicli is achnowledged to be most pro unit, dissiculi, and obscuro, andat the fame time set sortii by Philalethes and many others, as the greates instance that has ever been gi ven of the extent of human abilities' hether sor the salae of a great man's discoveries, we must adopt his errors tLastly, whether in an age wherein ali other principies are canuasied withthe ut most freedom, the principies of fluxions are to be alone excepted '
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Mr. Waltons Vindication os Fluxions Was put into my hands. As this Dublin professor gleans aster the Cantabrigian, only endeavouring to translate a seis passages stom Sir I ac Neistons Principia, and enlarge on ahini or two os Philalethes, he deserves no particular notice. It may suffice to advertise the reader, that the foregoing defence, contains a fulland explicit answer to Mr. Giton, as he will find, is he thin ks it worthhis palns to read what this gentieman hath written, and compare it there-with. Particularly with Sect. I 8, 2O, 3O, 32, 33, 3 , 33, 36, 43, Itis not, I am fure, worth mine to repeat the fame things, or confute thesime notions twice over, in mere regard to a writer who hath copled even the manners of Philalethes, and whom in an Mering the other Ihave, is I am not much mistahen, sufficiently an Mered. II. Mr.
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II. Mr. Giton touches on the fame potnis that the other had touchedupon be te him. He pursues a hint whicli the other had given, about Sir Isaac's fir st sect ion concerning the rationes primae G ultimae. He dis. creetly avolds, like the other, to say one syllabie of second, third, or urthfluxions, and of divers other potnis mentioned in the Analyst, about allwhicli I observe in him a most prudent and pro und silence. And yethe very modestly gives his reader to understand, that he is able to clearup ali dissiculties and objections, that have ever been made P. s). ML Giton in the beginning, like Philalethes, Dom a particular case mahes a generat inference, supposing that infidelity to be imputed to mathematicians in general, whicli I suppose only in the person to whom the Analystwas addressed, and certa in other persons of the fame mind with him. Whether this extraordinary way of rea ning he the cause or effect of his passion, I know not: but be re I had got to the cnd of his Vindication, I cea sed to be surprised at his logic and his temper in the begin- ning. The doubie error, whicli in the Analyst was plainly meant to be-
writer also, as weli as the Cantabrilian, must necds take upon him to explain the motive of my writ ing against fluxions: which he gives oui, with great assurance, to have been, because Sir I ac Newton had presumed to interpose in prophecies and rcvelations, and to decide in religio us assairs P. ), whicli is Q far Dom being true, that, on the contrary, I have a high value ser those learned rema ins of that great man, Whose original and Dee genius is an eternat reproach to that tribe of sollowers, who a re alNays imitating, but never resemble hi m. This specimen ofMr. Mallon s truth will be a Warning to the reader to use his own eyes, and in obscure potnis ne ver to trust the gentie mari's candour, who daresto misrepresent the pia inest.
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2 8 An Appendis, i 'c. III. I was thinhing to have suid no more concerning this author'S per- formance, but test he mould imagine himself too much neglected, I intreat the reader to have the patience to per u se it; and is he finds any one potnt of the doctrine os fluxions cleared up, or any one objection in the Analyst anfwered, or so much as fairly stated, let hi in then malae his
compli ments to the author. But, is he can no more malae sense of what this gentiem an has writ ten than I can, he will need no answer to it. Nothing is easter, than for a man to translate or copy, or compose a plausi-ble discourse of so me pages in technical ternas, whereby hel mali mal ea me v oi saying mewhat, although nei ther the reader nor himself un- derstand one titile of it. Whether this be the case of Mr. Walton, and whether he underctan is cither Sir Isaac Newton, or me, or himself, Whate ver I may thin kὶ Ι shali not talae iapon me to say. But one thing I know, that many an unmean ing speech pas etli for significant by the mere as- Drance of the speatior, tili he cometh to be catechised ut on it , and thenthe truth sheweth it self This vindicator, indeed, by his disi emblingnitae paris in ten of the difficulties proposed in the Analyst, s heu eth no inclination to be catechised by me. But his scholars have a right to beinforme l. I theresere, recommend it to them, not to be imposed on hyhard words and magisteriai assertions, but caresully to pry into his sense, and sist his mean ingi and particularly to insist on a distinct an Mer to thesello ing question S.
IV. Let them assi him, whether he can conceive veloci ty without morion, Or motion without extension, or extension without magnitudet Ishe aras ers that he can, let him teacti them to do the fame. I f he can
nothing be not the produci of nothing multiplied by something t Anii is