It is attempted to put this Controversy in such a Light as that every Reader may be able to judge thereof.By George Berkeley 1.When I read your'Defence of the British Mathematicians,'

I could not,Sir,but admire your courage in asserting with such undoubting assurance things so easily disproved.This to me seemed unaccountable,till I reflected on what you say (p.32),when,upon my having appealed to every thinking reader,whether it be possible to frame any clear conception of Fluxions,you express yourself in the following manner,"Pray,Sir,who are those thinking readers you appeal to?Are they geometricians,or persons wholly ignorant of geometry?If the former,I leave it to them:

if the latter,I ask,How well are they qualified to judge of the method of fluxions?''It must be acknowledged you seem by this dilemma secure in the favour of one part of your readers,and the ignorance of the other.

I am nevertheless persuaded there are fair and candid men among the mathematicians.

And for those who are not mathematicians,I shall endeavour so to unveil this mystery,and put the controversy between us in such a light as that every reader of ordinary sense and reflection may be a competent judge thereof.

2.You express an extreme surprise and concern,"that I should take so much pains to depreciate one of the noblest sciences,to disparage and traduce a set of learned men,whose labours so greatly conduce to the honour of this island (p.5);to lessen the reputation and authority of Sir Isaac Newton and his followers,by shewing that they are not such masters of reason as they are generally presumed to be;and to depreciate the science they profess,by demonstrating to the world that it is not of that clearness and certainty as is commonly imagined.''All which,you insist,"appears very strange to you and the rest of that famous University,who plainly see of how great use mathematical learning is to mankind.''Hence you take occasion to declaim on the usefulness of mathematics in the several branches,and then to redouble your surprise and amazement (p.19and 20).To all which declamation I reply,that it is quite beside the purpose.For,I allow,and always have allowed,its full claim of merit to whatever is useful and true in the mathematics:but that which is not so,the less it employs men's time and thoughts the better.And,after all you have said or can say,I believe the unprejudiced reader will think with me,that things obscure are not therefore sacred;and that it is no more a crime to canvass and detect unsound principles or false reasonings in mathematics than in any other part of learning.

3.You are,it seems,much at a loss to understand the usefulness,or tendency,or prudence of my attempt.I thought I had sufficiently explained this in the'Analyst.'But for your further satisfaction shall here tell you,it is very well known that several persons who deride Faith and Mysteries in Religion,admit the doctrine of Fluxions for true and certain.Now,if it be shewn that fluxions are really most incomprehensible mysteries,and that those who believe them to be clear and scientific do entertain an implicit faith in the author of that method:will not this furnish a fair argumentum ad hominem against men who reject that very thing in religion which they admit in human learning?And is it not a proper way to abate the pride,and discredit the pretensions of those who insist upon clear ideas in points of faith,if it be shewn that they do without them even in science.

4.As to my timing this charge;why now and not before,since I had published hints thereof many years ago?Surely I am obliged to give no account of this:if what hath been said in the'Analyst'be not sufficient.Suppose that I had not leisure,or that I did not think it expedient,or that I had no mind to it.When a man thinks fit to publish anything,either in mathematics or in other part of learning,what avails it,or indeed what right hath any one to ask,Why at this or that time;in this or that manner;upon this or that motive?Let the reader judge if it suffice not that what I publish is true,and that I have a right to publish such truths when and how I please in a free country.

5.I do not say that mathematicians,as such,are infidels;or that geometry is a friend to infidelity,which you untruly insinuate,as you do many other things;whence you raise topics for invective.

But I say there are certain mathematicians who are known to be so;and that there are others who are not mathematicians who are influenced by a regard for their authority.Some,perhaps,who live in the University,may not be apprised of this:but the intelligent and observing reader,who lives in the world,and is acquainted with the humour of the times and the characters of men,is well aware there are too many who deride mysteries and yet admire fluxions;who yield that faith to a mere mortal which they deny to Jesus Christ,whose religion they make it their study and business to discredit.The owning this is not to own that men who reason well are enemies to religion,as you would represent it:on the contrary,I endeavour to shew that such men are defective in point of reason and judgement,and that they do the very thing they would seem to despise.

6.There are,I make no doubt,among the mathematicians many sincere believers in Jesus Christ:I know several such myself:but I addressed my'Analyst'to an infidel;and,on very good grounds,I supposed that,besides him,there were other deriders of faith who had nevertheless a profound veneration for fluxions:and I was willing to set forth the inconsistence of such men.If there be no such thing as infidels who pretend to knowledge in the modern analysis,I own myself misinformed,and shall gladly be found in a mistake;but even in that case,my remarks on fluxions are not the less true;nor will it follow that I have no right to examine them on the foot of human science,even though religion were quite unconcerned,and though I had no end to serve but truth.But you are very angry (p.

13and 14)that I should enter the lists with reasoning infidels,and attack them upon their pretensions to science:and hence you take occasions to shew your spleen against the clergy.I will not take upon me to say that I know you to be a Minute Philosopher yourself;but I know the Minute Philosophers make just such compliments as you do to our church,and are just as angry as you can be at any who undertake to defend religion by reason.If we resolve all into faith,they laugh at us and our faith:and if we attempt to reason,they are angry at us:they pretend we go out of our province,and they recommend to us a blind implicit faith.Such is the inconsistence of our adversaries.But it is to be hoped there will never be wanting men to deal with them at their own weapons;and to shew they are by no means those masters of reason which they would fain pass for.

7.I do not say,as you would represent me,that we have no better reason for our religion than you have for fluxions:but I say that an infidel,who believes the doctrine of fluxions,acts a very inconsistent part in pretending to reject the Christian religion because he cannot believe what he doth not comprehend;or because he cannot assent without evidence;or because he cannot submit his faith to authority.Whether there are such infidels,I submit to the judgement of the reader.For my own part I make no doubt of it,having seen some shrewd signs thereof myself,and having been very credibly informed thereof by others.Nor doth this charge seem the less credible,for your being so sensibly touched,and denying it with so much passion.You,indeed,do not stick to affirm,that the persons who informed me are"a pack of base,profligate,and impudent liars''(p.27).How far the reader will think fit to adopt your passions,I cannot say;but I can truly say,the late celebrated Mr.Addison is one of the persons whom you are pleased to characterise in these modest and mannerly terms.He assured me that the infidelity of a certain noted mathematician,still living,was one principal reason assigned by a witty man of those times for his being an infidel.Not that I imagine geometry disposeth men to infidelity:but that,from other causes,such as presumption,ignorance,or vanity,like other men geometricians also become infidels,and that the supposed light and evidence of their science gains credit to their infidelity.

8.You reproach me with calumny,detraction,and artifice (p.15).You recommend such means as are innocent and just,rather than the criminal method of lessening or detracting from my opponents (Ibid.).

You accuse me of the odium theologicum ,the intemperate zeal of divines,that I do stare super vias antiquas (p.13);with much more to the same effect.For all which charge I depend on the reader's candour,that he will not take your word,but read and judge for himself.

In which case he will be able to discern (though he should be no mathematician)how passionate and unjust your reproaches are,and how possible it is for a man to cry out against calumny and practise it in the same breath.Considering how impatient all mankind are when their prejudices are looked into,Ido not wonder to see you rail and rage at the rate you do.But if your own imagination be strongly shocked and moved,you cannot therefore conclude that a sincere endeavour to free a science,so useful and ornamental to human life,from those subtleties,obscurities,and paradoxes which render it inaccessible to most men,will be thought a criminal undertaking by such as are in their right mind.Much less can you hope that an illustrious Seminary of learned men,which hath produced so many free-spirited inquiries after truth,will at once enter into your passions,and degenerate into a nest of bigots.

9.I observe upon the inconsistency of certain infidel analysts.I remark some defects in the principles of the modern analysis.

I take the liberty decently to dissent from Sir Isaac Newton.I propose some helps to abridge the trouble of mathematical studies,and render them more useful.What is there in all this that should make you declaim on the usefulness of practical mathematics;that should move you to cry out,Spain,Inquisition,Odium Theologicum?By what figure of speech do you extend what is said of the modern analysis to mathematics in general;or what is said of mathematical infidels to all mathematicians;or the confuting an error in science to burning or hanging the authors?But it is nothing new or strange that men should choose to indulge their passions,rather than quit their opinions,how absurd soever.Hence the frightful visions and tragical uproars of bigoted men,be the subject of their bigotry what it will.A very remarkable instance of this you give (p.27),where,upon my having said that a deference to certain mathematical infidels,as I was credibly informed,had been one motive to infidelity,you ask,with no small emotion,"For God's sake are we in England or in Spain?''

"Is this the language of a familiar who is whispering an inquisitor,&c.?''

And the page before you exclaim in the following words -"Let us burn or hang up all the mathematicians in Great Britain,or halloo the mob upon them to tear them to pieces every mother's son of them,Tros Rutulusve fuat ,laymen or clergymen,&c.Let us dig up the bodies of Dr.

Barrow and Sir Isaac Newton,and burn them under the gallows.''

10.The reader need not be a mathematician to see how vain all this tragedy of yours is.And if he be as thoroughly satisfied as I am that the cause of fluxions cannot be defended by reason,he will be as little surprised as I am to see you betake yourself to the arts of all bigoted men,raising terror and calling in the passions to your assistance.

Whether those rhetorical flourishes about the inquisition and the gallows are not quite ridiculous,I leave to be determined by the reader.Who will also judge (though he should not be skilled in geometry)whether I have given the least grounds for this and a world of such-like declamation?

And whether I have not constantly treated those celebrated writers with all proper respect,though I take the liberty in certain points to differ from them?

11.As I heartily abhor an inquisition in faith,so I think you have no right to erect one in science.At the time of writing your Defence you seem to have been overcome with passion:but,now you may be supposed cool,I desire you to reflect whether it be not wrote in the true spirit of an inquisitor?Whether this becomes a person so exceeding delicate himself upon that point?And whether your brethren the analysts will think themselves honoured or obliged by you,for having defended their doctrine in the same manner as any declaiming bigot would defend transubstantiation?

The same false colours,the same intemperate sallies,and the same indignation against common sense!

12.In a matter of mere science,where authority hath nothing to do,you constantly endeavour to overbear me with authorities,and load me with envy.If I see a sophism in the writings of a great author,and,in compliment to his understanding,suspect he could hardly be quite satisfied with his own demonstration;this sets you on declaiming for several pages.It is pompously set forth,as a criminal method of detracting from great men,as a concerted project to lessen their reputation,as making them pass for imposters.If I publish my free thoughts,which I have as much right to publish as any other man,it is imputed to rashness,and vanity,and the love of opposition.Though perhaps my late publication,of what had been hinted twenty-five years ago,may acquit me of this charge in the eyes of an impartial reader.But when I consider the perplexities that beset a man who undertakes to defend the doctrine of fluxions,I can easily forgive your anger.

13.Two sorts of learned men there are:one who candidly seek truth by rational means.These are never averse to have their principles looked into,and examined by the test of reason.Another sort there is who learn by rote a set of principles and a way of thinking which happen to be in vogue.These betray themselves by their anger and surprise,whenever their principles are freely canvassed.But you must not expect that your reader will make himself a party to your passions or your prejudices.I freely own that Sir Isaac Newton hath shewed himself an extraordinary mathematician,a profound naturalist,a person of the greatest abilities and erudition.Thus far I can readily go;but I cannot go the lengths that you do.I shall never say of him as you do,Vestigia pronus adoro (p.70).This same adoration that you pay to him I will pay only to truth.

14.You may,indeed,yourself be an idolater of whom you please:but then you have no right to insult and exclaim at other men,because they do not adore your idol.Great as Sir Isaac Newton was,I think he hath,on more occasions than one,shewed himself not to be infallible.

Particularly,his demonstration of the doctrine of fluxions I take to be defective;and I cannot help thinking that he was not quite pleased with it himself.And yet this doth not hinder but that the method may be useful,considered as an art of invention.You,who are a mathematician,must acknowledge there have been divers such methods admitted in mathematics,which are not demonstrative.Such,for instance,are the inductions of Dr.Wallis,in his Arithmetic of Infinites,and such what Harriot,and after him,Descartes,have wrote concerning the roots of affected equations.It will not,nevertheless,thence follow that those methods are useless;but only that they are not to be allowed of as premises in a strict demonstration.

15.No great name upon earth shall ever make me accept things obscure for clear,or sophisms for demonstrations.Nor may you ever hope to deter me from freely speaking what I freely think,by those arguments ad invidia which at every turn you employ against me.You represent yourself (p.52)as a man"whose highest ambition is in the lowest degree to imitate Sir Isaac Newton.''It might,perhaps,have suited better with your appellation of Philalethes ,and been altogether as laudable,if your highest ambition had been to discover truth.

Very consistently with the character you give of yourself,you speak of it as a sort of crime (p.70)to think it possible you should ever"see farther,or go beyond Sir Isaac Newton.''And I am persuaded you speak the sentiments of many more besides yourself.But there are others who are not afraid to sift the principles of human science,who think it no honour to imitate the greatest man in his defects,who even think it no crime to desire to know,not only beyond Sir Isaac Newton,but beyond all mankind.And whoever thinks otherwise,I appeal to the reader whether he can properly be called a philosopher.