第4章

16.Because I am not guilty of your mean idolatry,you inveigh against me as a person conceited of my own abilities;not considering that a person of less abilities may know more on a certain point than one of greater;not considering that a purblind eye,in a close and narrow view,may discern more of a thing than a much better eye in a more extensive prospect;not considering that this is to fix a ne plus ultra ,to put a stop to all future inquiries;lastly,not considering that this is in fact,so much as in you lies,converting the republic of letters into an absolute monarchy,that it is even introducing a kind of philosophic popery among a free people.

17.I have said (and I venture still to say)that a fluxion is incomprehensible:that second,third,and fourth fluxions are yet more incomprehensible:that it is not possible to conceive a simple infinitesimal:that it is yet less possible to conceive an infinitesimal of an infinitesimal,and so onward.[`Analyst,'sect.4,5,6,&c.]

What have you to say in answer to this?Do you attempt to clear up the notion of a fluxion or a difference?Nothing like it.You only"assure me (upon your bare word)from your own experience,and that of several others whom you could name,that the doctrine of fluxions may be clearly conceived and distinctly comprehended;and that if I am puzzled about it and do not understand it,yet others do.''But can you think,Sir,I shall take your word,when I refuse to take your master's?

18.Upon this point every reader of common sense may judge as well as the most profound mathematician.The simple apprehension of a thing defined is not made more perfect by any subsequent progress in mathematics.What any man evidently knows,he knows as well as you or Sir Isaac Newton.And every one can know whether the object of this method be (as you would have us think)clearly conceivable.To judge of this no depth of science is requisite,but only a bare attention to what passes in his own mind.And the same is to be understood of all definitions in all sciences whatsoever.In none of which can it be supposed that a man of sense and spirit will take any definition or principle on trust,without sifting it to the bottom,and trying how far he can or he cannot conceive it.This is the course I have taken,and shall take,however you and your brethren may declaim against it,and place it in the most invidious light.

19.It is usual with you to admonish me to look over a second time,to consult,examine,weigh the words of Sir Isaac.

In answer to which I will venture to say that I have taken as much pains as (I sincerely believe)any man living to understand that great author,and to make sense of his principles.No industry,nor caution,nor attention,I assure you,have been wanting on my part.So that,if I do not understand him,it is not my fault but my misfortune.Upon other subjects you are pleased to compliment me with depth of thought and uncommon abilities (p.

5and 84).But I freely own,I have no pretence to those things.The only advantage I pretend to is that I have always thought and judged for myself.

And,as I never had a master in mathematics,so I fairly followed the dictates of my own mind in examining and censuring the authors I read upon that subject,with the same freedom that I used upon any other;taking nothing on trust,and believing that no writer was infallible.And a man of moderate parts,who takes this painful course in studying the principles of any science,may be supposed to walk more surely than those of greater abilities,who set out with more speed and less care.

20.What I insist on is,that the idea of a fluxion,simply considered,is not at all improved or amended by any progress,though ever so great,in the analysis:neither are the demonstrations of the general rules of that method at all cleared up by applying them.The reason of which is,because,in operating or calculating,men do not return to contemplate the original principles of the method,which they constantly presuppose,but are employed in working,by notes and symbols denoting the fluxions supposed to have been at first explained,and according to rules supposed to have been at first demonstrated.This I say to encourage those who are not too far gone in these studies,to use intrepidly their own judgement,without a blind or a mean deference to the best of mathematicians,who are no more qualified than they are to judge of the simple apprehension,or the evidence of what is delivered in the first elements of the method;men by further and frequent use or exercise becoming only more accustomed to the symbols and rules,which doth not make either the foregoing notions more clear,or the foregoing proofs more perfect.Every reader of common sense,that will but use his faculties,knows as well as the most profound analyst what idea he frames or can frame of velocity without motion,or of motion without extension,of magnitude which is neither finite or infinite,or of a quantity having no magnitude which is yet divisible,of a figure where there is no space,of proportion between nothings,or of a real product from nothing multiplied by something.He need not be far gone in geometry to know that obscure principles are not to be admitted in demonstration;that if a man destroys his own hypothesis,he at the same time destroys what was built upon it:that error in the premises,not rectified,must produce error in the conclusion.