A

DEFENCE

OF

FREE-THINKING IN MATHEMATICS,

&c.

I. 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 foriner, 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.

"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. 12 and 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 imploys 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 is no more a crime, to canvass and detect unsound principles or false reasonings in mathematics, than in any other part of learning.

III. 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 farther 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 dis

credit 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.

IV. 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 any thing, either in mathematics, or in any 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.

V. 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 mathematicans, 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 that 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 judgment, and that they do the very thing they would seem to despise.

VI. There are, I make no doubt, among the mathema