Reasons for not replying to Mr. Walton's Full Answer
By George Berkeley
1. There are some men that can neither give nor take an answer, but, writing merely for the sake of writing, multiply words to no purpose. There are also certain careless writers that, in defiance of common sense, publish such things as, though they are not ashamed to utter, yet, other men may well be ashamed to answer. Whether there be anything in Mr. Walton's method of vindicating Fluxions, that might justify my taking no further notice of him, on the above-mentioned considerations, I leave you and every other reader to judge. But those, Sir, are not the reasons I shall assign for not replying to Mr. Walton's full answer. The true reason is, that he seems at bottom a facetious man, who, under the colour of an opponent, writes on my side of the question, and really believes no more than I do of Sir Isaac Newton's doctrine about fluxions, which he exposes, contradicts, and confutes, with great skill and humour, under the mask of a grave vindication.
2. At first I considered him in another light, as one who had good reason for keeping to the beaten track, who had been used to dictate, who had terms of art at will, but was indeed at small trouble about putting them together, and perfectly easy about his readers understanding them. It must be owned, in an age of so much ludicrous humour, it is not every one can at first sight discern a writer's real design. But, be a man's assertions ever so strong in favour of a doctrine, yet if his reasonings are directly levelled against it, whatever question there may be about the matter in dispute, there can be none about the intention of the writer. Should a person, so knowing and discreet as Mr. Walton, thwart and contradict Sir Isaac Newton, under pretence of defending his fluxions, and should he at every turn say such uncouth things of these same fluxions, and place them in such odd lights as must set all men in their wits against them, could I hope for a better second in this cause? Or could there remain any doubt of his being a disguised Free-thinker in mathematics, who defended fluxions just as a certain Free-thinker in religion did the rights of the Christian church?
3. Mr Walton indeed after his free manner calls my `Analyst' a libel. [`Vindication,p. 1.] But this ingenious gentleman well knows a bad vindication is the bitterest libel. Had you a mind, Sir, to betray and ridicule any cause under the notion of vindicating it, would you not think it the right way to be very strong and dogmatical in the affirmative, and very weak and puzzled in the argumentative parts of your performance? To utter contradictions and paradoxes without remorse, and to be at no pains about reconciling or explaining them? And with great good-humour, to be at perpetual variance with yourself and the author you pretend to vindicate? How successfully Mr. Walton hath practiced these arts, and how much to the honour of the great client he would seem to take under his protection, I shall particularly examine throughout every article of his full answer.
4. First, then, saith Mr. Walton, ``I am to be asked, whether I can conceive velocity without motion, or motion without extension, or extension without magnitude?To which he answereth in positive terms, that he can conceive velocity and motion in a point (p. 7). And to make out this he undertakes to demonstrate, ``that if a thing be moved by an agent operating continually by the same force, the velocity will not be the same in any two different points of the described space; but that it must vary upon the least change of space.Now, admitting thus much to be demonstrated, yet I am still at a loss to conceive how Mr. Walton's conclusion will follow, to wit, ``that I am greatly mistaken in imagining there can be no motion, no velocity, in a point of space'' (p. 10). Pray, Sir, consider his reasoning. The same velocity cannot be in two points of space; therefore velocity can be in a point of space. Would it not be just as good reasoning to say, the same man cannot be in two nutshells; therefore a man can be in a nutshell? Again, velocity must vary upon the least change of space; therefore there may be velocity without space. Make sense of this if you can. What have these consequences to to with their premises? Who but Mr. Walton could have inferred them? Or how could even he have inferred them had it not been in jest?
5. Suppose the centre of a falling body to describe a line; divide the time of its fall into equal parts, for instance, into minutes. The spaces described in those equal parts of time will be unequal. That is, from whatsoever points of the described line you measure a minute's descent, you will still find it a different space. This is true. But how or why from this plain truth a man should infer, that motion can be conceived in a point, is to me as obscure as any the most obscure mysteries that occur in this profound author. Let the reader make the best of it. For my part, I can as easily conceive Mr. Walton should walk without stirring, as I can his idea of motion without space. After all, the question was not whether motion could be proved to exist in a point, but only whether it could be conceived in a point. For, as to the proof of things impossible, some men have a way of proving that may equally prove anything. But I much question whether any reader of common sense will undertake to conceive what this pleasant man at inference undertakes to prove.
6. If Mr. Walton really meant to defend the author of the fluxionary method, would he not have done it in a way consistent with this illustrious author's own principles? Let us now see what may be Sir Isaac's notion about this matter. He distinguisheth two sorts of motion, absolute and relative. The former he defineth to be a translation from absolute place to absolute place, the latter from one relative place to another. [See Schol. def. VIII., `Philos. Nat. Princip. Math.Mr. Walton's is plainly neither of these sorts of motion. But some third kind, which what it is, I am at a loss to comprehend. But I can clearly comprehend that, if we admit motion without space, then Sir Isaac Newton's account of it must be wrong: for place by which he defines motion is, according to him, a part of space. And if so, then this notable defender hath cut out new work for himself to defend and explain. But about this, if I mistake not, he will be very easy. For, as I said before, he seems at bottom a back friend to that great man; which opinion you will see father confirmed in the sequel.
7. I shall no more ask Mr. Walton to explain anything: for I can honestly say, the more he explains, the more I am puzzled. But I will ask his readers to explain, by what art a man may conceive motion without space. And, supposing this to be done, in the second place to explain, how it consists with Sir Isaac Newton's account of motion. Is it not evident that Mr. Walton hath deserted from his old master, and been at some pains to expose him, while he defends one part of his principles by overturning another? Let any reader tell me, what Mr. Walton means by motion, or, if he can guess, what this third kind is, which is neither absolute nor relative, which exists in a point, which may be conceived without space. This learned professor saith, ``I have no clear conception of the principles of motion.p. 24). And in another place (p. 7) he saith, ``I might have conceived velocity in a point, if I had understood and considered the nature of motion.I believe I am not alone in not understanding his principles. For myself, I freely confess the case to be desparate. I neither understand them, nor have any hopes of ever being able to understand them.
8. Being now satisfied that Mr. Walton's aim is not to clear up or defend Sir Isaac's principles, but rather to contradict and expose them, you will not, I suppose, think it strange, if, instead of putting questions to this intrepid answerer, who is never at a loss, how often soever his readers may, I entreat you, or any other man of plain sense, to read the following passage, cited from the thirty first section of the `Analyst,'' and then try to apply Mr. Walton's answer to it: whereby you will clearly perceive what ...
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