A Defence of FreeThinking in Mathematics.docx

1、A Defence of FreeThinking in MathematicsA Defence of Free-Thinking in Mathematics A Defence of Free-Thinking in Mathematics In answer to a Pamphlet of Philalethes Cantabrigiensis , intituled, Geometry no Friend to Infidelity, or a Defence of Sir ISAAC NEWTON, and the BRITISH Mathematicians . Also an

2、 Appendix concerning Mr. WALTONS Vindication of the Principle of Fluxions against the Objections contained in the ANALYST.WHEREINIt 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 Ma

3、thematicians,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

4、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

5、 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 thi

6、s 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

7、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

8、, 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

9、on the usefulness of mathematics in the several branches, and then to redouble your surprise and amazement (p. 19 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 mathe

10、matics: but that which is not so, the less it employs mens 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 principle

11、s 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

12、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 fait

13、h 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 fai

14、th, 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 Analystbe not sufficient. Suppose that I had not leis

15、ure, 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?

16、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 ma

17、ny 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: b

18、ut 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 relig

19、ion 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 w

20、ould 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

21、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

22、 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.13 and 14) that I should enter the lists with reasoning infidels, and attack th

23、em 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

24、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

25、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

26、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 a

27、uthority. 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 t

28、ouched, 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

29、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 dispo

30、seth 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.

31、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 a

32、ll which charge I depend on the readers 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 a

33、nd 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 orname