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whereof may not really exist: whatsoever therefore is said to be somewhat which cannot exist, the idea thereof must be inconsistent. Mr. Locke acknowledgeth it doth require pains and skill to form his general idea of a triangle. He farther expressly saith, it must be neither oblique nor rectangular, neither equilateral, nor scalenum; but all and none of these at once. He also saith, it is an idea wherein some parts of several different and incufistent ideas are put together.* All this looks very like a contradiction. But, to put the matter past dispute, it must be noted, that he affirms it to be somewhat imperfect that cannot exist; consequently, the idea thereof is impossible or inconsistent.
XLVI. I desire to know, whether it is not impossible for any thing to exist which doth not include a contradiction: and, if it is, whether we may not infer, that what cannot possibly exist, the same doth include a contradiction: I further desire to know, whether the reader can frame a distinct idea of any thing that includes a contradiction? For my part, I cannot, nor consequently of the abovementioned triangle ; though you (who it seems know better than myself what I can do) are pleased to assure me of the contrary. Again, I ask, whether that, which it is above the power of man to form a complete idea of, may not be called incomprehensible? And whether the reader can frame a complete idea of this imperfect impossible triangle? And, if not, whether it doth not follow, that it is incomprehensible? It should seem, that a distinct aggregate of a few consistent parts was nothing so difficult to conceive or impossible to exist; and that, therefore, your comment must be wide of the author's meaning. You give me to understand (p. 82) that this account of a general triangle was a trap which Mr. Locke set to catch fools. Who is caught therein let the reader judge.
* Essay on Human Understanding, b. iv. c. vii. §. ix.
XLVII. It is Mr. Locke's opinion, that every general name stands for a general abstract idea, which prescinds from the species or individuals comprehended under it. Thus, for example, according to him, the general name colour stands for an idea, which is neither blue, red, green, nor any other particular colour, but somewhat distinct and abstracted from them all. To me it seems the word colour is only a more general name applicable to all and each of the particular colours: while the other specific names, as blue, red, green, and the like, are each restrained to a more limited signification. The same may be said of the word triangle. Let the reader judge whether this be not the case; and whether he can distinctly frame such an idea of colour as shall prescind from all the species thereof, or of a triangle which shall answer Mr. Locke's account, prescinding and abstracting from all the particular sorts of triangles, in the manner aforesaid.
XLVIII. I entreat my reader to think. For, if he doth not, he may be under some influence from your confident and positive way of talking. But any one who thinks may, if I mistake not, plainly perceive that you are deluded, as it often happens, by mistaking the terms for ideas. Nothing is easier, than to define in terms or words that which is incomprehensible in idea, forasmuch as any words can be either separated or joined as you please, but ideas always cannot. It is as easy to say a round square as an oblong square, though the former be inconceivable. If the reader will but take a little care to distinguish between the definition and the idea, between words or expressions and the conceptions of the mind, he will judge of the truth of what I now advance, and clearly perceive how far you are mistaken in attempting to illustrate Mr. Locke's doctrine, and where your mistake lies. Or, if the reader is minded to make a short work, he needs only at once to try whether laying aside the words he can frame in his mind the
idea of an impossible triangle; upon which trial the issue of this dispute may be fairly put. This doctrine of abstract general ideas seemed to me a capital error, productive of numberless difficulties and disputes, that runs not only throughout Mr. Locke's book, but through most parts of learning. Consequently, my animadversions thereupon were not an effect of being inclined to carp or cavil at a single passage, as you would wrongfully insinuate, but proceeded from a love of truth, and a desire to banish, so far as in me lay, false principles and wrong ways of thinking, without respect of persons. And, indeed, though you and other party-men are violently attached to your respective masters, yet I, who profess myself only attached to truth, see no reason why I may not as freely animadvert on Mr. Locke or Sir Isaac Newton, as they would on Aristotle or Descartes. Certainly the more extensive the influence of any error, and the greater the authority which supports it, the more it deserves to be considered and detected by sincere inquirers after knowledge.
XLIX. In the close of your performance you let me understand, that your zeal for truth and the reputation of your masters have occasioned your reprehending me with the utmost freedom. And it must be owned you have shewn a singular talent therein. But I am comforted under the severity of your reprehensions, when I consider the weakness of your arguments, which, were they as strong as your reproofs, could leave no doubt in the mind of the reader concerning the matters in dispute between us. As it is, I leave him to reflect and examine by your light, how clearly he is enabled to conceive a fluxion, or the fluxion of a fluxion, a part infinitely small subdivided into an infinity of parts, a nascent or evanescent increment, that which is neither something nor nothing, a triangle formed in a point, velocity without motion, and the rest of those arcana of the modern analysis. To conclude, I had some thoughts of advising
you how to conduct yourself for the future, in return for the advice you have so freely imparted to me: but, as you think it becomes me rather to inform myself than instruct others, I shall, for my farther information, take leave to propose a few queries to those learned gentlemen of Cambridge, whom you associate with yourself, and represent as being equally surprised at the tendency of my Analyst.
L. I desire to know, whether those who can neither demonstrate nor conceive the principles of the modern analysis, and yet give in to it, may not be justly said to have faith, and be styled believers of mysteries? Whether it is impossible to find among the physicians, mechanical philosophers, mathematicians, and philomathematicians, of the present age, some such believers who yet deride Christians for their belief of mysteries. Whether with such men it is not a fair, reasonable, and legitimate method to use the argumentum ad hominem? And, being so, whether it ought to surprise either Christians or scholars? Whether in an age wherein so many pretenders to science attack the Christian religion, we may not be allowed to make reprisals, in order to shew, that the irreligion of those men is not to be presumed an effect of deep and just thinking? Whether an attempt to detect false reasonings, and remedy defects in mathematics, ought to be ill received by mathematicians? Whether the introducing more easy methods and more intelligible principles in any science should be discountenanced? Whether there may not be fair objections as well as cavils? And whether to inquire diligently into the mean. ing of terms and the proof of propositions, not excepting against any thing without assigning a reason, nor affecting to mistake the signification of words, or stick at an expression where the sense was clear, but considering the subject in all lights, sincerely endeavouring to find out any sense or meaning whatsoever, candidly setting forth what seems obscure and what fallacious, and calling
upon those, who profess the knowledge of such matters, to explain them, whether I say such a proceeding can be justly called cavilling? Whether there be an ipse dixit erected? And, if so, when, where, by whom, and upon what authority? Whether even where authority was to take place, one might not hope the mathematics, at least, would be excepted? Whether the chief end, in making mathematics so considerable a part of academical education, be not to form in the minds of young students habits of just and exact reasoning? And whether the study of abstruse and subtile matters can conduce to this end, unless they are well understood, examined, and sifted to the bottom? Whether, therefore, the bringing geometrical demonstrations to the severest test of reason should be reckoned a discouragement to the studies of any learned society? Whether, to separate the clear parts of things from the obscure, to distinguish the real principles, whereon truths rest and whence they are derived, and to proportion the just measures of assent according to the various degrees of evidence, be a useless or unworthy undertaking? Whether the making more of an argument than it will bear, and placing it in an undue rank of evidence, be not the likely way to disparage it? Whether it may not be of some use, to provoke and stir up the learned professors to explain a part of mathematical learning, which is acknowledged to be most profound, difficult, and obscure, and at the same time set forth by Philalethes and many others, as the greatest instance that has ever been given of the extent of human abilities? Whether, for the sake of a great man's discoveries, we must adopt his errors? Lastly, whether in an age wherein all other principles are canvassed with the utmost freedom, the principles of fluxions are to be alone excepted?