The Works of George Berkeley. Vol. 1 of 4 · George Berkeley
ERRATA
Mem. The surds, doubling the cube, &c. We think that if just made to see we should judge of the distance & magnitude of things as we do now; but this is false. So also wt we think so positively of the situation of objects. Hays’s, Keill’s(243), &c. method of proving the infinitesimals of the 3d order absurd, & perfectly contradictions. Angles of contact, & verily all angles comprehended by a right line & a curve, cannot be measur’d, the arches intercepted not being similar. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ The danger of expounding the H. Trinity by extension. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M412) Qu. Why should the magnitude seen at a near distance be deem’d the true one rather than that seen at a farther distance? Why should the sun be thought many 1000 miles rather than one foot in diameter—both being equally apparent diameters? Certainly men judg’d of the sun not in himself, but wth relation to themselves. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M413) 4 Principles whereby to answer objections, viz. 1. Bodies do really exist, tho’ not perceiv’d by us. 2. There is a law or course of nature. 3. Language & knowledge are all about ideas; words stand for nothing else. 4. Nothing can be a proof against one side of a contradiction that bears equally hard upon the other(244). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ What shall I say? Dare I pronounce the admired ἀκρίβεια mathematica, that darling of the age, a trifle?
Most certainly no finite extension divisible _ad infinitum_. (M414) Difficulties about concentric circles. (M415) Mem. To examine & accurately discuss the scholium of the 8th definition of Mr. Newton’s(245) Principia. Ridiculous in the mathematicians to despise Sense. Qu. Is it not impossible there should be abstract general ideas? All ideas come from without. They are all particular. The mind, ’tis true, can consider one thing wthout another; but then, considered asunder, they make not 2 ideas. Both together can make but one, as for instance colour & visible extension(246). The end of a mathematical line is nothing. Locke’s argument that the end of his pen is black or white concludes nothing here. Mem. Take care how you pretend to define extension, for fear of the geometers. Qu. Why difficult to imagine a minimum? Ans. Because we are not used to take notice of ’em singly; they not being able singly to pleasure or hurt us, thereby to deserve our regard. Mem. To prove against Keill yt the infinite divisibility of matter makes the half have an equal number of equal parts with the whole. Mem. To examine how far the not comprehending infinites may be admitted as a plea. Qu. Why may not the mathematicians reject all the extensions below the M. as well as the dd, &c., wch are allowed to be something, & consequently may be magnify’d by glasses into inches, feet, &c., as well as the quantities next below the M.?
Big, little, and number are the works of the mind. How therefore can ye extension you suppose in Matter be big or little? How can it consist of any number of points? (M416) Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8. Schoolmen compar’d with the mathematicians. Extension is blended wth tangible or visible ideas, & by the mind præscinded therefrom. Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in ye parabola is double the abscisse. Wt need of the utmost accuracy wn the mathematicians own _in rerum natura_ they cannot find anything corresponding wth their nice ideas. One should endeavour to find a progression by trying wth the scale. Newton’s fluxions needless. Anything below an M might serve for Leibnitz’s Differential Calculus. How can they hang together so well, since there are in them (I mean the mathematiques) so many _contradictoriæ argutiæ_. V. Barrow, Lect. A man may read a book of Conics with ease, knowing how to try if they are right. He may take ’em on the credit of the author. Where’s the need of certainty in such trifles? The thing that makes it so much esteem’d in them is that we are thought not capable of getting it elsewhere. But we may in ethiques and metaphysiques. The not leading men into mistakes no argument for the truth of the infinitesimals. They being nothings may perhaps do neither good nor harm, except wn they are taken for something, & then the contradiction begets a contradiction.
The M. S. is not near so inconceivable as the _signum in magnitudine individuum_. Mem. To examine the math, about their _point_—what it is—something or nothing; and how it differs from the M. S. All might be demonstrated by a new method of indivisibles, easier perhaps and juster than that of Cavalierius(249). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M418) Unperceivable perception a contradiction. (M419) Proprietates reales rerum omnium in Deo, tam corporum quum spirituum continentur. Clerici, Log. cap. 8. Let my adversaries answer any one of mine, I’ll yield. If I don’t answer every one of theirs, I’ll yield. The loss of the excuse(250) may hurt Transubstantiation, but not the Trinity. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ We need not strain our imaginations to conceive such little things. Bigger may do as well for infinitesimals, since the integer must be an infinite. Evident yt wch has an infinite number of parts must be infinite. Qu. Whether extension be resoluble into points it does not consist of? Nor can it be objected that we reason about numbers, wch are only words & not ideas(251); for these infinitesimals are words of no use, if not supposed to stand for ideas. Axiom. No reasoning about things whereof we have no idea. Therefore no reasoning about infinitesimals. Much less infinitesimals of infinitesimals, &c. Axiom. No word to be used without an idea. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M420) Our eyes and senses inform us not of the existence of matter or ideas existing without the mind(252). They are not to be blam’d for the mistake.
I defy any man to assign a right line equal to a paraboloid, but wn look’d at thro’ a microscope they may appear unequall. (M421) Newton’s harangue amounts to no more than that gravity is proportional to gravity. One can’t imagine an extended thing without colour. V. Barrow, L. G. (M422) Men allow colours, sounds, &c.(253) not to exist without the mind, tho’ they have no demonstration they do not. Why may they not allow my Principle with a demonstration? (M423) Qu. Whether I had not better allow colours to exist without the mind; taking the mind for the active thing wch I call “I,” “myself”—yt seems to be distinct from the understanding(254)? (M424) The taking extension to be distinct from all other tangible & visible qualities, & to make an idea by itself, has made men take it to be without the mind. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ I see no wit in any of them but Newton. The rest are meer triflers, mere Nihilarians. The folly of the mathematicians in not judging of sensations by their senses. Reason was given us for nobler uses. (M425) Keill’s filling the world with a mite(255). This follows from the divisibility of extension _ad infinitum_. Extension, or length without breadth, seems to be nothing save the number of points that lie betwixt any 2 points(256). It seems to consist in meer proportion—meer reference of the mind.
To what purpose is it to determine the forms of glasses geometrically? Sir Isaac(257) owns his book could have been demonstrated on the supposition of indivisibles. (M426) Innumerable vessels of matter. V. Cheyne. I’ll not admire the mathematicians. ’Tis wt any one of common sense might attain to by repeated acts. I prove it by experience. I am but one of human sense, and I &c. Mathematicians have some of them good parts—the more is the pity. Had they not been mathematicians they had been good for nothing. They were such fools they knew not how to employ their parts. The mathematicians could not so much as tell wherein truth & certainty consisted, till Locke told ’em(258). I see the best of ’em talk of light and colours as if wthout the mind. By _thing_ I either mean ideas or that wch has ideas(259). Nullum præclarum ingenium unquam fuit magnus mathematicus. Scaliger(260). A great genius cannot stoop to such trifles & minutenesses as they consider. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 1. (261)All significant words stand for ideas(262). 2. All knowledge about our ideas. 3. All ideas come from without or from within. 4. If from without it must be by the senses, & they are call’d sensations(263). 5. If from within they are the operations of the mind, & are called thoughts. 6. No sensation can be in a senseless thing.
N. B. Other arguments innumerable, both _a priori_ & _a posteriori_, drawn from all the sciences, from the clearest, plainest, most obvious truths, whereby to demonstrate the Principle, i.e. that neither our ideas, nor anything like our ideas, can possibly be in an unperceiving thing(266). N. B. Not one argument of any kind wtsoever, certain or probable, _a priori_ or _a posteriori_, from any art or science, from either sense or reason, against it. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Mathematicians have no right idea of angles. Hence angles of contact wrongly apply’d to prove extension divisible _ad infinitum_. We have got the Algebra of pure intelligences. We can prove Newton’s propositions more accurately, more easily, & upon truer principles than himself(267). Barrow owns the downfall of geometry. However I’ll endeavour to rescue it—so far as it is useful, or real, or imaginable, or intelligible. But for _the nothings_, I’ll leave them to their admirers. I’ll teach any one the whole course of mathematiques in 1/100 part the time that another will. Much banter got from the prefaces of the mathematicians. (M427) Newton says colour is in the subtil matter. Hence Malbranch proves nothing, or is mistaken, in asserting there is onely figure & motion. I can square the circle, &c.; they cannot. Wch goes on the best principles? ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ The Billys(268) use a finite visible line for an 1/m.
(M428) Marsilius Ficinus—his appearing the moment he died solv’d by my idea of time(269). (M429) The philosophers lose their abstract or unperceived Matter. The mathematicians lose their insensible sensations. The profane [lose] their extended Deity. Pray wt do the rest of mankind lose? As for bodies, &c., we have them still(270). N. B. The future nat. philosoph. & mathem. get vastly by the bargain(271). (M430) There are men who say there are insensible extensions. There are others who say the wall is not white, the fire is not hot, &c. We Irishmen cannot attain to these truths. The mathematicians think there are insensible lines. About these they harangue: these cut in a point at all angles: these are divisible _ad infinitum_. We Irishmen can conceive no such lines. The mathematicians talk of wt they call a point. This, they say, is not altogether nothing, nor is it downright something. Now we Irishmen are apt to think something(272) & nothing are next neighbours. Engagements to P.(273) on account of ye Treatise that grew up under his eye; on account also of his approving my harangue. Glorious for P. to be the protector of usefull tho’ newly discover’d truths. How could I venture thoughts into the world before I knew they would be of use to the world? and how could I know that till I had try’d how they suited other men’s ideas?
I publish not this so much for anything else as to know whether other men have the same ideas as we Irishmen. This is my end, & not to be inform’d as to my own particular. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ My speculations have the same effect as visiting foreign countries: in the end I return where I was before, but my heart at ease, and enjoying life with new satisfaction. Passing through all the sciences, though false for the most part, yet it gives us the better insight and greater knowledge of the truth. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ He that would bring another over to his opinion, must seem to harmonize with him at first, and humour him in his own way of talking(274). From my childhood I had an unaccountable turn of thought that way. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ It doth not argue a dwarf to have greater strength than a giant, because he can throw off the molehill which is upon him, while the other struggles beneath a mountain. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ The whole directed to practise and morality—as appears 1st, from making manifest the nearness and omnipresence of God; 2dly, from cutting off the useless labour of sciences, and so forth.
Ideas discussed in this chapter
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