Part 13

(M403) The great danger of making extension exist without the mind is, that if it does it must be acknowledg’d infinite, immutable, eternal, &c.;—wch will be to make either God extended (wch I think dangerous), or an eternal, immutable, infinite, increate Being beside God.

(M404) Finiteness of our minds no excuse for the geometers.

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(M405) The Principle easily proved by plenty of arguments _ad absurdum_.

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The twofold signification of Bodies, viz.

1. Combinations of thoughts(239);

2. Combinations of powers to raise thoughts.

These, I say, in conjunction with homogeneous particles, may solve much better the objections from the creation than the supposition that Matter does exist. Upon wch supposition I think they cannot be solv’d.

Bodies taken for powers do exist wn not perceiv’d; but this existence is not actual(240). Wn I say a power exists, no more is meant than that if in the light I open my eyes, and look that way, I shall see it, i.e. the body, &c.

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Qu. whether blind before sight may not have an idea of light and colours & visible extension, after the same manner as we perceive them wth eyes shut, or in the dark—not imagining, but seeing after a sort?

Visible extension cannot be conceiv’d added to tangible extension. Visible and tangible points can’t make one sum. Therefore these extensions are heterogeneous.

A probable method propos’d whereby one may judge whether in near vision there is a greater distance between the crystalline & fund than usual, or whether the crystalline be onely render’d more convex. If the former, then the v. s. is enlarg’d, & the m. v. corresponds to less than 30 minutes, or wtever it us’d to correspond to.

Stated measures, inches, feet, &c., are tangible not visible extensions.

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(M406) Locke, More, Raphson, &c. seem to make God extended. ’Tis nevertheless of great use to religion to take extension out of our idea of God, & put a power in its place. It seems dangerous to suppose extension, wch is manifestly inert, in God.

(M407) But, say you, The thought or perception I call extension is not itself in an unthinking thing or Matter—but it is like something wch is in Matter. Well, say I, Do you apprehend or conceive wt you say extension is like unto, or do you not? If the later, how know you they are alike? How can you compare any things besides your own ideas? If the former, it must be an idea, i.e. perception, thought, or sensation—wch to be in an unperceiving thing is a contradiction(241).

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(M408) I abstain from all flourish & powers of words & figures, using a great plainness & simplicity of simile, having oft found it difficult to understand those that use the lofty & Platonic, or subtil & scholastique strain(242).

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(M409) Whatsoever has any of our ideas in it must perceive; it being that very having, that passive recognition of ideas, that denominates the mind perceiving—that being the very essence of perception, or that wherein perception consists.

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The faintness wch alters the appearance of the horizontal moon, rather proceeds from the quantity or grossness of the intermediate atmosphere, than from any change of distance, wch is perhaps not considerable enough to be a total cause, but may be a partial of the phenomenon. N. B. The visual angle is less in cause the horizon.

We judge of the distance of bodies, as by other things, so also by the situation of their pictures in the eye, or (wch is the same thing) according as they appear higher or lower. Those wch seem higher are farther off.

Qu. why we see objects greater in ye dark? whether this can be solv’d by any but my Principles?

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(M410) The reverse of ye Principle introduced scepticism.

(M411) N. B. On my Principles there is a reality: there are things: there is a _rerum natura_.

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.

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The danger of expounding the H. Trinity by extension.

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(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.

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(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).

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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.

a + 500 nothings = a + 50 nothings—an innocent silly truth.

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(M417) My doctrine excellently corresponds wth the creation. I suppose no matter, no stars, sun, &c. to have existed before(247).

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It seems all circles are not similar figures, there not being the same proportion betwixt all circumferences & their diameters.

When a small line upon paper represents a mile, the mathematicians do not calculate the 1/10000 of the paper line, they calculate the 1/10000 of the mile. ’Tis to this they have regard, ’tis of this they think; if they think or have any idea at all. The inch perhaps might represent to their imaginations the mile, but ye 1/10000 of the inch cannot be made to represent anything, it not being imaginable.

But the 1/10000 of a mile being somewhat, they think the 1/10000 inch is somewhat: wn they think of yt they imagine they think on this.

3 faults occur in the arguments of the mathematicians for divisibility _ad infinitum_—

1. They suppose extension to exist without the mind, or not perceived.

2. They suppose that we have an idea of length without breadth(248), or that length without breadth does exist.

3. That unity is divisible _ad infinitum_.

To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas.

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).

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(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.

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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.

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(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.

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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.

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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.

7. No thought can be in a thoughtless thing.

8. All our ideas are either sensations or thoughts(264), by 3, 4, 5.

9. None of our ideas can be in a thing wch is both thoughtless & senseless(265), by 6, 7, 8.

10. The bare passive recognition or having of ideas is called perception.

11. Whatever has in it an idea, tho’ it be never so passive, tho’ it exert no manner of act about it, yet it must perceive. 10.

12. All ideas either are simple ideas, or made up of simple ideas.

13. That thing wch is like unto another thing must agree wth it in one or more simple ideas.

14. Whatever is like a simple idea must either be another simple idea of the same sort, or contain a simple idea of the same sort. 13.

15. Nothing like an idea can be in an unperceiving thing. 11, 14. Another demonstration of the same thing.

16. Two things cannot be said to be alike or unlike till they have been compar’d.

17. Comparing is the viewing two ideas together, & marking wt they agree in and wt they disagree in.

18. The mind can compare nothing but its own ideas. 17.

19. Nothing like an idea can be in an unperceiving thing. 11, 16, 18.

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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.

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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?

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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.

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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.

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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.

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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.

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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.

AN ESSAY TOWARDS A NEW THEORY OF VISION

_First published in 1709_

Editor’s Preface To The Essay Towards A New Theory Of Vision

Berkeley’s _Essay towards a New Theory of Vision_ was meant to prepare the way for the exposition and defence of the new theory of the material world, its natural order, and its relation to Spirit, that is contained in his book of _Principles_ and in the relative _Dialogues_, which speedily followed. The _Essay_ was the firstfruits of his early philosophical studies at Dublin. It was also the first attempt to show that our apparently immediate Vision of Space and of bodies extended in three-dimensioned space, is either tacit or conscious inference, occasioned by constant association of the phenomena of which alone we are visually percipient with assumed realities of our tactual and locomotive experience.

The first edition of the _Essay_ appeared early in 1709, when its author was about twenty-four years of age. A second edition, with a few verbal changes and an Appendix, followed before the end of that year. Both were issued in Dublin, “printed by Aaron Rhames, at the back of Dick’s Coffeehouse, for Jeremy Pepyat, bookseller in Skinner Row.” In March, 1732, a third edition, without the Appendix, was annexed to _Alciphron,_ on account of its relation to the Fourth Dialogue in that book. This was the author’s last revision.

In the present edition the text of this last edition is adopted, after collation with those preceding. The Appendix has been restored, and also the Dedication to Sir John Percival, which appeared only in the first edition.

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A due appreciation of Berkeley’s theory of seeing, and his conception of the visible world, involves a study, not merely of this tentative juvenile _Essay_, but also of its fuller development and application in his more matured works. This has been commonly forgotten by his critics.

Various circumstances contribute to perplex and even repel the reader of the _Essay_, making it less fit to be an easy avenue of approach to Berkeley’s _Principles_.

Its occasion and design, and its connexion with his spiritual conception of the material world, are suggested in Sections 43 and 44 of the _Principles_. Those sections are a key to the _Essay_. They inform us that in the _Essay_ the author intentionally uses language which seems to attribute a reality independent of all percipient spirit to the ideas or phenomena presented in Touch; it being beside his purpose, he says, to “examine and refute” that “vulgar error” in “a work on Vision.” This studied reticence of a verbally paradoxical conception of Matter, in reasonings about vision which are fully intelligible only under that conception, is one cause of a want of philosophical lucidity in the _Essay_.

Another circumstance adds to the embarrassment of those who approach the _Principles_ and the three _Dialogues_ through the _Essay on Vision_. The _Essay_ offers no exception to the lax employment of equivocal words familiar in the early literature of English philosophy, but which is particularly inconvenient in the subtle discussions to which we are here introduced. At the present day we are perhaps accustomed to more precision and uniformity in the philosophical use of language; at any rate we connect other meanings than those here intended with some of the leading words. It is enough to refer to such terms as _idea_, _notion_, _sensation_, _perception_, _touch_, _externality_, _distance_, and their conjugates. It is difficult for the modern reader to revive and remember the meanings which Berkeley intends by _idea_ and _notion_—so significant in his vocabulary; and _touch_ with him connotes muscular and locomotive experience as well as the pure sense of contact. Interchange of the terms _outward_, _outness_, _externality_, _without the mind_, and _without the eye_ is confusing, if we forget that Berkeley implies that percipient mind is virtually coextensive with our bodily organism, so that being “without” or “at a distance from” our bodies is being at a distance from the percipient mind. I have tried in the annotations to relieve some of these ambiguities, of which Berkeley himself warns us (cf. sect. 120).

The _Essay_ moreover abounds in repetitions, and interpolations of antiquated optics and physiology, so that its logical structure and even its supreme generalisation are not easily apprehended. I will try to disentangle them.

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