Chapter VI: Part 6

Apparent magnitude of a line is not simply as the optique angle, but directly as the optique angle, & reciprocally as the confusion, &c. (i.e. the other sensations, or want of sensation, that attend near vision). Hence great mistakes in assigning the magnifying power of glasses. Vid. Moly[neux], p. 182.

Glasses or speculums may perhaps magnify or lessen without altering the optique angle, but to no purpose.

Qu. Whether purblind would think objects so much diminished by a convex speculum as another?

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Qu. Wherein consists identity of person? Not in actual consciousness; for then I’m not the same person I was this day twelvemonth but while I think of wt I then did. Not in potential; for then all persons may be the same, for ought we know.

Mem. Story of Mr. Deering’s aunt.

Two sorts of potential consciousness—natural & præternatural. In the last § but one, I mean the latter.

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If by magnitude be meant the proportion anything bears to a determined tangible extension, as inch, foot, &c., this, ’tis plain, cannot be properly & _per se_ perceived by sight; & as for determin’d visible inches, feet, &c., there can be no such thing obtain’d by the meer act of seeing—abstracted from experience, &c.

The greatness _per se_ perceivable by the sight is onely the proportion any visible appearance bears to the others seen at the same time; or (which is the same thing) the proportion of any particular part of the visual orb to the whole. But mark that we perceive not it is an orb, any more than a plain, but by reasoning.

This is all the greatness the pictures have _per se_.

Hereby meere seeing cannot at all judge of the extension of any object, it not availing to know the object makes such a part of a sphærical surface except we also know the greatness of the sphærical surface; for a point may subtend the same angle wth a mile, & so create as great an image in the retina, i.e. take up as much of the orb.

Men judge of magnitude by faintness and vigorousness, by distinctness and confusion, with some other circumstances, by great & little angles.

Hence ’tis plain the ideas of sight which are now connected with greatness might have been connected wth smallness, and vice versâ: there being no necessary reason why great angles, faintness, and distinctness without straining, should stand for great extension, any more than a great angle, vigorousness, and confusion(227).

My end is not to deliver metaphysiques altogether in a general scholastic way, but in some measure to accommodate them to the sciences, and shew how they may be useful in optiques, geometry, &c.(228)

Qu. Whether _per se_ proportion of visible magnitudes be perceivable by sight? This is put on account of distinctness and confusedness, the act of perception seeming to be as great in viewing any point of the visual orb distinctly, as in viewing the whole confusedly.

Mem. To correct my language & make it as philosophically nice as possible—to avoid giving handle.

If men could without straining alter the convexity of their crystallines, they might magnify or diminish the apparent diameters of objects, the same optic angle remaining.

The bigness in one sense of the pictures in the fund is not determin’d; for the nearer a man views them, the images of them (as well as other objects) will take up the greater room in the fund of his eye.

Mem. Introduction to contain the design of the whole, the nature and manner of demonstrating, &c.

Two sorts of bigness accurately to be distinguished, they being perfectly and _toto cælo_ different—the one the proportion that any one appearance has to the sum of appearances perceived at the same time wth it, wch is proportional to angles, or, if a surface, to segments of sphærical surfaces;—the other is tangible bigness.

Qu. wt would happen if the sphæræ of the retina were enlarged or diminish’d?

We think by the meer act of vision we perceive distance from us, yet we do not; also that we perceive solids, yet we do not; also the inequality of things seen under the same angle, yet we do not.

Why may I not add, We think we see extension by meer vision? Yet we do not.

Extension seems to be perceived by the eye, as thought by the ear.

As long as the same angle determines the _minimum visibile_ to two persons, no different conformation of the eye can make a different appearance of magnitude in the same thing. But, it being possible to try the angle, we may certainly know whether the same thing appears differently big to two persons on account of their eyes.

If a man could see ... objects would appear larger to him than to another; hence there is another sort of purely visible magnitude beside the proportion any appearance bears to the visual sphere, viz. its proportion to the M. V.

Were there but one and the same language in the world, and did children speak it naturally as soon as born, and were it not in the power of men to conceal their thoughts or deceive others, but that there were an inseparable connexion between words & thoughts, so yt _posito uno, ponitur alterum_ by the laws of nature; Qu. would not men think they heard thoughts as much as that they see extension(229)?

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All our ideas are adæquate: our knowledge of the laws of nature is not perfect & adæquate(230).

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(M388) Men are in the right in judging their simple ideas to be in the things themselves. Certainly heat & colour is as much without the mind as figure, motion, time, &c.

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We know many things wch we want words to express. Great things discoverable upon this principle. For want of considering wch divers men have run into sundry mistakes, endeavouring to set forth their knowledge by sounds; wch foundering them, they thought the defect was in their knowledge, while in truth it was in their language.

Qu. Whether the sensations of sight arising from a man’s head be liker the sensations of touch proceeding from thence or from his legs?

Or, Is it onely the constant & long association of ideas entirely different that makes me judge them the same?

Wt I see is onely variety of colours & light. Wt I feel is hard or soft, hot or cold, rough or smooth, &c. Wt resemblance have these thoughts with those?

A picture painted wth great variety of colours affects the touch in one uniform manner. I cannot therefore conclude that because I see 2, I shall feel 2; because I see angles or inequalities, I shall feel angles or inequalities. How therefore can I—before experience teaches me—know that the visible leggs are (because 2) connected wth the tangible ones, or the visible head (because one) connected wth the tangible head(231)?

(M389) All things by us conceivable are—

1st, thoughts;

2ndly, powers to receive thoughts;

3rdly, powers to cause thoughts; neither of all wch can possibly exist in an inert, senseless thing.

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An object wthout a glass may be seen under as great an angle as wth a glass. A glass therefore does not magnify the appearance by the angle.

(M390) Absurd that men should know the soul by idea—ideas being inert, thoughtless. Hence Malbranch confuted(232).

I saw gladness in his looks. I saw shame in his face. So I see figure or distance.

Qu. Why things seen confusedly thro’ a convex glass are not magnify’d?

Tho’ we should judge the horizontal moon to be more distant, why should we therefore judge her to be greater? What connexion betwixt the same angle, further distant, and greaterness?

(M391) My doctrine affects the essences of the Corpuscularians.

Perfect circles, &c. exist not without (for none can so exist, whether perfect or no), but in the mind.

Lines thought divisible _ad infinitum_, because they are suppos’d to exist without. Also because they are thought the same when view’d by the naked eye, & wn view’d thro’ magnifying glasses.

They who knew not glasses had not so fair a pretence for the divisibility _ad infinitum_.

No idea of circle, &c. in abstract.

Metaphysiques as capable of certainty as ethiques, but not so capable to be demonstrated in a geometrical way; because men see clearer & have not so many prejudices in ethiques.

Visible ideas come into the mind very distinct. So do tangible ideas. Hence extension seen & felt. Sounds, tastes, &c. are more blended.

Qu. Why not extension intromitted by the taste in conjunction with the smell—seeing tastes & smells are very distinct ideas?

Blew and yellow particles mixt, while they exhibit an uniform green, their extension is not perceiv’d; but as soon as they exhibit distinct sensations of blew and yellow, then their extension is perceiv’d.

Distinct perception of visible ideas not so perfect as of tangible—tangible ideas being many at once equally vivid. Hence heterogeneous extension.

Object. Why a mist increases not the apparent magnitude of an object, in proportion to the faintness(233)?

Mem. To enquire touching the squaring of the circle, &c.

That wch seems smooth & round to the touch may to sight seem quite otherwise. Hence no _necessary_ connexion betwixt visible ideas and tangible ones.

In geometry it is not prov’d that an inch is divisible _ad infinitum_.

Geometry not conversant about our compleat determined ideas of figures, for these are not divisible _ad infinitum_.

Particular circles may be squar’d, for the circumference being given a diameter may be found betwixt wch & the true there is not any perceivable difference. Therefore there is no difference—extension being a perception; & a perception not perceivd is contradiction, nonsense, nothing. In vain to alledge the difference may be seen by magnifying-glasses, for in yt case there is (’tis true) a difference perceiv’d, but not between the same ideas, but others much greater, entirely different therefrom(234).

Any visible circle possibly perceivable of any man may be squar’d, by the common way, most accurately; or even perceivable by any other being, see he never so acute, i.e. never so small an arch of a circle; this being wt makes the distinction between acute & dull sight, and not the m.v., as men are perhaps apt to think.

The same is true of any tangible circle. Therefore further enquiry of accuracy in squaring or other curves is perfectly needless, & time thrown away.

Mem. To press wt last precedes more homely, & so think on’t again.

A meer line or distance is not made up of points, does not exist, cannot be imagin’d, or have an idea framed thereof,—no more than meer colour without extension(235).

Mem. A great difference between _considering_ length wthout breadth, & having an _idea_ of, or _imagining_, length without breadth(236).

Malbranch out touching the crystallines diminishing, L. 1. c. 6.

’Tis possible (& perhaps not very improbable, that is, is sometimes so) we may have the greatest pictures from the least objects. Therefore no necessary connexion betwixt visible & tangible ideas. These ideas, viz. great relation to _sphæra visualis_, or to the m. v. (wch is all that I would have meant by having a greater picture) & faintness, might possibly have stood for or signify’d small tangible extensions. Certainly the greater relation to s. v. and m. v. does frequently, in that men view little objects near the eye.

Malbranch out in asserting we cannot possibly know whether there are 2 men in the world that see a thing of the same bigness. V. L. 1. c. 6.

Diagonal of particular square commensurable wth its side, they both containing a certain number of m. v.

I do not think that surfaces consist of lines, i.e. meer distances. Hence perhaps may be solid that sophism wch would prove the oblique line equal to the perpendicular between 2 parallels.

Suppose an inch represent a mile. 1/1000 of an inch is nothing, but 1/1000 of ye mile represented is something: therefore 1/1000 an inch, tho’ nothing, is not to be neglected, because it represents something, i.e. 1/1000 of a mile.

Particular determin’d lines are not divisible _ad infinitum_, but lines as us’d by geometers are so, they not being determin’d to any particular finite number of points. Yet a geometer (he knows not why) will very readily say he can demonstrate an inch line is divisible _ad infinitum_.

A body moving in the optique axis not perceiv’d to move by sight merely, and without experience. There is (’tis true) a successive change of ideas,—it seems less and less. But, besides this, there is no visible change of place.

Mem. To enquire most diligently concerning the incommensurability of diagonale & side—whether it does not go on the supposition of units being divisible _ad infinitum_, i.e. of the extended thing spoken of being divisible _ad infinitum_ (unit being nothing; also v. Barrow, Lect. Geom.), & so the infinite indivisibility deduced therefrom is a _petitio principii_?

The diagonal is commensurable with the side.

(M392) From Malbranch, Locke, & my first arguings it can’t be prov’d that extension is not in matter. From Locke’s arguings it can’t be proved that colours are not in bodies.

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Mem. That I was distrustful at 8 years old; and consequently by nature disposed for these new doctrines(237).

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Qu. How can a line consisting of an unequal number of points be divisible [_ad infinitum_] in two equals?

Mem. To discuss copiously how & why we do not see the pictures.

(M393) Allowing extensions to exist in matter, we cannot know even their proportions—contrary to Malbranch.

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(M394) I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance.

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(M395) Species of all sensible things made by the mind. This prov’d either by turning men’s eyes into magnifyers or diminishers.

Yr m. v. is, suppose, less than mine. Let a 3rd person have perfect ideas of both our m. vs. His idea of my m. v. contains his idea of yours, & somewhat more. Therefore ’tis made up of parts: therefore his idea of my m. v. is not perfect or just, which diverts the hypothesis.

Qu. Whether a m. v. or t. be extended?

Mem. The strange errours men run into about the pictures. We think them small because should a man be suppos’d to see them their pictures would take up but little room in the fund of his eye.

It seems all lines can’t be bisected in 2 equall parts. Mem. To examine how the geometers prove the contrary.

’Tis impossible there should be a m. v. less than mine. If there be, mine may become equal to it (because they are homogeneous) by detraction of some part or parts. But it consists not of parts, ergo &c.

Suppose inverting perspectives bound to ye eyes of a child, & continu’d to the years of manhood—when he looks up, or turns up his head, he shall behold wt we call _under_. Qu. What would he think of _up_ and _down_(238)?

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(M396) I wonder not at my sagacity in discovering the obvious tho’ amazing truth. I rather wonder at my stupid inadvertency in not finding it out before—’tis no witchcraft to see.

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(M397) Our simple ideas are so many simple thoughts or perceptions; a perception cannot exist without a thing to perceive it, or any longer than it is perceiv’d; a thought cannot be in an unthinking thing; one uniform simple thought can be like to nothing but another uniform simple thought. Complex thoughts or ideas are onely an assemblage of simple ideas, and can be the image of nothing, or like unto nothing, but another assemblage of simple ideas, &c.

(M398) The Cartesian opinion of light & colours &c. is orthodox enough even in their eyes who think the Scripture expression may favour the common opinion. Why may not mine also? But there is nothing in Scripture that can possibly be wrested to make against me, but, perhaps, many things for me.

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(M399) Bodies &c. do exist whether we think of ’em or no, they being taken in a twofold sense—

1. Collections of thoughts.

2. Collections of powers to cause those thoughts.

These later exist; tho’ perhaps _a parte rei_ it may be one simple perfect power.

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Qu. whether the extension of a plain, look’d at straight and slantingly, survey’d minutely & distinctly, or in the bulk and confusedly at once, be the same? N. B. The plain is suppos’d to keep the same distance.

The ideas we have by a successive, curious inspection of ye minute parts of a plain do not seem to make up the extension of that plain view’d & consider’d all together.

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Ignorance in some sort requisite in ye person that should disown the Principle.

Thoughts do most properly signify, or are mostly taken for the interior operations of the mind, wherein the mind is active. Those yt obey not the acts of volition, and in wch the mind is passive, are more properly call’d sensations or perceptions. But yt is all a case of words.

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Extension being the collection or distinct co-existence of minimums, i.e. of perceptions intromitted by sight or touch, it cannot be conceiv’d without a perceiving substance.

(M400) Malbranch does not prove that the figures & extensions exist not when they are not perceiv’d. Consequently he does not prove, nor can it be prov’d on his principles, that the sorts are the work of the mind, and onely in the mind.

(M401) The great argument to prove that extension cannot be in an unthinking substance is, that it cannot be conceiv’d distinct from or without all tangible or visible quality.

(M402) Tho’ matter be extended wth an indefinite extension, yet the mind makes the sorts. They were not before the mind perceiving them, & even now they are not without the mind. Houses, trees, &c., tho’ indefinitely extended matter do exist, are not without the mind.

(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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The reader must remember that this _Essay on Vision_ is professedly an introspective appeal to human consciousness. It is an analysis of what human beings are conscious of when they see, the results being here and there applied, partly by way of verification, to solve some famous optical or physiological puzzle. The aim is to present the facts, the whole facts, and nothing but the facts of our internal visual experience, as distinguished from supposed facts and empty abstractions, which an irregular exercise of imagination, or abuse of words, had put in their place. The investigation, moreover, is not concerned with Space in its metaphysical infinity, but with finite sections of Space and their relations, which concern the sciences, physical and mathematical, and with real or tangible Distance, Magnitude, and Place, in their relation to seeing.

From the second section onwards the _Essay_ naturally falls into six Parts, devoted successively to the proof of the six following theses regarding the relation of Sight to finite spaces and to things extended:—

I. (Sect. 2-51.) Distance, or outness from the eye in the line of vision, is not seen: it is only suggested to the mind by visible phenomena and by sensations felt in the eye, all which are somehow its arbitrarily constituted and non-resembling Signs.

II. (Sect. 52-87.) Magnitude, or the amount of space that objects of sense occupy, is really invisible: we only see a greater or less quantity of colour, and colour depends upon percipient mind: our supposed visual perceptions of real magnitude are only our own interpretations of the tactual meaning of the colours we see, and of sensations felt in the eye, which are its Signs.

III. (Sect. 88-120.) Situation of objects of sense, or their real relation to one another in ambient space, is invisible: what we see is variety in the relations of colours to one another: our supposed vision of real tangible locality is only our interpretation of its visual non-resembling Signs.

IV. (Sect. 121-46.) There is no object that is presented in common to Sight and Touch: space or extension, which has the best claim to be their common object, is specifically as well as numerically different in Sight and in Touch.

V. (Sect. 147-48.) The explanation of the tactual significance of the visible and visual Signs, upon which human experience proceeds, is offered in the Theory that all visible phenomena are arbitrary signs in what is virtually the Language of Nature, addressed by God to the senses and intelligence of Man.

VI. (Sect. 149-60.) The true object studied in Geometry is the kind of Extension given in Touch, not that given in Sight: real Extension in all its phases is tangible, not visible: colour is the only immediate object of Sight, and colour being mind-dependent sensation, cannot be realised without percipient mind. These concluding sections are supplementary to the main argument.

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The fact that distance or outness is invisible is sometimes regarded as Berkeley’s contribution to the theory of seeing. It is rather the assumption on which the _Essay_ proceeds (sect. 2). The _Essay_ does not prove this invisibility, but seeks to shew how, notwithstanding, we learn to find outness through seeing. That the relation between the visual signs of outness, on the one hand, and the real distance which they signify, on the other, is in all cases arbitrary, and discovered through experience, is the burden of sect. 2-40. The previously recognised signs of “considerably remote” distances, are mentioned (sect. 3). But _near_ distance was supposed to be inferred by a visual geometry—and to be “suggested,” not signified by arbitrary signs. The determination of the visual signs which suggest outness, near and remote, is Berkeley’s professed discovery regarding vision.

An induction of the visual signs which “suggest” distance, is followed (sect. 43) by an assertion of the wholly sensuous reality of _colour_, which is acknowledged to be the only immediate object of sight. Hence _visible_ extension, consisting in colour, must be dependent for its realisation upon sentient or percipient mind. It is then argued (sect. 44) that this mind-dependent visible outness has no resemblance to the tangible reality (sect. 45). This is the first passage in the _Essay_ in which Touch and its data are formally brought into view. Tactual or locomotive experience, it is implied, is needed to infuse true reality into our conceptions of distance or outness. This cannot be got from seeing any more than from hearing, or tasting, or smelling. It is as impossible to see and touch the same object as it is to hear and touch the same object. Visible objects and ocular sensations can only be _ideal signs_ of _real things_.

The sections in which Touch is thus introduced are among the most important in the _Essay_. They represent the outness given in hearing as wholly sensuous, ideal, or mind-dependent: they recognise as more truly real that got by contact and locomotion. But if this is all that man can see, it follows that his _visible_ world, at any rate, becomes real only in and through percipient mind. The problem of an _Essay on Vision_ is thus, to explain _how_ the visible world of extended colour can inform us of tangible realities, which it does not in the least resemble, and with which it has no _necessary_ connexion. That visible phenomena, or else certain organic sensations involved in seeing (sect. 3, 16, 21, 27), gradually _suggest_ the real or tangible outness with which they are connected in the divinely constituted system of nature, is the explanation which now begins to dawn upon us.

Here an ambiguity in the _Essay_ appears. It concludes that the _visible_ world cannot be real without percipient realising mind, i.e. not otherwise than ideally: yet the argument seems to take for granted that we are percipient of a _tangible_ world that is independent of percipient realising mind. The reader is apt to say that the tangible world must be as dependent on percipient mind for its reality as the visible world is concluded to be, and for the same reason. This difficulty was soon afterwards encountered in the book of _Principles_, where the worlds of sight and touch are put on the same level; and the possibility of unperceived reality in both cases is denied; on the ground that a material world cannot be realised in the total absence of Spirit—human and divine. The term “external” may still be applied to tactual and locomotive phenomena alone, if men choose; but this not because of the ideal character of what is seen, and the unideal reality of what is touched, but only because tactual perceptions are found to be more firm and steady than visual. Berkeley preferred in this way to _insinuate_ his new conception of the material world by degrees, at the risk of exposing this juvenile and tentative _Essay on Vision_ to a charge of incoherence.

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The way in which visual ideas or phenomena “suggest” the outness or distance of things from the organ of sight having been thus explained, in what I call the First Part of the _Essay_, the Second and Third Parts (sect. 52-120) argue for the invisibility of real extension in two other relations, viz. magnitude and locality or situation. An induction of the visual signs of tangible size and situation is given in those sections. The result is applied to solve two problems then notable in optics, viz. (1) the reason for the greater visible size of the horizontal moon than of the moon in its meridian (sect. 67-87); and (2) the fact that objects are placed erect in vision only on condition that their images on the retina are inverted (sect. 88-120). Here the antithesis between the ideal world of coloured extension, and the real world of resistant extension is pressed with vigour. The “high” and “low” of the visible world is not the “high” and “low” of the tangible world (sect. 91-106). There is no resemblance and no necessary relation, between those two so-called extensions; not even when the number of visible objects happen to coincide with the number of tangible objects of which they are the visual signs, e.g. the visible and tangible fingers on the hand: for the born-blind, on first receiving sight, could not parcel out the visible phenomena in correspondence with the tangible.

The next Part of the _Essay_ (sect. 121-45) argues for a specific as well as a numerical difference between the original data of sight and the data of touch and locomotion. Sight and touch perceive nothing in common. Extension in its various relations differs in sight from extension in touch. Coloured extension, which alone is visible, is found to be different in kind from resistant extension, which alone is tangible. And if actually perceived or concrete extensions differ thus, the question is determined. For all extension with which man can be concerned must be concrete (sect. 23). Extension in the abstract is meaningless (sect. 124-25). What remains is to marshal the scattered evidence, and to guard the foregoing conclusions against objections. This is attempted in sections 128-46.

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The enunciation of the summary generalisation, which forms the “New Theory of Vision” (sect. 147-8), may be taken as the Fifth and culminating Part of the _Essay_.

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The closing sections (149-60), as I have said, are supplementary, and profess to determine the sort of extension—visible or tangible—with which Geometry is concerned. In concluding that it is tangible, he tries to picture the mental state of Idominians, or unbodied spirits, endowed with visual perceptions _only_, and asks what _their_ conception of outness and solid extension must be. Here further refinements in the interpretation of visual perception, and its organic conditions, which have not escaped the attention of latter psychologists and biologists, are hinted at.

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Whether the data of sight consist of non-resembling arbitrary Signs of the tactual distances, sizes, and situations of things, is a question which some might prefer to deal with experimentally—by trial of the experience of persons in circumstances fitted to supply an answer. Of this sort would be the experience of the born-blind, immediately after their sight has been restored; the conception of extension and its relations found in persons who continue from birth unable to see; the experience (if it could be got) of persons always destitute of all tactual and locomotive perceptions, but familiar with vision; and the facts of seeing observed in infants of the human species, and in the lower animals.

Berkeley did not try to verify his conclusions in this way. Here and there (sect. 41, 42, 79, 92-99, 103, 106, 110, 128, 132-37), he conjectures what the first visual experience of those rescued from born-blindness is likely to be; he also speculates, as we have seen, about the experience of unbodied spirits supposed to be able to see, but unable to touch or move (sect. 153-59); and in the Appendix he refers, in confirmation of his New Theory, to a reported case of one born blind who had obtained sight. But he forms his Theory independently of those delicate and difficult investigations. His testing facts were sought introspectively. Indeed those physiologists and mental philosophers who have since tried to determine what vision in its purity is, by cases either of communicated sight or of continued born-blindness, have illustrated the truth of Diderot’s remark—“préparer et interroger un aveugle-né n’eût point été une occupation indigne des talens réunis de Newton, Des Cartes, Locke, et Leibniz(275).”

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Berkeley’s _New Theory_ has been quoted as a signal example of discovery in metaphysics. The subtle analysis which distinguishes _seeing_ strictly so called, from judgments about extended things, suggested by what we see, appears to have been imperfectly known to the ancient philosophers. Aristotle, indeed, speaks of colour as the only proper object of sight; but, in passages of the _De Anima_(276) where he names properties peculiar to particular senses, he enumerates others, such as motion, figure, and magnitude, which belong to all the senses in common. His distinction of Proper and Common Sensibles appears at first to contradict Berkeley’s doctrine of the heterogeneity of the ideal visible and the real tangible worlds. Aristotle, however, seems to question the immediate perceptibility of Common Sensibles, and to regard them as realised through the activity of intelligence(277).