Chapter VII: Part 7

Some writers in Optics, in mediaeval times, and in early modern philosophy, advanced beyond Aristotle, in explaining the relation of our matured notion of distance to what we originally perceive in seeing, and in the fifteenth century it was discovered by Maurolyco that the rays of light from the object converge to a focus in the eye; but I have not been able to trace even the germ of the _New Theory_ in these speculations.

Excepting some hints by Descartes, Malebranche was among the first dimly to anticipate Berkeley, in resolving our supposed power of seeing outness into an interpretation of visual signs which we learn by experience to understand. The most important part of Malebranche’s account of seeing is contained in the _Recherche de la Vérité_ (Liv. I. ch. 9), in one of those chapters in which he discusses the frequent fallaciousness of the senses, and in particular of our visual perceptions of extension. He accounts for their inevitable uncertainty by assigning them not to sense but to misinterpretation of what is seen. He also enumerates various visual signs of distance.

That the _Recherche_ of Malebranche, published more than thirty years before the _Essay_, was familiar to Berkeley before the publication of his _New Theory_, is proved by internal evidence, and by his juvenile _Commonplace Book_. I am not able to discover signs of a similar connexion between the _New Theory_ and the chapter on the mystery of sensation in Glanvill’s _Scepsis Scientifica_ (ch. 5), published some years before the _Recherche_ of Malebranche, where Glanvill refers to “a secret deduction,” through which—from motions, &c., of which we are immediately percipient—we “spell out” figures, distances, magnitudes, and colours, which have no resemblance to them.

An approach to the _New Theory_ is found in a passage which first appeared in the second edition of Locke’s _Essay_, published in 1694, to which Berkeley refers in his own _Essay_ (sect. 132-35), and which, on account of its relative importance, I shall here transcribe at length:—

“We are further to consider concerning Perception that the ideas we receive by sensation are often, in grown people, altered by the judgment, without our taking notice of it. When we set before our eyes a round globe of any uniform colour, e.g. gold, alabaster, or jet, it is certain that the idea thereby imprinted in our mind is of a flat circle, variously shadowed, with several degrees of light and brightness coming to our eyes. But, we having by use been accustomed to perceive what kind of appearance convex bodies are wont to make in us, what alterations are made in the reflection of light by the difference in the sensible figures of bodies—the judgment presently, by an habitual custom, alters the appearances into their causes; so that, from that which is truly variety of shadow or colour, collecting the figure, it makes it pass for a mark of figure, and frames to itself the perception of a convex figure and an uniform colour, when the idea we receive from them is only a plane variously coloured, as is evident in painting.

“To which purpose I shall here insert a problem of that very ingenious and studious promoter of real knowledge, the learned and worthy Mr. Molyneux, which he was pleased to send me in a letter some months since, and it is this:—Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt the one and the other, which is the cube and which the sphere. Suppose then the cube and the sphere placed on a table, and the blind man be made to see: quere, whether, by his sight, before he touched them, he could not distinguish and tell, which is the globe and which the cube? To which the acute and judicious proposer answers: ‘Not.’ For, though he has obtained the experience of how a globe, how a cube affects his touch; yet he has not obtained the experience that what affects his touch so and so, must affect his sight so and so; so that a protuberant angle in the cube, that pressed his hand unequally, shall appear to his eye as it does in the cube.—I agree with this thinking gentleman, whom I am proud to call my friend, in his answer to this his problem, and am of opinion that the blind man, at first sight, would not be able to say with certainty which was the globe and which the cube, whilst he only saw them; though he would unerringly name them by his touch, and certainly distinguish them by the difference in their figures felt.

“This I have set down, and leave with my reader, as an occasion for him to consider how much he may be beholden to experience, improvement, and acquired notions, where he thinks he had not the least use of, or help from them: and the rather because this observing gentleman further adds that, having, upon the occasion of my book, proposed this problem to divers very ingenious men, he hardly ever met with one that at first gave the answer to it which he thinks true, till by hearing his reasons they were convinced.

“But this is not I think usual in any of our ideas but those received by sight: because sight, the most comprehensive of the senses, conveying to our minds the ideas of light and colours, which are peculiar only to that sense; and also the far different ideas of space, figure, and motion, the several varieties of which change the appearance of its proper object, i.e. light and colours; we bring ourselves by use to judge of the one by the other. This, in many cases, by a settled habit, in things whereof we have frequent experience, is performed so constantly and so quick, that we take that for the perception of our sensation, which is an idea formed by our judgment; so that one, i.e. that of sensation, serves only to excite the other, and is scarce taken notice of itself; as a man who reads or hears with attention and understanding takes little notice of the character or sounds, but of the ideas that are excited in him by them.

“Nor need we wonder that this is done with so little notice, if we consider how very quick the actions of the mind are performed; for, as itself is thought to take up no space, to have no extension, so its actions seem to require no time, but many of them seem to be crowded into an instant. I speak this in comparison of the actions of the body.... Secondly, we shall not be much surprised that this is done with us in so little notice, if we consider how the facility we get of doing things, by a custom of doing, makes them often pass in us without notice. Habits, especially such as are begun very early, come at last to produce actions in us which often escape our observation.... And therefore it is not so strange that our mind should often change the idea of its sensation into that of its judgment, and make the one serve only to excite the other, without our taking notice of it.” (_Essay concerning Human Understanding_, Book II. ch. 9. § 8.)

This remarkable passage anticipates by implication the view of an interpretation of materials originally given in the visual sense, which, under the name of “suggestion,” is the ruling factor in the _New Theory of Vision_.

The following sentences relative to the invisibility of distances, contained in the _Treatise of Dioptrics_ (published in 1690) of Locke’s friend and correspondent William Molyneux, whose son was Berkeley’s pupil, illustrate Locke’s statements, and may be compared with the opening sections of the _Essay on Vision_:—

“In plain vision the estimate we make of the distance of objects (especially when so far removed that the interval between our two eyes bears no sensible proportion thereto, or when looked upon with one eye only) is rather the act of our judgment than of sense; and acquired by exercise, and a faculty of comparing, rather than natural. For, distance of itself is not to be perceived; for, ’tis a line (or a length) presented to our eye with its end toward us, which must therefore be only a point, and that is invisible. Wherefore distance is chiefly perceived by means of interjacent bodies, as by the earth, mountains, hills, fields, trees, houses, &c. Or by the estimate we make of the comparative magnitude of bodies, or of their faint colours, &c. These I say are the chief means of apprehending the distance of objects that are considerably remote. But as to nigh objects—to whose distance the interval of the eyes bears a sensible proportion—their distance is perceived by the turn of the eyes, or by the angle of the optic axes (_Gregorii Opt. Promot._ prop. 28). This was the opinion of the ancients, Alhazen, Vitellio, &c. And though the ingenious Jesuit Tacquet (_Opt. Lib. I._ prop. 2) disapprove thereof, and objects against it a new notion of Gassendus (of a man’s seeing only with one eye at a time one and the same object), yet this notion of Gassendus being absolutely false (as I could demonstrate were it not beside my present purpose), it makes nothing against this opinion.

“Wherefore, distance being only a line and not of itself perceivable, if an object were conveyed to the eye by one single ray only, there were no other means of judging of its distance but by some of those hinted before. Therefore when we estimate the distance of nigh objects, either we take the help of both eyes; or else we consider the pupil of one eye as having breadth, and receiving a parcel of rays from each radiating point. And, according to the various inclinations of the rays from one point on the various parts of the pupil, we make our estimate of the distance of the object. And therefore (as is said before), by one single eye we can only judge of the distance of such objects to whose distance the breadth of the pupil has a sensible proportion.... For, it is observed before (prop. 29, sec. 2, see also _Gregorii Opt. Promot._ prop. 29) that for viewing objects remote and nigh, there are requisite various conformations of the eye—the rays from nigh objects that fall on the eye diverging more than those from more remote objects.” (_Treatise of Dioptrics_, Part I. prop. 31.)

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All this helps to shew the state of science regarding vision about the time Berkeley’s _Essay_ appeared, especially among those with whose works he was familiar(278). I shall next refer to illustrations of the change which the _Essay_ produced.

The _New Theory_ has occasioned some interesting criticism since its appearance in 1709. At first it drew little attention. For twenty years after its publication the allusions to it were few. The account of Cheselden’s experiment upon one born blind, published in 1728, in the _Philosophical Transactions_, which seemed to bring the Theory to the test of scientific experiment, recalled attention to Berkeley’s reasonings. The state of religious thought about the same time confirmed the tendency to discuss a doctrine which represented human vision as interpretation of a natural yet divine language, thus suggesting Omnipresent Mind.

Occasional discussions of the _New Theory_ may be found in the _Gentleman’s Magazine_, from 1732 till Berkeley’s death in 1753. Some criticisms may also be found in Smith’s _Optics_, published in 1738.

Essential parts of Berkeley’s analysis are explained by Voltaire, in his _Élémens de la Philosophie de Newton_. The following from that work is here given on its own account, and also as a prominent recognition of the new doctrine in France, within thirty years from its first promulgation:—

“Il faut absolument conclure de tout ceci, que les distances, les
grandeurs, les situations, ne sont pas, à proprement parler, des
choses visibles, c’est-à-dire, ne sont pas les objets propres et
immédiats de la vue. L’objet propre et immédiat de la vue n’est
autre chose que la lumière colorée: tout le reste, nous ne le
sentons qu’à la longue et par expérience. Nous apprenons à voir
précisément comme nous apprenons à parler et à lire. La différence
est, que l’art de voir est plus facile, et que la nature est
également à tous notre maître.

“Les jugements soudains, presque uniformes, que toutes nos âmes, à
un certain âge, portent des distances, des grandeurs, des
situations, nous font penser qu’il n’y a qu’à ouvrir les yeux pour
voir la manière dont nous voyons. On se trompe; il y faut le
secours des autres sens. Si les hommes n’avaient que le sens de la
vue, ils n’auraient aucun moyen pour connaître l’étendue en
longueur, largeur et profondeur; et un pur esprit ne la
connaîtrait pas peutêtre, à moins que Dieu ne la lui révélât. Il
est très difficile de séparer dans notre entendement l’extension
d’un objet d’avec les couleurs de cet objet. Nous ne voyons jamais
rien que d’étendu, et de là nous sommes tous portés à croire que
nous voyons en effet l’étendue.” (_Élémens de la Philos. de
Newton_, Seconde Partie, ch. 7.)

Condillac, in his _Essais sur l’Origine des Connaissances Humaines_ (Part I. sect. 6), published in 1746, combats Berkeley’s _New Theory_, and maintains that an extension exterior to the eye is immediately discernible by sight; the eye being naturally capable of judging at once of figures, magnitudes, situations, and distances. His reasonings in support of this “prejudice,” as he afterwards allowed it to be, may be found in the section entitled “De quelques jugemens qu’on a attribués à l’âme sans fondement, ou solution d’un problème de métaphysique.” Here Locke, Molyneux, Berkeley, and Voltaire are criticised, and Cheselden’s experiment is referred to. Condillac’s subsequent recantation is contained in his _Traité des Sensations_, published in 1754, and in his _L’Art de Penser_. In the _Traité des Sensations_ (Troisième Partie, ch. 3, 4, 5, 6, 7, 8, &c.) the whole question is discussed at length, and Condillac vindicates what he allows must appear a marvellous paradox to the uninitiated—that we only gradually learn to see, hear, smell, taste, and touch. He argues in particular that the eye cannot originally perceive an extension that is beyond itself, and that perception of trinal space is due to what we experience in touch.

Voltaire and Condillac gave currency to the _New Theory_ in France, and it soon became a commonplace with D’Alembert, Diderot, Buffon, and other French philosophers. In Germany we have allusions to it in the Berlin Memoirs and elsewhere; but, although known by name, if not in its distinctive principle and latent idealism, it has not obtained the consideration which its author’s developed theory of the material as well as the visible world has received. The Kantian _a priori_ criticism of our cognition of Space, and of our mathematical notions, subsequently indisposed the German mind to the _a posteriori_ reasoning of Berkeley’s _Essay_.

Its influence is apparent in British philosophy. The following passages in Hartley’s _Observations on Man_, published in 1749, illustrate the extent to which some of the distinctive parts of the new doctrine were at that time received by an eminent English psychologist:—

“Distance is judged of by the quantity of motion, and figure by the relative quantity of distance.... And, as the sense of sight is much more extensive and expedite than feeling, we judge of tangible qualities chiefly by sight, which therefore may be considered, agreeably to Bishop Berkeley’s remark, as a philosophical language for the ideas of feeling; being, for the most part, an adequate representative of them, and a language common to all mankind, and in which they all agree very nearly, after a moderate degree of experience.

“However, if the informations from touch and sight disagree at any time, we are always to depend upon touch, as that which, according to the usual ways of speaking upon these subjects, is the true representation of the essential properties, i.e. as the earnest and presage of what other tangible impressions the body under consideration will make upon our feeling in other circumstances; also what changes it will produce in other bodies; of which again we are to determine by our feeling, if the visual language should not happen to correspond to it exactly. And it is from this difference that we call the touch the reality, light the representative—also that a person born blind may foretell with certainty, from his present tangible impressions, what others would follow upon varying the circumstances; whereas, if we could suppose a person to be born without feeling, and to arrive at man’s estate, he could not, from his present visible impressions, judge what others would follow upon varying the circumstances. Thus the picture of a knife, drawn so well as to deceive his eye, would not, when applied to another body, produce the same change of visible impressions as a real knife does, when it separates the parts of the body through which it passes. But the touch is not liable to these deceptions. As it is therefore the fundamental source of information in respect of the essential properties of matter, it may be considered as our first and principal key to the knowledge of the external world.” (Prop. 30.)

In other parts of Hartley’s book (e.g. Prop. 58) the relation of our visual judgments of magnitude, figure, motion, distance, and position to the laws of association is explained, and the associating circumstances by which these judgments are formed are enumerated in detail.

Dr. Porterfield of Edinburgh, in his _Treatise on the Eye, or the Manner and Phenomena of Vision_ (Edinburgh, 1759), is an exception to the consent which the doctrine had then widely secured. He maintains, in opposition to Berkeley, that “the judgments we form of the situation and distance of visible objects, depend not on custom and experience, but on original instinct, to which mind is subject in our embodied state(279).”

Berkeley’s Theory of Vision, in so far as it resolves our visual perceptions of distance into interpretation of arbitrary signs, received the qualified approbation of Reid, in his _Inquiry into the Human Mind on the Principles of Common Sense_ (1764). He criticises it in the _Inquiry_, where the doctrine of visual signs, of which Berkeley’s whole philosophy is a development, is accepted, and to some extent applied. With Reid it is divorced, however, from the Berkeleian conception of the material world, although the Theory of Vision was the seminal principle of Berkeley’s Theory of Matter(280).

This Theory of Matter was imperfectly conceived and then rejected by Reid and his followers, while the New Theory of Vision obtained the general consent of the Scottish metaphysicians. Adam Smith refers to it in his _Essays_ (published in 1795) as “one of the finest examples of philosophical analysis that is to be found either in our own or in any other language.” Dugald Stewart characterises it in his _Elements_ as “one of the most beautiful, and at the same time one of the most important theories of modern philosophy.” “The solid additions,” he afterwards remarks in his _Dissertation_, “made by Berkeley to the stock of human knowledge, were important and brilliant. Among these the first place is unquestionably due to his _New Theory of Vision_, a work abounding with ideas so different from those commonly received, and at the same time so profound and refined, that it was regarded by all but a few accustomed to deep metaphysical reflection, rather in the light of a philosophical romance than of a sober inquiry after truth. Such, however, has since been the progress and diffusion of this sort of knowledge, that the leading and most abstracted doctrines contained in it form now an essential part of every elementary treatise on optics, and are adopted by the most superficial smatterers in science as fundamental articles of their faith.” The _New Theory_ is accepted by Thomas Brown, who proposes (_Lectures_, 29) to extend the scope of its reasonings. With regard to perceptions of sight, Young, in his _Lectures on Intellectual Philosophy_ (p. 102), says that “it has been universally admitted, at least since the days of Berkeley, that many of those which appear to us at present to be instantaneous and primitive, can yet be shewn to be acquired; that most of the adult perceptions of sight are founded on the previous information of touch; that colour can give us no conception originally of those qualities of bodies which produce it in us; and that primary vision gives us no notion of distance, and, as I believe, no notion of magnitude.” Sir James Mackintosh, in his _Dissertation_, characterises the _New Theory of Vision_ as “a great discovery in Mental Philosophy.” “Nothing in the compass of inductive reasoning,” remarks Sir William Hamilton (Reid’s _Works_, p. 182, note), “appears more satisfactory than Berkeley’s demonstration of the necessity and manner of our learning, by a slow process of observation and comparison alone, the connexion between the perceptions of vision and touch, and, in general, all that relates to the distance and magnitude of external things(281).”

The New Theory of Vision has in short been generally accepted, so far as it was understood, alike by the followers of Hartley and by the associates and successors of Reid. Among British psychologists, it has recommended itself to rationalists and sensationalists, to the advocates of innate principles, and to those who would explain by accidental association what their opponents attribute to reason originally latent in man. But this wide conscious assent is I think chiefly confined to the proposition that distance is invisible, and hardly reaches the deeper implicates of the theory, on its extension to all the senses, leading to a perception of the final unity of the natural and the supernatural, and the ultimate spirituality of the universe(282).

Dedication

TO THE RT. HON. SIR JOHN PERCIVALE, BART.(283),

ONE OF HER MAJESTY’S MOST HONOURABLE PRIVY COUNCIL

IN THE KINGDOM OF IRELAND.

Sir,

I could not, without doing violence to myself, forbear upon this occasion to give some public testimony of the great and well-grounded esteem I have conceived for you, ever since I had the honour and happiness of your acquaintance. The outward advantages of fortune, and the early honours with which you are adorned, together with the reputation you are known to have amongst the best and most considerable men, may well imprint veneration and esteem on the minds of those who behold you from a distance. But these are not the chief motives that inspire me with the respect I bear you. A nearer approach has given me the view of something in your person infinitely beyond the external ornaments of honour and estate. I mean, an intrinsic stock of virtue and good sense, a true concern for religion, and disinterested love of your country. Add to these an uncommon proficiency in the best and most useful parts of knowledge; together with (what in my mind is a perfection of the first rank) a surpassing goodness of nature. All which I have collected, not from the uncertain reports of fame, but from my own experience. Within these few months that I have the honour to be known unto you, the many delightful hours I have passed in your agreeable and improving conversation have afforded me the opportunity of discovering in you many excellent qualities, which at once fill me with admiration and esteem. That one at those years, and in those circumstances of wealth and greatness, should continue proof against the charms of luxury and those criminal pleasures so fashionable and predominant in the age we live in; that he should preserve a sweet and modest behaviour, free from that insolent and assuming air so familiar to those who are placed above the ordinary rank of men; that he should manage a great fortune with that prudence and inspection, and at the same time expend it with that generosity and nobleness of mind, as to shew himself equally remote from a sordid parsimony and a lavish inconsiderate profusion of the good things he is intrusted with—this, surely, were admirable and praiseworthy. But, that he should, moreover, by an impartial exercise of his reason, and constant perusal of the sacred Scriptures, endeavour to attain a right notion of the principles of natural and revealed religion; that he should with the concern of a true patriot have the interest of the public at heart, and omit no means of informing himself what may be prejudicial or advantageous to his country, in order to prevent the one and promote the other; in fine, that, by a constant application to the most severe and useful studies, by a strict observation of the rules of honour and virtue, by frequent and serious reflections on the mistaken measures of the world, and the true end and happiness of mankind, he should in all respects qualify himself bravely to run the race that is set before him, to deserve the character of great and good in this life, and be ever happy hereafter—this were amazing and almost incredible. Yet all this, and more than this, SIR, might I justly say of you, did either your modesty permit, or your character stand in need of it. I know it might deservedly be thought a vanity in me to imagine that anything coming from so obscure a hand as mine could add a lustre to your reputation. But, I am withal sensible how far I advance the interest of my own, by laying hold on this opportunity to make it known that I am admitted into some degree of intimacy with a person of your exquisite judgment. And, with that view, I have ventured to make you an address of this nature, which the goodness I have ever experienced in you inclines me to hope will meet with a favourable reception at your hands. Though I must own I have your pardon to ask, for touching on what may possibly be offensive to a virtue you are possessed of in a very distinguishing degree. Excuse me, SIR, if it was out of my power to mention the name of SIR JOHN PERCIVALE without paying some tribute to that extraordinary and surprising merit whereof I have so clear and affecting an idea, and which, I am sure, cannot be exposed in too full a light for the imitation of others,

Of late I have been agreeably employed in considering the most noble, pleasant, and comprehensive of all the senses(284). The fruit of that (labour shall I call it or) diversion is what I now present you with, in hopes it may give some entertainment to one who, in the midst of business and vulgar enjoyments, preserves a relish for the more refined pleasures of thought and reflexion. My thoughts concerning Vision have led me into some notions so far out of the common road(285) that it had been improper to address them to one of a narrow and contracted genius. But, you, SIR, being master of a large and free understanding, raised above the power of those prejudices that enslave the far greater part of mankind, may deservedly be thought a proper patron for an attempt of this kind. Add to this, that you are no less disposed to forgive than qualified to discern whatever faults may occur in it. Nor do I think you defective in any one point necessary to form an exact judgment on the most abstract and difficult things, so much as in a just confidence of your own abilities. And, in this one instance, give me leave to say, you shew a manifest weakness of judgment. With relation to the following _Essay_, I shall only add that I beg your pardon for laying a trifle of that nature in your way, at a time when you are engaged in the important affairs of the nation, and desire you to think that I am, with all sincerity and respect,

SIR,

Your most faithful and most humble servant,

GEORGE BERKELEY.

An Essay Towards A New Theory Of Vision

1. My design is to shew the manner wherein we perceive by Sight the Distance, Magnitude, and Situation of objects: also to consider the difference there is betwixt the ideas of Sight and Touch, and whether there be any idea common to both senses(286).

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2. It is, I think, agreed by all that Distance, of itself and immediately, cannot be seen(287). For, distance(288) being a line directed endwise to the eye, it projects only one point in the fund of the eye, which point remains invariably the same, whether the distance be longer or shorter(289).

3. I find it also acknowledged that the estimate we make of the distance of objects considerably remote is rather an act of judgment grounded on experience than of sense. For example, when I perceive a great number of intermediate objects, such as houses, fields, rivers, and the like, which I have experienced to take up a considerable space, I thence form a judgment or conclusion, that the object I see beyond them is at a great distance. Again, when an object appears faint and small which at a near distance I have experienced to make a vigorous and large appearance, I instantly conclude it to be far off(290). And this, it is evident, is the result of experience; without which, from the faintness and littleness, I should not have inferred anything concerning the distance of objects.

4. But, when an object is placed at so near a distance as that the interval between the eyes bears any sensible proportion to it(291), the opinion of speculative men is, that the two optic axes (the fancy that we see only with one eye at once being exploded), concurring at the object, do there make an angle, by means of which, according as it is greater or lesser, the object is perceived to be nearer or farther off(292).

5. Betwixt which and the foregoing manner of estimating distance there is this remarkable difference:—that, whereas there was no apparent _necessary_ connexion between small distance and a large and strong appearance, or between great distance and a little and faint appearance, there appears a very _necessary_ connexion between an obtuse angle and near distance, and an acute angle and farther distance. It does not in the least depend upon experience, but may be evidently known by any one before he had experienced it, that the nearer the concurrence of the optic axes the greater the angle, and the remoter their concurrence is, the lesser will be the angle comprehended by them.

6. There is another way, mentioned by optic writers, whereby they will have us judge of those distances in respect of which the breadth of the pupil hath any sensible bigness. And that is the greater or lesser divergency of the rays which, issuing from the visible point, do fall on the pupil—that point being judged nearest which is seen by most diverging rays, and that remoter which is seen by less diverging rays, and so on; the apparent distance still increasing, as the divergency of the rays decreases, till at length it becomes infinite, when the rays that fall on the pupil are to sense parallel. And after this manner it is said we perceive distance when we look only with one eye.

7. In this case also it is plain we are not beholden to experience: it being a certain necessary truth that, the nearer the direct rays falling on the eye approach to a parallelism, the farther off is the point of their intersection, or the visible point from whence they flow.

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8. (293)Now, though the accounts here given of perceiving _near_ distance by sight are received for true, and accordingly made use of in determining the apparent places of objects, they do nevertheless seem to me very unsatisfactory, and that for these following reasons:—

9. [_First_(294),] It is evident that, when the mind perceives any idea not immediately and of itself, it must be by the means of some other idea. Thus, for instance, the passions which are in the mind of another are of themselves to me invisible. I may nevertheless perceive them by sight; though not immediately, yet by means of the colours they produce in the countenance. We often see shame or fear in the looks of a man, by perceiving the changes of his countenance to red or pale.

10. Moreover, it is evident that no idea which is not itself perceived can be to me the means of perceiving any other idea. If I do not perceive the redness or paleness of a man’s face themselves, it is impossible I should perceive by them the passions which are in his mind.

11. Now, from sect. ii., it is plain that distance is in its own nature imperceptible, and yet it is perceived by sight(295). It remains, therefore, that it be brought into view by means of some other idea, that is itself immediately perceived in the act of vision.

12. But those lines and angles, by means whereof some men(296) pretend to explain the perception(297) of distance, are themselves not at all perceived; nor are they in truth ever thought of by those unskilful in optics. I appeal to any one’s experience, whether, upon sight of an object, he computes its distance by the bigness of the angle made by the meeting of the two optic axes? or whether he ever thinks of the greater or lesser divergency of the rays which arrive from any point to his pupil? nay, whether it be not perfectly impossible for him to perceive by sense the various angles wherewith the rays, according to their greater or lesser divergence, do fall on the eye? Every one is himself the best judge of what he perceives, and what not. In vain shall any man(298) tell me, that I perceive certain lines and angles, which introduce into my mind the various ideas of distance, so long as I myself am conscious of no such thing.

13. Since therefore those angles and lines are not themselves perceived by sight, it follows, from sect. x., that the mind does not by them judge of the distance of objects.

14. [_Secondly_(299),] The truth of this assertion will be yet farther evident to any one that considers those lines and angles have no real existence in nature, being only an hypothesis framed by the mathematicians, and by them introduced into optics, that they might treat of that science in a geometrical way.

15. The [_third_ and(300)] last reason I shall give for rejecting that doctrine is, that though we should grant the real existence of those optic angles, &c., and that it was possible for the mind to perceive them, yet these principles would not be found sufficient to explain the phenomena of distance, as shall be shewn hereafter.

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16. Now it being already shewn(301) that distance is _suggested_(302) to the mind, by the mediation of some other idea which is itself perceived in the act of seeing, it remains that we inquire, what ideas or sensations there be that attend vision, unto which we may suppose the ideas of distance are connected, and by which they are introduced into the mind.

And, _first_, it is certain by experience, that when we look at a near object with both eyes, according as it approaches or recedes from us, we alter the disposition of our eyes, by lessening or widening the interval between the pupils. This disposition or turn of the eyes is attended with a sensation(303), which seems to me to be that which in this case brings the idea of greater or lesser distance into the mind.

17. Not that there is any natural or necessary(304) connexion between the sensation we perceive by the turn of the eyes and greater or lesser distance. But—because the mind has, by constant experience, found the different sensations corresponding to the different dispositions of the eyes to be attended each with a different degree of distance in the object—there has grown an habitual or customary connexion between those two sorts of ideas: so that the mind no sooner perceives the sensation arising from the different turn it gives the eyes, in order to bring the pupils nearer or farther asunder, but it withal perceives the different idea of distance which was wont to be connected with that sensation. Just as, upon hearing a certain sound, the idea is immediately suggested to the understanding which custom had united with it(305).

18. Nor do I see how I can easily be mistaken in this matter. I know evidently that distance is not perceived of itself(306); that, by consequence, it must be perceived by means of some other idea, which is immediately perceived, and varies with the different degrees of distance. I know also that the sensation arising from the turn of the eyes is of itself immediately perceived; and various degrees thereof are connected with different distances, which never fail to accompany them into my mind, when I view an object distinctly with both eyes whose distance is so small that in respect of it the interval between the eyes has any considerable magnitude.

19. I know it is a received opinion that, by altering the disposition of the eyes, the mind perceives whether the angle of the optic axes, or the lateral angles comprehended between the interval of the eyes or the optic axes, are made greater or lesser; and that, accordingly, by a kind of natural geometry, it judges the point of their intersection to be nearer or farther off. But that this is not true I am convinced by my own experience; since I am not conscious that I make any such use of the perception I have by the turn of my eyes. And for me to make those judgments, and draw those conclusions from it, without knowing that I do so, seems altogether incomprehensible(307).

20. From all which it follows, that the judgment we make of the distance of an object viewed with both eyes is entirely the result of experience. If we had not constantly found certain sensations, arising from the various disposition of the eyes, attended with certain degrees of distance, we should never make those sudden judgments from them concerning the distance of objects; no more than we would pretend to judge of a man’s thoughts by his pronouncing words we had never heard before.

21. _Secondly_, an object placed at a certain distance from the eye, to which the breadth of the pupil bears a considerable proportion, being made to approach, is seen more confusedly(308). And the nearer it is brought the more confused appearance it makes. And this being found constantly to be so, there arises in the mind an habitual connexion between the several degrees of confusion and distance; the greater confusion still implying the lesser distance, and the lesser confusion the greater distance of the object.

22. This confused appearance of the object doth therefore seem to be the medium whereby the mind judges of distance, in those cases wherein the most approved writers of optics will have it judge by the different divergency with which the rays flowing from the radiating point fall on the pupil(309). No man, I believe, will pretend to see or feel those imaginary angles that the rays are supposed to form, according to their various inclinations on his eye. But he cannot choose seeing whether the object appear more or less confused. It is therefore a manifest consequence from what has been demonstrated that, instead of the greater or lesser divergency of the rays, the mind makes use of the greater or lesser confusedness of the appearance, thereby to determine the apparent place of an object.

23. Nor doth it avail to say there is not any necessary connexion between confused vision and distance great or small. For I ask any man what necessary connexion he sees between the redness of a blush and shame? And yet no sooner shall he behold that colour to arise in the face of another but it brings into his mind the idea of that passion which hath been observed to accompany it.

24. What seems to have misled the writers of optics in this matter is, that they imagine men judge of distance as they do of a conclusion in mathematics; betwixt which and the premises it is indeed absolutely requisite there be an apparent necessary connexion. But it is far otherwise in the sudden judgments men make of distance. We are not to think that brutes and children, or even grown reasonable men, whenever they perceive an object to approach or depart from them, do it by virtue of geometry and demonstration.

25. That one idea may suggest another to the mind, it will suffice that they have been observed to go together, without any demonstration of the _necessity_ of their coexistence, or without so much as knowing what it is that makes them so to coexist. Of this there are innumerable instances, of which no one can be ignorant(310).

26. Thus, greater confusion having been constantly attended with nearer distance, no sooner is the former idea perceived but it suggests the latter to our thoughts. And, if it had been the ordinary course of nature that the farther off an object were placed the more confused it should appear, it is certain the very same perception that now makes us think an object approaches would then have made us to imagine it went farther off; that perception, abstracting from custom and experience, being equally fitted to produce the idea of great distance, or small distance, or no distance at all.

27. _Thirdly_, an object being placed at the distance above specified, and brought nearer to the eye, we may nevertheless prevent, at least for some time, the appearance’s growing more confused, by straining the eye(311). In which case that sensation supplies the place of confused vision, in aiding the mind to judge of the distance of the object; it being esteemed so much the nearer by how much the effort or straining of the eye in order to distinct vision is greater.

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28. I have here(312) set down those sensations or ideas(313) that seem to be the constant and general occasions of introducing into the mind the different ideas of near distance. It is true, in most cases, that divers other circumstances contribute to frame our idea of distance, viz. the particular number, size, kind, &c. of the things seen. Concerning which, as well as all other the forementioned occasions which suggest distance, I shall only observe, they have none of them, in their own nature, any relation or connexion with it: nor is it possible they should ever signify the various degrees thereof, otherwise than as by experience they have been found to be connected with them.

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29. I shall proceed upon these principles to account for a phenomenon which has hitherto strangely puzzled the writers of optics, and is so far from being accounted for by any of their theories of vision, that it is, by their own confession, plainly repugnant to them; and of consequence, if nothing else could be objected, were alone sufficient to bring their credit in question. The whole difficulty I shall lay before you in the words of the learned Doctor Barrow, with which he concludes his _Optic Lectures_(314):—

“Hæc sunt, quæ circa partem opticæ præcipue mathematicam dicenda
mihi suggessit meditatio. Circa reliquas (quæ φυσικώτεραι sunt,
adeoque sæpiuscule pro certis principiis plausibiles conjecturas
venditare necessum habent) nihil fere quicquam admodum verisimile
succurrit, a pervulgatis (ab iis, inquam, quæ Keplerus,
Scheinerus(315), Cartesius, et post illos alii tradiderunt)
alienum aut diversum. Atqui tacere malo, quam toties oblatam
cramben reponere. Proinde receptui cano; nee ita tamen ut prorsus
discedam, anteaquam improbam quandam difficultatem (pro
sinceritate quam et vobis et veritati debeo minime dissimulandam)
in medium protulero, quæ doctrinæ nostræ, hactenus inculcatæ, se
objicit adversam, ab ea saltem nullam admittit solutionem. Illa,
breviter, talis est. Lenti vel speculo cavo _EBF_ exponatur
punctum visibile _A_, ita distans, ut radii ex _A_ manantes ex
inflectione versus axem _AB_ cogantur. Sitque radiationis limes
(seu puncti _A_ imago, qualem supra passim statuimus) punctum _Z_.
Inter hoc autem et inflectentis verticem _B_ uspiam positus
concipiatur oculus. Quæri jam potest, ubi loci debeat punctum _A_
apparere? Retrorsum ad punctum _Z_ videri non fert natura (cum
omnis impressio sensum afficiens proveniat a partibus _A_) ac
experientia reclamat. Nostris autem e placitis consequi videtur,
ipsum ad partes anticas apparens, ab intervallo longissime dissito
(quod et maximum sensibile quodvis intervallum quodammodo
exsuperet), apparere. Cum enim quo radiis minus divergentibus
attingitur objectum, eo (seclusis utique prænotionibus et
præjudiciis) longius abesse sentiatur; et quod parallelos ad
oculum radios projicit, remotissime positum æstimetur: exigere
ratio videtur, ut quod convergentibus radiis apprehenditur, adhuc
magis, si fieri posset, quoad apparentiam elongetur. Quin et circa
casum hunc generatim inquiri possit, quidnam omnino sit, quod
apparentem puncti _A_ locum determinet, faciatque quod constanti
ratione nunc propius, nunc remotius appareat? Cui itidem dubio
nihil quicquam ex hactenus dictorum analogia responderi posse
videtur, nisi debere punctum _A_ perpetuo longissime semotum
videri. Verum experientia secus attestatur, illud pro diversa
oculi inter puncta _B_, _Z_, positione varie distans, nunquam fere
(si unquam) longinquius ipso _A_ libere spectato, subinde vero
multo propinquius adparere; quinimo, quo oculum appellentes radii
magis convergunt, eo speciem objecti propius accedere. Nempe, si
puncto _B_ admoveatur oculus, suo (ad lentem) fere nativo in loco
conspicitur punctum _A_ (vel æque distans, ad speculum); ad _O_
reductus oculus ejusce speciem appropinquantem cernit; ad _P_
adhuc vicinius ipsum existimat; ac ita sensim, donec alicubi
tandem, velut ad _Q_, constituto oculo, objectum summe propinquum
apparens in meram confusionem incipiat evanescere. Quæ sane cuncta
rationibus atque decretis nostris repugnare videntur, aut cum iis
saltem parum amice conspirant. Neque nostram tantum sententiam
pulsat hoc experimentum, at ex æquo cæteras quas norim omnes:
veterem imprimis ac vulgatam, nostræ præ reliquis affinem, ita
convellere videtur, ut ejus vi coactus doctissimus A. Tacquetus
isti principio (cui pene soli totam inædificaverat _Catoptricam_
suam) ceu infido ac inconstanti renunciarit, adeoque suam ipse
doctrinam labefactarit? id tamen, opinor, minime facturus, si rem
totam inspexissit penitius, atque difficultatis fundum attigissit.
Apud me vero non ita pollet hæc, nec eousque præpollebit ulla
difficultas, ut ab iis quæ manifeste rationi consentanea video,
discedam; præsertim quum, ut his accidit, ejusmodi difficultas in
singularis cujuspiam casus disparitate fundetur. Nimirum in
præsente casu peculiare quiddam, naturæ subtilitati involutum,
delitescit, ægre fortassis, nisi perfectius explorato videndi
modo, detegendum. Circa quod nil, fateor, hactenus excogitare
potui, quod adblandiretur animo meo, nedum plane satisfaceret.
Vobis itaque nodum hunc, utinam feliciore conatu, resolvendum
committo.”

_In English as follows_:

“I have here delivered what my thoughts have suggested to me
concerning that part of optics which is more properly
mathematical. As for the other parts of that science (which, being
rather physical, do consequently abound with plausible conjectures
instead of certain principles), there has in them scarce anything
occurred to my observation different from what has been already
said by Kepler, Scheinerus, Des Cartes, &c. And methinks I had
better say nothing at all than repeat that which has been so often
said by others. I think it therefore high time to take my leave of
this subject. But, before I quit it for good and all, the fair and
ingenuous dealing that I owe both to you and to truth obliges me
to acquaint you with a certain untoward difficulty, which seems
directly opposite to the doctrine I have been hitherto
inculcating, at least admits of no solution from it. In short it
is this. Before the double convex glass or concave speculum _EBF_,
let the point _A_ be placed at such a distance that the rays
proceeding from _A_, after refraction or reflection, be brought to
unite somewhere in the axis _AB_. And suppose the point of union
(i.e. the image of the point _A_, as hath been already set forth)
to be _Z_; between which and _B_, the vertex of the glass or
speculum, conceive the eye to be anywhere placed. The question now
is, where the point _A_ ought to appear. Experience shews that it
doth not appear behind at the point _Z_; and it were contrary to
nature that it should; since all the impression which affects the
sense comes from towards _A_. But, from our tenets it should seem
to follow that it would appear before the eye at a vast distance
off, so great as should in some sort surpass all sensible
distance. For since, if we exclude all anticipations and
prejudices, every object appears by so much the farther off by how
much the rays it sends to the eye are less diverging; and that
object is thought to be most remote from which parallel rays
proceed unto the eye; reason would make one think that object
should appear at yet a greater distance which is seen by
converging rays. Moreover, it may in general be asked concerning
this case, what it is that determines the apparent place of the
point _A_, and maketh it to appear after a constant manner,
sometimes nearer, at other times farther off? To which doubt I see
nothing that can be answered agreeable to the principles we have
laid down, except only that the point _A_ ought always to appear
extremely remote. But, on the contrary, we are assured by
experience, that the point _A_ appears variously distant,
according to the different situations of the eye between the
points _B_ and _Z_. And that it doth almost never (if at all) seem
farther off than it would if it were beheld by the naked eye; but,
on the contrary, it doth sometimes appear much nearer. Nay, it is
even certain that by how much the rays falling on the eye do more
converge, by so much the nearer does the object seem to approach.
For, the eye being placed close to the point _B_, the object _A_
appears nearly in its own natural place, if the point _B_ is taken
in the glass, or at the same distance, if in the speculum. The eye
being brought back to _O_, the object seems to draw near; and,
being come to _P_, it beholds it still nearer: and so on by little
and little, till at length the eye being placed somewhere, suppose
at _Q_, the object appearing extremely near begins to vanish into
mere confusion. All which doth seem repugnant to our principles;
at least, not rightly to agree with them. Nor is our tenet alone
struck at by this experiment, but likewise all others that ever
came to my knowledge are every whit as much endangered by it. The
ancient one especially (which is most commonly received, and comes
nearest to mine) seems to be so effectually overthrown thereby
that the most learned Tacquet has been forced to reject that
principle, as false and uncertain, on which alone he had built
almost his whole _Catoptrics_, and consequently, by taking away
the foundation, hath himself pulled down the superstructure he had
raised on it. Which, nevertheless, I do not believe he would have
done, had he but considered the whole matter more thoroughly, and
examined the difficulty to the bottom. But as for me, neither this
nor any other difficulty shall have so great an influence on me,
as to make me renounce that which I know to be manifestly
agreeable to reason. Especially when, as it here falls out, the
difficulty is founded in the peculiar nature of a certain odd and
particular case. For, in the present case something peculiar lies
hid, which, being involved in the subtilty of nature, will perhaps
hardly be discovered till such time as the manner of vision is
more perfectly made known. Concerning which, I must own I have
hitherto been able to find out nothing that has the least show of
probability, not to mention certainty. I shall therefore leave
this knot to be untied by you, wishing you may have better success
in it than I have had.”

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30. The ancient and received principle, which Dr. Barrow here mentions as the main foundation of Tacquet’s(316) _Catoptrics_, is, that every “visible point seen by reflection from a speculum shall appear placed at the intersection of the reflected ray and the perpendicular of incidence.” Which intersection in the present case happening to be behind the eye, it greatly shakes the authority of that principle whereon the aforementioned author proceeds throughout his whole _Catoptrics_, in determining the apparent place of objects seen by reflection from any kind of speculum.

31. Let us now see how this phenomenon agrees with our tenets(317). The eye, the nearer it is placed to the point _B_ in the above figures, the more distinct is the appearance of the object: but, as it recedes to _O_, the appearance grows more confused; and at _P_ it sees the object yet more confused; and so on, till the eye, being brought back to _Z_, sees the object in the greatest confusion of all. Wherefore, by sect. 21, the object should seem to approach the eye gradually, as it recedes from the point _B_; that is, at _O_ it should (in consequence of the principle I have laid down in the aforesaid section) seem nearer than it did at _B_, and at _P_ nearer than at _O_, and at _Q_ nearer than at _P_, and so on, till it quite vanishes at _Z_. Which is the very matter of fact, as any one that pleases may easily satisfy himself by experiment.