An Essay Towards a New Theory of Vision by George Berkeley (1685-1753) CONTENTS Sect. 1 Design 2 Distance of itself invisible 3 Remote distance perceived rather by experience than by sense 4 Near distance thought to be perceived by the ANGLE of the OPTIC AXES 5 Difference between this and the former manner of perceiving distance 6 Also by diverging rays 7 This depends not on experience 8 These the common accounts, but not satisfactory 9 Some IDEAS perceived by the mediation of others 10 No IDEA which is not itself perceived, can be the means of perceiving another 11 Distance perceived by means of some other IDEA 12 Those lines and angles mentioned in optics, are not themselves perceived 13 Hence the mind does not perceive distance by lines and angles 14 Also because they have no real existence 15 And because they are insufficient to explain the phenomena 16 The IDEAS that suggest distance are, 1st, the sensation arising from the turn of the eyes 17 Betwixt which and distance there is no necessary connection 18 Scarce room for mistake in this matter 19 No regard had to the angle of the OPTIC AXES 20 Judgment of distance made with both eyes, the result of EXPERIENCE 21 2ndly, Confusedness of appearance 22 This the occasion of those judgments attributed to diverging rays 23 Objection answered 24 What deceives the writers of optics in this matter 25 The cause why one IDEA may suggest another 26 This applied to confusion and distance 27 Thirrdly, the straining of the eye 28 The occasions which suggest distance have in their own nature no relation to it 29 A difficult case proposed by Dr. Barrow as repugnant to all the known theories 30 This case contradicts a received principle in catoptrics 31 It is shown to agree with the principles we have laid down 32 This phenomenon illustrated 33 It confirms the truth of the principle whereby it is explained 34 Vision when distinct, and when confused 35 The different effects of parallel diverging and converging rays 36 How converging and diverging rays come to suggest the same distance 37 A person extreme purblind would judge aright in the forementioned case 38 Lines and angles, why useful in optics 39 The not understanding this, a cause of mistake 40 A query proposed, by Mr. Molyneux in his DIOPTRICS, considered 41 One born blind would not at first have any IDEA of distance by sight 42 This not agreeable to the common principles 43 The proper objects of sight, not without the mind, nor the images of any thing without the mind 44 This more fully explained 45 In what sense we must be understood to see distance and external things 46 Distance, and things placed at a distance, not otherwise perceived by the eye than by the ear 47 The IDEAS of sight more apt to be confounded with the IDEAS of touch than those of hearing are 48 How this comes to pass 49 Strictly speaking, we never see and feel the same thing 50 Objects of SIGHT twofold, mediate and immediate 51 These hard to separate in our thoughts 52 The received accounts of our perceiving magnitude by sight, false 53 Magnitude perceived as immediately as distance 54 Two kinds of sensible extension, neither of which is infinitely divisible 55 The tangible magnitude of an OBJECT steady, the visible not 56 By what means tangible magnitude is perceived by sight 57 This further enlarged on 58 No necessary connection between confusion or faintness of appearance, and small or great magnitude 59 The tangible magnitude of an OBJECT more heeded than the visible, and why 60 An instance of this 61 Men do not measure by visible feet or inches 62 No necessary connection between visible and tangible extension 63 Greater visible magnitude might signify lesser tangible magnitude 64 The judgments we make of magnitude depend altogether on experience 65 Distance and magnitude seen as shame or anger 66 But we are prone to think otherwise, and why 67 The moon seems greater in the horizon than in the meridian 68 The cause of this phenomenon assigned 69 The horizontal moon, why greater at one time than another. 70 The account we have given proved to be true 71 And confirmed by the moon's appearing greater in a mist 72 Objection answered 73 The way wherein faintness suggests greater magnitude illustrated 74 Appearance of the horizontal moon, why thought difficult to explain 75 Attempts towards the solution of it made by several, but in vain 76 The opinion of Dr. Wallis 77 It is shown to be unsatisfactory 78 How lines and angles may be of use in computing apparent magnitudes 79 One born blind, being made to see, what judgment he would make of magnitude 80 The MINIMUM VISIBLE the same to all creatures 81 Objection answered 82 The eye at all times perceives the same number of visible points 83 Two imperfections in the VISIVE FACULTY 84 Answering to which, we may conceive two perfections 85 In neither of these two ways do microscopes improve the sight 86 The case of microscopical eyes, considered 87 The sight, admirably adapted to the ends of seeing 88 Difficulty concerning erect vision 89 The common way of explaining it 90 The same shown to be false 91 Not distinguishing between IDEAS of sight and touch, cause of mistake in this matter 92 The case of one born blind, proper to be considered 93 Such a one might by touch attain to have IDEAS of UPPER and LOWER 94 Which modes of situation he would attribute only to things tangible 95 He would not at first sight think anything he saw, high or low, erect or inverted 96 This illustrated by an example 97 By what means he would come to denominate visible OBJECTS, high or low, etc. 98 Why he should think those OBJECTS highest, which are painted on the lowest part of his eye, and VICE VERSA 99 How he would perceive by sight, the situation of external objects 100 Our propension to think the contrary, no argument against what has been said 101 Objection 102 Answer 103 An object could not be known at first sight by the colour 104 Nor by the magnitude thereof 105 Nor by the figure 106 In the first act of vision, no tangible thing would be suggested by sight 107 Difficulty proposed concerning number 108 Number of things visible, would not at first sight suggest the like number of things tangible 109 Number the creature of the mind 110 One born blind would not at first sight number visible things as others do 111 The situation of any object determined with respect only to objects of the same sense 112 No distance, great or small, between a visible and tangible thing 113 The not observing this, cause of difficulty in erect vision 114 Which otherwise includes nothing unaccountable 115 What is meant by the picture being inverted 116 Cause of mistake in this matter 117 Images in the eye, not pictures of external objects 118 In what sense they are pictures 119 In this affair we must carefully distinguish between ideas of sight and touch 120 Difficult to explain by words the true Theory of Vision 121 The question, whether there is any IDEA common to sight and touch, stated 122 Abstract extension inquired into 123 It is incomprehensible 124 Abstract extension not the OBJECT of geometry 125 The general IDEA of a triangle, considered 126 Vacuum, or pure space, not common to sight and touch 127 There is no idea, or kind of idea, common to both senses 128 First argument in proof hereof 129 Second argument 130 Visible figure and extension, not distinct IDEAS from colour 131 Third argument 132 Confirmation drawn from Mr. Molyneux's problem of a sphere and a cube, published by Mr. Locke 133 Which is falsely solved, if the common supposition be true 134 More might be said in proof of our tenet, but this suffices 135 Further reflection on the foregoing problem 136 The same thing doth not affect both sight and touch 137 The same idea of motion not common to sight and touch 138 The way wherein we apprehend motion by sight, easily collected from what hath been said 139 QU. How visible and tangible IDEAS came to have the same name if not of the same kind 140 This accounted for without supposing them of the same kind 141 OBJ. That a tangible square is liker to a visible square than to a visible circle 142 ANS. That a visible square is fitter than a visible circle, to represent a tangible square 143 But it doth not hence follow, that a visible square is like a tangible square 144 Why we are more apt to confound visible with tangible IDEAS, than other signs with the things signified 145 Several other reasons hereof, assigned 146 Reluctancy in rejecting any opinion, no argument of its truth 147 Proper objects of vision the language of nature 148 In it there is much admirable, and deserving our attention 149 Question proposed, concerning the object of geometry 150 At first view we are apt to think visible extension the object of geometry 151 Visible extension shown not to be the object of geometry 152 Words may as well be thought the object of geometry, as visible extension 153 It is proposed to inquire, what progress an intelligence that could see, but not feel, might make in geometry 154 He cannot understand those parts which relate to solids, and their surfaces, and lines generated by their section 155 Nor even the elements of plane geometry 156 The proper objects of sight incapable of being managed as geometrical figures 157 The opinion of those who hold plane figures to be the immediate objects of sight, considered 158 Planes no more the immediate objects of sight, than solids 159 Difficult to enter precisely into the thoughts of the above-mentioned intelligence 160 The object of geometry, its not being sufficiently understood, cause of difficulty, and useless labour in that science AN ESSAY TOWARDS A NEW THEORY OF VISION 1. My design is to show the manner wherein we perceive by sight thedistance, magnitude, and situation of OBJECTS. Also to consider thedifference there is betwixt the IDEAS of sight and touch, and whetherthere be any IDEA common to both senses. 2. It is, I think, agreed by all that DISTANCE, of itself andimmediately, cannot be seen. For DISTANCE being a Line directed end-wiseto the eye, it projects only one point in the fund of the eye, whichpoint remains invariably the same, whether the distance be longer orshorter. 3. I find it also acknowledged that the estimate we make of the distanceof OBJECTS considerably remote is rather an act of judgment grounded onEXPERIENCE than of SENSE. For example, when I perceive a great number ofintermediate OBJECTS, such as houses, fields, rivers, and the like, whichI have experienced to take up a considerable space, I thence form ajudgment or conclusion that the OBJECT I see beyond them is at a greatdistance. Again, when an OBJECT appears faint and small, which at a neardistance I have experienced to make a vigorous and large appearance, Iinstantly conclude it to be far off: And this, it is evident, is theresult of EXPERIENCE; without which, from the faintness and littleness Ishould not have inferred anything concerning the distance of OBJECTS. 4. But when an OBJECT is placed at so near a distance as that theinterval between the eyes bears any sensible proportion to it, theopinion of speculative men is that the two OPTIC AXES (the fancy that wesee only with one eye at once being exploded) concurring at the OBJECT dothere make an ANGLE, by means of which, according as it is greater orlesser, the OBJECT is perceived to be nearer or farther off. 5. Betwixt which and the foregoing manner of estimating distance there isthis remarkable difference: that whereas there was no apparent, necessaryconnection between small distance and a large and strong appearance, orbetween great distance and a little and faint appearance, there appears avery necessary connection between an obtuse angle and near distance, andan acute angle and farther distance. It does not in the least depend uponexperience, but may be evidently known by anyone before he hadexperienced it, that the nearer the concurrence of the OPTIC AXES, thegreater the ANGLE, and the remoter their concurrence is, the lesser willbe the ANGLE comprehended by them. 6. There is another way mentioned by optic writers, whereby they willhave us judge of those distances, in respect of which the breadth of thePUPIL hath any sensible bigness: And that is the greater or lesserdivergency of the rays, which issuing from the visible point do fall onthe PUPIL, that point being judged nearest which is seen by mostdiverging rays, and that remoter which is seen by less diverging rays:and so on, the apparent distance still increasing, as the divergency ofthe rays decreases, till at length it becomes infinite, when the raysthat fall on the PUPIL are to sense parallel. And after this manner it issaid we perceive distance when we look only with one eye. 7. In this case also it is plain we are not beholding to experience: itbeing a certain, necessary truth that the nearer the direct rays fallingon the eye approach to a PARALLELISM, the farther off is the point oftheir intersection, or the visible point from whence they flow. 8. I have here set down the common, current accounts that are given ofour perceiving near distances by sight, which, though they areunquestionably received for true by MATHEMATICIANS, and accordingly madeuse of by them in determining the apparent places of OBJECTS, do, nevertheless seem to me very unsatisfactory: and that for these followingreasons:-- 9. FIRST, It is evident that when the mind perceives any IDEA, notimmediately 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 ofthemselves to me invisible. I may nevertheless perceive them by sight, though not immediately, yet by means of the colours they produce in thecountenance. We often see shame or fear in the looks of a man, byperceiving the changes of his countenance to red or pale. 10. Moreover it is evident that no IDEA which is not itself perceived canbe the means of perceiving any other IDEA. If I do not perceive theredness or paleness of a man's face themselves, it is impossible I shouldperceive by them the passions which are in his mind. 11. Now from sect. 2 it is plain that distance is in its own natureimperceptible, and yet it is perceived by sight. It remains, therefore, that it be brought into view by means of some other IDEA that is itselfimmediately perceived in the act of VISION. 12. But those LINES and ANGLES, by means whereof some MATHEMATICIANSpretend to explain the perception of distance, are themselves not at allperceived, nor are they in truth ever thought of by those unskilful inoptics. I appeal to anyone's experience whether upon sight of an OBJECT hecomputes its distance by the bigness of the ANGLE made by the meeting ofthe two OPTIC AXES? Or whether he ever thinks of the greater or lesserdivergency of the rays, which arrive from any point to his PUPIL? Everyoneis himself the best judge of what he perceives, and what not. In vainshall all the MATHEMATICIANS in the world tell me, that I perceive certainLINES and ANGLES which introduce into my mind the various IDEAS ofDISTANCE, so long as I myself am conscious of no such thing. 13. Since, therefore, those ANGLES and LINES are not themselves perceivedby sight, it follows from sect. 10 that the mind doth not by them judgeof the distance of OBJECTS. 14. Secondly, the truth of this assertion will be yet farther evident toanyone that considers those LINES and ANGLES have no real existence innature, being only an HYPOTHESIS framed by the MATHEMATICIANS, and by themintroduced into OPTICS, that they might treat of that science in aGEOMETRICAL way. 15. The third and last reason I shall give for rejecting that doctrine is, that though we should grant the real existence of those OPTIC ANGLES, etc. , and that it was possible for the mind to perceive them, yet theseprinciples would not be found sufficient to explain the PHENOMENA ofDISTANCE, as shall be shown hereafter. 16. Now, it being already shown that distance is suggested to the mind bythe mediation of some other IDEA which is itself perceived in the act ofseeing, it remains that we inquire what IDEAS or SENSATIONS there be thatattend VISION, unto which we may suppose the IDEAS of distance areconnected, and by which they are introduced into the mind. And FIRST, itis certain by experience that when we look at a near OBJECT with botheyes, according as it approaches or recedes from us, we alter thedisposition of our eyes, by lessening or widening the interval betweenthe PUPILS. This disposition or turn of the eyes is attended with asensation, which seems to me to be that which in this case brings theIDEA of greater or lesser distance into the mind. 17. Not that there is any natural or necessary connection between thesensation we perceive by the turn of the eyes and greater or lesserdistance, but because the mind has by constant EXPERIENCE found thedifferent sensations corresponding to the different dispositions of theeyes to be attended each with a different degree of distance in theOBJECT: there has grown an habitual or customary connection between thosetwo sorts of IDEAS, so that the mind no sooner perceives the sensationarising from the different turn it gives the eyes, In order to bring thePUPILS nearer or farther asunder, but it withal perceives the differentIDEA of distance which was wont to be connected with that sensation; justas upon hearing a certain sound, the IDEA is immediately suggested to theunderstanding which custom had united with it. 18 Nor do I see how I can easily be mistaken in this matter. I knowevidently that distance is not perceived of itself. That by consequenceit must be perceived by means of some other IDEA which is immediatelyperceived, and varies with the different degrees of distance. I know alsothat the sensation arising from the turn of the eyes is of itselfimmediately perceived, and various degrees thereof are connected withdifferent distances, which never fail to accompany them into my mind, when I view an OBJECT distinctly with both eyes, whose distance is sosmall that in respect of it the interval between the eyes has anyconsiderable magnitude. 19. I know it is a received opinion that by altering the disposition ofthe eyes the mind perceives whether the angle of the OPTIC AXES is madegreater or lesser. And that accordingly by a kind of NATURALGEOMETRY it judges the point of their intersection to be neareror farther off. But that this is not true I am convinced by my ownexperience, since I am not conscious that I make any such use of theperception I have by the turn of my eyes. And for me to make thosejudgments, and draw those conclusions from it, without knowing that I doso, seems altogether incomprehensible. 20. From all which it follows that the judgment we make of the distanceof an OBJECT, viewed with both eyes, is entirely the RESULT OFEXPERIENCE. If we had not constantly found certain sensations arisingfrom the various disposition of the eyes, attended with certain degreesof distance, we should never make those sudden judgments from themconcerning the distance of OBJECTS; no more than we would pretend tojudge a man's thoughts by his pronouncing words we had never heardbefore. 21. Secondly, an OBJECT placed at a certain distance from the eye, towhich the breadth of the PUPIL bears a considerable proportion, beingmade to approach, is seen more confusedly: and the nearer it is broughtthe more confused appearance it makes. And this being found constantly tobe so, there ariseth in the mind an habitual CONNECTION between theseveral degrees of confusion and distance; the greater confusion stillimplying the lesser distance, and the lesser confusion the greaterdistance of the OBJECT. 22. This confused appearance of the OBJECT doth therefore seem to be theMEDIUM whereby the mind judgeth of distance in those cases wherein themost approved writers of optics will have it judge by the differentdivergency with which the rays flowing from the radiating point fall onthe PUPIL. No man, I believe, will pretend to see or feel those imaginaryangles that the rays are supposed to form according to their variousinclinations on his eye. But he cannot choose seeing whether the OBJECTappear more or less confused. It is therefore a manifest consequence fromwhat bath been demonstrated, that instead of the greater or lesserdivergency of the rays, the mind makes use of the greater or lesserconfusedness of the appearance, thereby to determine the apparent placeof an OBJECT. 23 Nor doth it avail to say there is not any necessary connection betweenconfused VISION and distance, great or small. For I ask any man whatnecessary connection he sees between the redness of a blush and shame? Andyet no sooner shall he behold that colour to arise in the face ofanother, but it brings into his and the IDEA of that passion which hathbeen observed to accompany it. 24. What seems to have misled the writers of optics in this matter isthat they imagine men judge of distance as they do of a conclusion inmathematics, betwixt which and the premises it is indeed absolutelyrequisite there be an apparent, necessary connection: but it is farotherwise in the sudden judgments men make of distance. We are not tothink that brutes and children, or even grown reasonable men, wheneverthey perceive an OBJECT to approach, or depart from them, do it by virtueof GEOMETRY and DEMONSTRATION. 25. That one IDEA may suggest another to the mind it will suffice thatthey have been observed to go together, without any demonstration of thenecessity of their coexistence, or without so much as knowing what it isthat makes them so to coexist. Of this there are innumerable instances ofwhich no one can be ignorant. 26. Thus, greater confusion having been constantly attended with nearerdistance, no sooner is the former IDEA perceived, but it suggests thelatter to our thoughts. And if it had been the ordinary course of Naturethat the farther off an OBJECT were placed, the more confused it shouldappear, it is certain the very same perception that now makes us think anOBJECT approaches would then have made us to imagine it went farther off. That perception, abstracting from CUSTOM and EXPERIENCE, being equallyfitted to produce the IDEA of great distance, or small distance, or nodistance at all. 27. Thirdly, an OBJECT being placed at the distance above specified, andbrought nearer to the eye, we may nevertheless prevent, at least for sometime, the appearances growing more confused, by straining the eye. Inwhich case that sensation supplies the place of confused VISION in aidingthe mind to judge of the distance of the OBJECT; it being esteemed somuch the nearer by how much the effort or straining of the eye in orderto distinct VISION is greater. 28. I have here set down those sensations or IDEAS that seem to be theconstant and general occasions of introducing into the mind the differentIDEAS of near distance. It is true in most cases that divers othercircumstances contribute to frame our IDEA of distance, to wit, theparticular number, size, kind, etc. , of the things seen. Concerningwhich, as well as all other the forementioned occasions which suggestdistance, I shall only observe they have none of them, in their ownnature, any relation or connection with it: nor is it possible they shouldever signify the various degrees thereof, otherwise than as by EXPERIENCEthey have been found to be connected with them. 29. I shall proceed upon these principles to account for a phenomenonwhich has hitherto strangely puzzled the writers of optics, and is so farfrom 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 theircredit in question. The whole difficulty I shall lay before you in thewords of the learned Dr. Barrow, with which he concludes his opticlectures:-- 'I have here delivered what my thoughts have suggested to me concerningthat part of optics which is more properly mathematical. As for the otherparts of that science (which being rather physical, do consequentlyabound with plausible conjectures instead of certain principles), therehas in them scarce anything occurred to my observation different from whathas been already said by Kepler, Scheinerus, Descartes, and others. Andmethinks, I had better say nothing at all, than repeat that which hasbeen so often said by others. I think it therefore high time to take myleave of this subject: but before I quit it for good and all, the fairand ingenuous dealing that I owe both to you and to truth obligeth me toacquaint you with a certain untoward difficulty, which seems directlyopposite to the doctrine I have been hitherto inculcating, at least, admits of no solution from it. In short it is this. Before the doubleconvex glass or concave speculum EBF, let the point A be placed at such adistance that the rays proceeding from A, after refraction or reflection, be brought to unite somewhere in the AxAB. 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 theeye to be anywhere placed. The question now is, where the point A oughtto appear? Experience shows that it does not appear behind at the pointZ, and it were contrary to nature that it should, since all theimpression which affects the sense comes from towards A. But from ourtenets it should seem to follow that it would appear before the eye at avast distance off, so great as should in some sort surpass all sensibledistance. For since if we exclude all anticipations and prejudices, everyOBJECT appears by so much the farther off, by how much the rays it sendsto the eye are less diverging. And that OBJECT is thought to be mostremote from which parallel rays proceed unto the eye. Reason would makeone think that OBJECT should appear at yet a greater distance which isseen by converging rays. Moreover it may in general be asked concerningthis case what it is that determines the apparent place of the point A, and maketh it to appear after a constant manner sometimes nearer, atother times farther off? To which doubt I see nothing that can beanswered agreeable to the principles we have laid down except only thatthe point A ought always to appear extremely remote. But on the contrarywe are assured by experience that the point A appears variously distant, according to the different situations of the eye between the points B andZ. And that it doth never (if at all) seem farther off, than it would ifit were beheld by the naked eye, but on the contrary it doth sometimesappear much nearer. Nay, it is even certain that by how much the raysfalling on the eye do more converge by so much the nearer doth the OBJECTseem to approach. For the eye being placed close to the point B, theOBJECT A appears nearly in its own natural place, if the point B is takenin the glass, or at the same distance, if in the speculum. The eye beingbrought back to O, the OBJECT seems to draw near: and being come to P itbeholds it still nearer. And so on little and little, till at length theeye being placed somewhere, suppose at Q, the OBJECT appearing extremelynear, begins to vanish into mere confusion. All which doth seem repugnantto our principles, at least not rightly to agree with them. Nor is ourtenet alone struck at by this experiment, but likewise all others thatever came to my knowledge are, every whit as much, endangered by it. Theancient one especially (which is most commonly received, and comesnearest to mine) seems to be so effectually overthrown thereby that themost learned Tacquet has been forced to reject that principle, as falseand uncertain, on which alone he had built almost his whole CATOPTRICS;and consequently by taking away the foundation, hath himself pulled downthe superstructure he had raised on it. Which, nevertheless, I do notbelieve he would have done had he but considered the whole matter morethoroughly, and examined the difficulty to the bottom. But as for me, neither this nor any other difficulty shall have so great an influence onme as to make me renounce that which I know to be manifestly agreeable toreason: especially when, as it here falls out, the difficulty is foundedin the peculiar nature of a certain odd and particular case. For in thepresent case something peculiar lies hid, which being involved in thesubtilty of nature will, perhaps, hardly be discovered till such time asthe manner of vision is more perfectly made known. Concerning which, Imust own, I have hitherto been able to find out nothing that has theleast show of PROBABILITY, not to mention CERTAINTY. I shall, therefore, leave this knot to be untied by you, wishing you may have better successin it than I have had. ' 30. The ancient and received principle, which Dr. Barrow here mentions asthe main foundation of Tacquet's CATOPTRICS, is that: 'every visible pointseen by reflection from a speculum shall appear placed at the intersectionof the reflected ray, and the perpendicular of incidence:' whichintersection in the present case, happening to be behind the eye, itgreatly shakes the authority of that principle, whereon theaforementioned author proceeds throughout his whole CATOPTRICS indetermining the apparent place of OBJECTS seen by reflection from any kindof speculum. 31. Let us now see how this phenomenon agrees with our tenets. The eyethe nearer it is placed to the point B in the foregoing figures, the moredistinct is the appearance of the OBJECT; but as it recedes to O theappearance grows more confused; and at P it sees the OBJECT yet moreconfused; and so on till the eye being brought back to Z sees the OBJECTin the greatest confusion of all. Wherefore by sect. 21 the OBJECT shouldseem to approach the eye gradually as it recedes from the point B, thatis, at O it should (in consequence of the principle I have laid down inthe aforesaid section) seem nearer than it did at B, and at P nearer thanat 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 anyone that pleases may easilysatisfy himself by experiment. 32. This case is much the same as if we should suppose an Englishman tomeet a foreigner who used the same words with the English, but in adirect contrary signification. The Englishman would not fail to make awrong judgment of the IDEAS annexed to those sounds in the mind of himthat used them. Just so, in the present case the OBJECT speaks (if I mayso say) with words that the eye is well acquainted with, that is, confusions of appearance; but whereas heretofore the greater confusionswere always wont to signify nearer distances, they have in this case adirect, contrary signification, being connected with the greaterdistances. Whence it follows that the eye must unavoidably be mistaken, since it will take the confusions in the sense it has been used to, whichis directly opposed to the true. 33. This phenomenon as it entirely subverts the opinion of those who willhave us judge of distance by lines and angles, on which supposition it isaltogether inexplicable, so it seems to me no small confirmation of thetruth of that principle whereby it is explained. But in order co a morefull explication of this point, and to show how far the hypothesis of themind's judging by the various divergency of rays may be of use indetermining the apparent place of an OBJECT, it will be necessary topremise some few things, which are already well known to those who haveany skill in dioptrics. 34. FIRST, any radiating point is then distinctly seen when the raysproceeding from it are, by the refractive power of the crystalline, accurately reunited in the retina or fund of the eye: but if they arereunited, either before they arrive at the retina, or after they havepassed it, then there is confused vision. 35. SECONDLY, suppose in the adjacent figures NP represent an eye dulyframed and retaining its natural figure. In Fig. 1 the rays fallingnearly parallel on the eye, are by the crystalline AB refracted, so astheir focus or point of union F falls exactly on the retina: but if therays fall sensibly diverging on the eye, as in Fig. 2, then their focusfalls beyond the retina: or if the rays are made to converge by the lensQS before they come at the eye, as in Fig. 3, their focus F will fallbefore the retina. In which two last cases it is evident from theforegoing section that the appearance of the point Z is confused. And byhow much the greater is the convergency, or divergency, of the raysfalling on the pupil, by so much the farther will the point of theirreunion be from the retina, either before or behind it, and consequentlythe point Z will appear by so much the more confused. And this, by thebye, may show us the difference between confused and faint vision. Confused vision is when the rays proceedings from each distinct point ofthe OBJECT are not accurately recollected in one corresponding point onthe retina, but take up some space thereon, so that rays from differentpoints become mixed and confused together. This is opposed to a distinctvision, and attends near objects. Faint vision is when by reason of thedistance of the object or grossness of the interjacent medium few raysarrive from the object to the eye. This is opposed to vigorous or clearvision, and attends remote objects. But to return. 36. The eye, or (to speak truly) the mind, perceiving only the confusionitself, without ever considering the cause from which it proceeds, dothconstantly annex the same degree of distance to the same degree ofconfusion. Whether that confusion be occasioned by converging or bydiverging rays, it matters not. Whence it follows that the eye viewingthe object Z through the glass QS (which by refraction causeth the raysZQ, ZS, etc. , to converge) should judge it to be at such a nearness atwhich if it were placed it would radiate on the eye with rays divergingto that degree as would produce the same confusion which is now producedby converging rays, i. E. Would cover a portion of the retina equal to DC(VID. Fig. 3 supra). But then this must be understood (to use Dr. Barrow's phrase) SECLUSIS PRAENOTIONIBUS ET PRAEJUDICIIS, in case weabstract from all other circumstances of vision, such as the figure, size, faintness, etc. Of the visible objects; all which do ordinarilyconcur to form our idea of distance, the mind having by frequentexperience observed their several sorts or degrees to be connected withvarious distances. 37. It plainly follows from what hath been said that a person perfectlypurblind (i. E. That could not see an object distinctly but when placedclose to his eye) would not make the same wrong judgment that others doin the forementioned case. For to him greater confusions constantlysuggesting greater distances, he must, as he recedes from the glass andthe object grows more confused, judge it to be at a farther distance, contrary to what they do who have had the perception of the objectsgrowing more confused connected with the idea of approach. 38. Hence also it doth appear there may be good use of computation bylines and angles in optics; not that the mind judgeth of distanceimmediately by them, but because it judgeth by somewhat which isconnected with them, and to the determination whereof they may besubservient. Thus the mind judging of the distance of an object by theconfusedness of its appearance, and this confusedness being greater orlesser to the naked eye, according as the object is seen by rays more orless diverging, it follows that a man may make use of the divergency ofthe rays in computing the apparent distance, though not for its own sake, yet on account of the confusion with which it is connected. But, so itis, the confusion itself is entirely neglected by mathematicians ashaving no necessary relation with distance, such as the greater or lesserangles of divergency are conceived to have. And these (especially forthat they fall under mathematical computation) are alone regarded indetermining the apparent places of objects, as though they were the soleand immediate cause of the judgments the mind makes of distance. Whereas, in truth, they should not at all be regarded in themselves, or anyotherwise, than as they are supposed to be the cause of confused vision. 39. The not considering of this has been a fundamental and perplexingoversight. For proof whereof we need go no farther than the case beforeus. It having been observed that the most diverging rays brought into themind the idea of nearest distance, and that still, as the divergencydecreased, the distance increased: and it being thought the connexionbetween the various degrees of divergency and distance was immediate;this naturally leads one to conclude, from an ill-grounded analogy, thatconverging rays shall make an object appear at an immense distance: andthat, as the convergency increases, the distance (if it were possible)should do so likewise. That this was the cause of Dr. Barrow's mistake isevident from his own words which we have quoted. Whereas had the learneddoctor observed that diverging and converging rays, how opposite soeverthey may seem, do nevertheless agree in producing the same effect, towit, confusedness of vision, greater degrees whereof are producedindifferently, either as the divergency or convergency and the raysincreaseth. And that it is by this effect, which is the same in both, that either the divergency or convergency is perceived by the eye; I say, had he but considered this, it is certain he would have made a quitecontrary judgment, and rightly concluded that those rays which fall onthe eye with greater degrees of convergency should make the object fromwhence they proceed appear by so much the nearer. But it is plain it wasimpossible for any man to attain to a right notion of this matter so longas he had regard only to lines and angles, and did not apprehend the truenature of vision, and how far it was of mathematical consideration. 40. Before we dismiss this subject, it is fit we take notice of a queryrelating thereto, proposed by the ingenious Mr. Molyneux, is his TREATISEOF DIOPTRICS, [Par. I. Prop. 31, Sect. 9. ] where speaking of thisdifficulty, he has these words: 'And so he (i. E. Dr. Barrow) leaves thisdifficulty to the solution of others, which I (after so great an example)shall do likewise; but with the resolution of the same admirable author ofnot quitting the evident doarine which we have before laid down, fordetermining the LOCUS OBJECTI, on account of being pressed by onedifficulty which seems inexplicable till a more intimate knowledge of thevisive faculty be obtained by mortals. In the meantime, I propose it tothe consideration of the ingenious, whether the LOCUS APPARENS of anobject placed as in this 9th section be not as much before the eye as thedistinct base is behind the eye!' To which query we may venture to answerin the negative. For in the present case the rule for determining thedistance of the distinct base, or respective focus from the glass, is this:as the difference between the distance of the object and focus is to thefocus or focal length, so the distance of the object from the glass is tothe distance of the respective focus or distinct base from the glass. [Molyneux Dioptr. , Par. I. Prop. 5. ] Let us now suppose the object to beplaced at the distance of the focal length, and one half of the focallength from the glass, and the eye close to the glass, hence it will followby the rule that the distance of the distinct base behind the eye is doublethe true distance of the object before the eye. If therefore Mr. Molyneux'sconjecture held good, it would follow that the eye should see the objecttwice as far off as it really is; and in other cases at three or four timesits due distance, or more. But this manifestly contradicts experience, theobject never appearing, at farthest, beyond its due distance. Whatever, therefore, is built on this supposition (VID. COROL. I. PROP. 57, IBID. )comes to the ground along with it. 41. From what hath been premised it is a manifest consequence that a manborn blind, being made to see, would, at first, have no idea of distanceby sight; the sun and stars, the remotest objects as well as the nearer, would all seem to be in his eye, or rather in his mind. The objectsintromitted by sight would seem to him (as in truth they are) no otherthan a new set of thoughts or sensations, each whereof is as near to himas the perceptions of pain or pleasure, or the most inward passions ofhis soul. For our judging objects provided by sight to be at anydistance, or without the mind, is (VID. Sect. 28) entirely the effect ofexperience, which one in those circumstances could not yet have attainedto. 42. It is indeed otherwise upon the common supposition that men judge ofdistance by the angle of the optic axes, just as one in the dark, or ablind-man by the angle comprehended by two sticks, one whereof he held ineach hand. For if this were true, it would follow that one blind from hisbirth being made to see, should stand in need of no new experience inorder to perceive distance by sight. But that this is false has, I think, been sufficiently demonstrated. 43. And perhaps upon a strict inquiry we shall not find that even thosewho from their birth have grown up in a continued habit of seeing areirrecoverably prejudiced on the other side, to wit, in thinking what theysee to be at a distance from them. For at this time it seems agreed onall hands, by those who have had any thoughts of that matter, thatcolours, which are the proper and immediate object of sight, are notwithout the mind. But then it will be said, by sight we have also theideas of extension, and figure, and motion; all which may well be thoughtwithout, and at some distance from the mind, though colour should not. Inanswer to this I appeal to any man's experience, whether the visibleextension of any object doth not appear as near to him as the colour ofthat object; nay, whether they do not both seem to be in the very sameplace. Is not the extension we see coloured, and is it possible for us, so much as in thought, to separate and abstract colour from extension?Now, where the extension is there surely is the figure, and there themotion too. I speak of those which are perceived by sight. 44. But for a fuller explication of this point, and to show that theimmediate objects of sight are not so much as the ideas or resemblancesof things placed at a distance, it is requisite that we look nearer intothe matter and carefully observe what is meant in common discourse, whenone says that which he sees is at a distance from him. Suppose, forexample, that looking at the moon I should say it were fifty or sixtysemidiameters of the earth distant from me. Let us see what moon this isspoken of: it is plain it cannot be the visible moon, or anything likethe visible moon, or that which I see, which is only a round, luminousplane of about thirty visible points in diameter. For in case I amcarried from the place where I stand directly towards the moon, it ismanifest the object varies, still as I go on; and by the time that I amadvanced fifty or sixty semidiameters of the earth, I shall be so farfrom being near a small, round, luminous flat that I shall perceivenothing like it; this object having long since disappeared, and if Iwould recover it, it must be by going back to the earth from whence I setout. Again, suppose I perceive by sight the faint and obscure idea ofsomething which I doubt whether it be a man, or a tree, or a tower, butjudge it to be at the distance of about a mile. It is plain I cannot meanthat what I see is a mile off, or that it is the image or likeness ofanything which is a mile off, since that every step I take towards it theappearance alters, and from being obscure, small, and faint, grows clear, large, and vigorous. And when I come to the mile's end, that which I sawfirst is quite lost, neither do I find anything in the likeness of it. 45. In these and the like instances the truth of the matter stands thus:having of a long time experienced certain ideas, perceivable by touch, asdistance, tangible figure, and solidity, to have been connected withcertain ideas of sight, I do upon perceiving these ideas of sightforthwith conclude what tangible ideas are, by the wonted ordinary courseof Nature like to follow. Looking at an object I perceive a certainvisible figure and colour, with some degree of faintness and othercircumstances, which from what I have formerly observed, determine me tothink that if I advance forward so many paces or miles, I shall beaffected with such and such ideas of touch: so that in truth andstrictness of speech I neither see distance itself, nor anything that Itake to be at a distance. I say, neither distance nor things placed at adistance are themselves, or their ideas, truly perceived by sight. This Iam persuaded of, as to what concerns myself: and I believe whoever willlook narrowly into his own thoughts and examine what he means by sayinghe sees this or that thing at a distance, will agree with me that what hesees only suggests to his understanding that after having passed acertain distance, to be measured by the motion of his body, which isperceivable by touch, he shall come to perceive such and such tangibleideas which have been usually connected with such and such visible ideas. But that one might be deceived by these suggestions of sense, and thatthere is no necessary connexion between visible and tangible ideassuggested by them, we need go no farther than the next looking-glass orpictures to be convinced. Note that when I speak of tangible ideas, Itake the word idea for any the immediate object of sense orunderstanding, in which large signification it is commonly used by themoderns. 46. From what we have shown it is a manifest consequence that the ideasof space, outness, and things placed at a distance are not, strictlyspeaking, the object of sight; they are not otherwise perceived by theeye than by the ear. Sitting in my study I hear a coach drive along thestreet; I look through the casement and see it; I walk out and enter intoit; thus, common speech would incline one to think I heard, saw, andtouched the same thing, to wit, the coach. It is nevertheless certain, the ideas intromitted by each sense are widely different and distinctfrom each other; but having been observed constantly to go together, theyare spoken of as one and the same thing. By the variation of the noise Iperceive the different distances of the coach, and know that itapproaches before I look out. Thus by the ear I perceive distance, justafter the same manner as I do by the eye. 47. I do not nevertheless say I hear distance in like manner as I saythat I see it, the ideas perceived by hearing not being so apt to beconfounded with the ideas of touch as those of sight are. So likewise aman is easily convinced that bodies and external things are not properlythe object of hearing; but only sounds, by the mediation whereof the ideaof this or that body or distance is suggested to his thoughts. But thenone is with more difficulty brought to discern the difference there isbetwixt the ideas of sight and touch: though it be certain a man no moresees and feels the same thing than he hears and feels the same thing. 48. One reason of which seems to be this. It is thought a great absurdityto imagine that one and the same thing should have any more than oneextension, and one figure. But the extension and figure of a body, beinglet into the mind two ways, and that indifferently either by sight ortouch, it seems to follow that we see the same extension and the samefigure which we feel. 49. But if we take a close and accurate view of things, it must beacknowledged that we never see and feel one and the same object. Thatwhich is seen is one thing, and that which is felt is another. If thevisible figure and extension be not the same with the tangible figure andextension, we are not to infer that one and the same thing has diversextensions. The true consequence is that the objects of sight and touchare two distinct things. It may perhaps require some thought rightly toconceive this distinction. And the difficulty seems not a littleincreased, because the combination of visible ideas hath constantly thesame name as the combination of tangible ideas wherewith it is connected:which doth of necessity arise from the use and end of language. 50. In order therefore to treat accurately and unconfusedly of vision, wemust bear in mind that there are two sorts of objects apprehended by theeye, the one primarily and immediately, the other secondarily and byintervention of the former. Those of the first sort neither are, norappear to be, without the mind, or at any distance off; they may indeedgrow greater or smaller, more confused, or more clear, or more faint, butthey do not, cannot approach or recede from us. Whenever we say an objectis at a distance, whenever we say it draws near, or goes farther off, wemust always mean it of the latter sort, which properly belong to thetouch, and are not so truly perceived as suggested by the eye in likemanner as thoughts by the ear. 51. No sooner do we hear the words of a familiar language pronounced inour ears, but the ideas corresponding thereto present themselves to ourminds: in the very same instant the sound and the meaning enter theunderstanding: so closely are they united that it is not in our power tokeep out the one, except we exclude the other also. We even act in allrespects as if we heard the very thoughts themselves. So likewise thesecondary objects, or those which are only suggested by sight, do oftenmore strongly affect us, and are more regarded than the proper objects ofthat sense; along with which they enter into the mind, and with whichthey have a far more strict connexion, than ideas have with words. Henceit is we find it so difficult to discriminate between the immediate andmediate objects of sight, and are so prone to attribute to the formerwhat belongs only to the latter. They are, as it were, most closelytwisted, blended, and incorporated together. And the prejudice isconfirmed and riveted in our thoughts by a long tract of time, by the useof language, and want of reflexion. However, I believe anyone that shallattentively consider what we have already said, and shall say, upon thissubject before we have done (especially if he pursue it in his ownthoughts) may be able to deliver himself from that prejudice. Sure I amit is worth some attention, to whoever would understand the true natureof vision. 52. I have now done with distance, and proceed to show how it is that weperceive by sight the magnitude of objects. It is the opinion of somethat we do it by angles, or by angles in conjunction with distance: butneither angles nor distance being perceivable by sight, and the things wesee being in truth at no distance from us, it follows that as we haveshown lines and angles not to be the medium the mind makes use of inapprehending the apparent place, so neither are they the medium wherebyit apprehends the apparent magnitude of objects. 53. It is well known that the same extension at a near distance shallsubtend a greater angle, and at a farther distance a lesser angle. And bythis principle (we are told) the mind estimates the magnitude of anobject, comparing the angle under which it is seen with its distance, andthence inferring the magnitude thereof. What inclines men to this mistake(beside the humour of making one see by geometry) is that the sameperceptions or ideas which suggest distance do also suggest magnitude. But if we examine it we shall find they suggest the latter as immediatelyas the former. I say, they do not first suggest distance, and then leaveit to the judgment to use that as a medium whereby to collect themagnitude; but they have as close and immediate a connexion with themagnitude as with the distance; and suggest magnitude as independently ofdistance as they do distance independently of magnitude. All which willbe evident to whoever considers what hath been already said, and whatfollows. 54. It hath been shown there are two sorts of objects apprehended bysight; each whereof hath its distinct magnitude, or extension. The one, properly tangible, i. E. To be perceived and measured by touch, and notimmediately falling under the sense of seeing: the other, properly andimmediately visible, by mediation of which the former is brought in view. Each of these magnitudes are greater or lesser, according as they containin them more or fewer points, they being made up of points or minimums. For, whatever may be said of extension in abstract, it is certain sensibleextension is not infinitely divisible. There is a MINIMUM TANGIBILE and aMINIMUM VISIBILE, beyond which sense cannot perceive. This everyone'sexperience will inform him. 55. The magnitude of the object which exists without the mind, and is ata distance, continues always invariably the same: but the visible objectstill changing as you approach to, or recede from, the tangible object, it hath no fixed and determinate greatness. Whenever, therefore, we speakof the magnitude of anything, for instance a tree or a house, we mustmean the tangible magnitude, otherwise there can be nothing steady andfree from ambiguity spoken of it. But though the tangible and visiblemagnitude in truth belong to two distinct objects: I shall nevertheless(especially since those objects are called by the same name, and areobserved to coexist), to avoid tediousness and singularity of speech, sometimes speak of them as belonging to one and the same thing. 56. Now in order to discover by what means the magnitude of tangibleobjects is perceived by sight. I need only reflect on what passes in myown mind, and observe what those things be which introduce the ideas ofgreater or lesser into my thoughts, when I look on any object. And theseI find to be, FIRST, the magnitude or extension of the visible object, which being immediately perceived by sight, is connected with that otherwhich is tangible and placed at a distance. SECONDLY, the confusion ordistinctness. And thirdly, the vigorousness or faintness of the aforesaidvisible appearance. CETERIS PARIBUS, by how much the greater or lesserthe visible object is, by so much the greater or lesser do I conclude thetangible object to be. But, be the idea immediately perceived by sightnever so large, yet if it be withal confused, I judge the magnitude ofthe thing to be but small. If it be distinct and clear, I judge itgreater. And if it be faint, I apprehend it to be yet greater. What ishere meant by confusion and faintness hath been explained in sect. 35. 57. Moreover the judgments we make of greatness do, in like manner asthose of distance, depend on the disposition of the eye, also on thefigure, number, and situation of objects and other circumstances thathave been observed to attend great or small tangible magnitudes. Thus, for instance, the very same quantity of visible extension, which in thefigure of a tower doth suggest the idea of great magnitude, shall in thefigure of a man suggest the idea of much smaller magnitude. That this isowing to the experience we have had of the usual bigness of a tower and aman no one, I suppose, need be told. 58. It is also evident that confusion or faintness have no more anecessary connexion with little or great magnitude than they have withlittle or great distance. As they suggest the latter, so they suggest theformer to our minds. And by consequence, if it were not for experience, we should no more judge a faint or confused appearance to be connectedwith great or little magnitude, than we should that it was connected withgreat or little distance. 59. Nor will it be found that great or small visible magnitude hath anynecessary relation to great or small tangible magnitude: so that the onemay certainly be inferred from the other. But before we come to the proofof this, it is fit we consider the difference there is betwixt theextension and figure which is the proper object of touch, and that otherwhich is termed visible; and how the former is principally, though notimmediately taken notice of, when we look at any object. This has beenbefore mentioned, but we shall here inquire into the cause thereof. Weregard the objects that environ us in proportion as they are adapted tobenefit or injure our own bodies, and thereby produce in our minds thesensation of pleasure or pain. Now bodies operating on our organs, by animmediate application, and the hurt or advantage arising therefrom, depending altogether on the tangible, and not at all on the visible, qualities of any object: this is a plain reason why those should beregarded by us much more than these: and for this end the visive senseseems to have been bestowed on animals, to wit, that by the perception ofvisible ideas (which in themselves are not capable of affecting or anywise altering the frame of their bodies) they may be able to foresee(from the experience they have had what tangible ideas are connected withsuch and such visible ideas) and damage or benefit which is like toensue, upon the application of their own bodies to this or that bodywhich is at a distance. Which foresight, how necessary it is to thepreservation of an animal, everyone's experience can inform him. Hence itis that when we look at an object, the tangible figure and extensionthereof are principally attended to; whilst there is small heed taken ofthe visible figure and magnitude, which, though more immediatelyperceived, do less concern us, and are not fitted to produce anyalteration in our bodies. 60. That the matter of fact is true will be evident to anyone whoconsiders that a man placed at ten foot distance is thought as great asif he were placed at a distance only of five foot: which is true not withrelation to the visible, but tangible greatness of the object: thevisible magnitude being far greater at one station: than it is at theother. 61. Inches, feet, etc. , are settled stated lengths whereby we measureobjects and estimate their magnitude: we say, for example, an objectappears to be six inches or six foot long. Now, that this cannot be meantof visible inches, etc. , is evident, because a visible inch is itself noconstant, determinate magnitude, and cannot therefore serve to mark outand determine the magnitude of any other thing. Take an inch marked upona ruler: view it, successively, at the distance of half a foot, a foot, afoot and a half, etc. , from the eye: at each of which, and at all theintermediate distances, the inch shall have a different visibleextension, i. E. There shall be more or fewer points discerned in it. NowI ask which of all these various extensions is that stated, determinateone that is agreed on for a common measure of other magnitudes? No reasoncan be assigned why we should pitch on one more than another: and exceptthere be some invariable, determinate extension fixed on to be marked tothe word inch, it is plain it can be used to little purpose; and to say athing contains this or that number of inches shall imply no more thanthat it is extended, without bringing any particular idea of thatextension into the mind. Farther, an inch and a foot, from differentdistances, shall both exhibit the same visible magnitude, and yet at thesame time you shall say that one seems several times greater than theother. From all which it is manifest that the judgments we make of themagnitude of objects by sight are altogether in reference to theirtangible extension. Whenever we say an object is great, or small, of thisor that determinate measure, I say it must be meant of the tangible, andnot the visible extension, which, though immediately perceived, isnevertheless little taken notice of. 62. Now, that there is no necessary connexion between these two distinctextensions is evident from hence: because our eyes might have been framedin such a manner as to be able to see nothing but what were less than theMINIMUM TANGIBILE. In which case it is not impossible we might haveperceived all the immediate objects of sight, the very same that we donow: but unto those visible appearances there would not be connectedthose different tangible magnitudes that are now. Which shows thejudgments we make of the magnitude of things placed at a distance fromthe various greatness of the immediate objects of sight do not arise fromany essential or necessary but only a customary tie, which has beenobserved between them. 63. Moreover, it is not only certain that any idea of sight might nothave been connected with this or that idea of touch, which we now observeto accompany it: but also that the greater visible magnitudes might havebeen connected with, and introduced into our minds lesser tangiblemagnitudes and the lesser visible magnitudes greater tangible magnitudes. Nay, that it actually is so we have daily experience; that object whichmakes a strong and large appearance, not seeming near so great asanother, the visible magnitude whereof is much less, but more faint, andthe appearance upper, or which is the same thing painted lower on theRETINA, which faintness and situation suggest both greater magnitude andgreater distance. 64. From which, and from sect. 57 and 58, it is manifest that as we donot perceive the magnitudes of objects immediately by sight, so neitherdo we perceive them by the mediation of anything which has a necessaryconnexion with them. Those ideas that now suggest unto us the variousmagnitudes of external objects before we touch them, might possibly havesuggested no such thing: or they might have signified them in a directcontrary manner: so that the very same ideas, on the perception whereofwe judge an object to be small, might as well have served to make usconclude it great. Those ideas being in their own nature equally fittedto bring into our minds the idea of small or great, or no size at all ofoutward objects; just as the words of any language are in their ownnature indifferent to signify this or that thing or nothing at all. 65. As we see distance, so we see magnitude. And we see both in the sameway that we see shame or anger in the looks of a man. Those passions arethemselves invisible, they are nevertheless let in by the eye along withcolours and alterations of countenance, which are the immediate object ofvision: and which signify them for no other reason than barely becausethey have been observed to accompany them. Without which experience weshould no more have taken blushing for a sign of shame than of gladness. 66. We are nevertheless exceeding prone to imagine those things which areperceived only by the mediation of others to be themselves the immediateobjects of sight; or, at least, to have in their own nature a fitness tobe suggested by them, before ever they had been experienced to coexistwith them. From which prejudice everyone, perhaps, will not find it easyto emancipate himself, by any [but] the clearest convictions of reason. And there are some grounds to think that if there was one only invariableand universal languages in the world, and that men were born with thefaculty of speaking it, it would be the opinion of many that the ideas ofother men's minds were properly perceived by the ear, or had at least anecessary and inseparable tie with the sounds that were affixed to them. All which seems to arise from want of a due application of our discerningfaculty, thereby to discriminate between the ideas that are in ourunderstandings, and consider them apart from each other; which wouldpreserve us from confounding those that are different, and make us seewhat ideas do, and what do not include or imply this or that other idea. 67. There is a celebrated phenomenon, the solution whereof I shallattempt to give by the principles that have been laid down, in referenceto the manner wherein we apprehend by sight the magnitude of objects. Theapparent magnitude of the moon when placed in the horizon is much greaterthan when it is in the meridian, though the angle under which thediameter of the moon is seen be not observed greater in the former casethan in the latter: and the horizontal moon doth not constantly appear ofthe same bigness, but at some times seemeth far greater than at others. 68. Now in order to explain the reason of the moon's appearing greaterthan ordinary in the horizon, it must be observed that the particleswhich compose our atmosphere intercept the rays of light proceeding fromany object to the eye; and by how much the greater is the portion ofatmosphere interjacent between the object and the eye, by so much themore are the rays intercepted; and by consequence the appearance of theobject rendered more faint, every object appearing more vigorous or morefaint in proportion as it sendeth more or fewer rays into the eye. Nowbetween the eye and the moon, when situated in the horizon, there lies afar greater quantity of atmosphere than there does when the moon is inthe meridian. Whence it comes to pass that the appearance of thehorizontal moon is fainter, and therefore by sect. 56 it should bethought bigger in that situation than in the meridian, or in any otherelevation above the horizon. 69. Farther, the air being variously impregnated, sometimes more andsometimes less, with vapours and exhalations fitted to retund andintercept the rays of light, it follows that the appearance of thehorizontal moon hath not always an equal faintness, and by consequencethat luminary, though in the very same situation, is at one time judgedgreater than at another. 70. That we have here given the true account of the phenomena of thehorizontal moon will, I suppose, be farther evident to anyone from thefollowing considerations. FIRST, it is plain that which in this casesuggests the idea of greater magnitude must be something which is itselfperceived; for that which is unperceived cannot suggest to our perceptionany other thing. SECONDLY, it must be something that does not constantlyremain the same, but is subject to some change or variation, since theappearance of the horizontal moon varies, being at one time greater thanat another. And yet, THIRDLY, it cannot be the visible figure ormagnitude, since that remains the same, or is rather lesser, by how muchthe moon is nearer to the horizon. It remains therefore that the truecause is that affection or alteration of the visible appearance whichproceeds from the greater paucity of rays arriving at the eye, and whichI term FAINTNESS: since this answers all the forementioned conditions, and I am not conscious of any other perception that doth. 71. Add to this that in misty weather it is a common observation that theappearance of the horizontal moon is far larger than usual, which greatlyconspires with and strengthens our opinion. Neither would it prove in theleast irreconcilable with what we have said, if the horizontal moonshould chance sometimes to seem enlarged beyond its usual extent, even inmore serene weather. For we must not only have regard to the mist whichhappens to be in the place where we stand; we ought also to take into ourthoughts the whole sum of vapours and exhalations which lie betwixt theeye and the moon: all which cooperating to render the appearance of themoon more faint, and thereby increase its magnitude, it may chance toappear greater than it usually does, even in the horizontal position, ata time when, though there be no extraordinary fog or haziness, just inthe place where we stand, yet the air between the eye and the moon, takenall together, may be loaded with a greater quantity of interspersedvapours and exhalations than at other times. 72. It may be objected that in consequence of our principles theinterposition of a body in some degree opaque, which may intercept agreat part of the rays of light, should render the appearance of the moonin the meridian as large as when it is viewed in the horizon. To which Ianswer, it is not faintness anyhow applied that suggests greatermagnitude, there being no necessary but only an experimental connexionbetween those two things. It follows that the faintness which enlargesthe appearance must be applied in such sort, and with such circumstances, as have been observed to attend the vision of great magnitudes. When froma distance we behold great objects, the particles of the intermediate airand vapours, which are themselves unperceivable, do interrupt the rays oflight, and thereby render the appearance less strong and vivid: now, faintness of appearance caused in this sort hath been experienced tocoexist with great magnitude. But when it is caused by the interpositionof an opaque sensible body, this circumstance alters the case, so that afaint appearance this way caused doth not suggest greater magnitude, because it hath not been experienced to coexist with it. 73. Faintness, as well as all other ideas or perceptions which suggestmagnitude or distance, doth it in the same way that words suggest thenotions to which they are annexed. Now, it is known a word pronouncedwith certain circumstances, or in a certain context with other words, hath not always the same import and signification that it hath whenpronounced in some other circumstances or different context of words. Thevery same visible appearance as to faintness and all other respects, ifplaced on high, shall not suggest the same magnitude that it would if itwere seen at an equal distance on a level with the eye. The reasonwhereof is that we are rarely accustomed to view objects at a greatheight; our concerns lie among things situated rather before than aboveus, and accordingly our eyes are not placed on the top of our heads, butin such a position as is most convenient for us to see distant objectsstanding in our way. And this situation of them being a circumstancewhich usually attends the vision of distant objects, we may from henceaccount for (what is commonly observed) an object's appearing ofdifferent magnitude, even with respect to its horizontal extension, onthe top of a steeple, for example, an hundred feet high to one standingbelow, from what it would if placed at an hundred feet distance on alevel with his eye. For it hath been shown that the judgment we make onthe magnitude of a thing depends not on the visible appearance alone, butalso on divers other circumstances, any one of which being omitted orvaried may suffice to make some alteration in our judgment. Hence, thecircumstances of viewing a distant object in such a situation as isusual, and suits with the ordinary posture of the head and eyes beingomitted, and instead thereof a different situation of the object, whichrequires a different posture of the head taking place, it is not to bewondered at if the magnitude be judged different: but it will be demandedwhy an high object should constantly appear less than an equidistant lowobject of the same dimensions, for so it is observed to be: it may indeedbe granted that the variation of some circumstances may vary the judgmentmade on the magnitude of high objects, which we are less used to look at:but it does not hence appear why they should be judged less rather thangreater? I answer that in case the magnitude of distant objects wassuggested by the extent of their visible appearance alone, and thoughtproportional thereto, it is certain they would then be judged much lessthan now they seem to be (VIDE sect. 79). But several circumstancesconcurring to form the judgment we make on the magnitude of distantobjects, by means of which they appear far larger than others, whosevisible appearance hath an equal or even greater extension; it followsthat upon the change or omission of any of those circumstances which arewont to attend the vision of distant objects, and so come to influencethe judgments made on their magnitude, they shall proportionably appearless than otherwise they would. For any of those things that caused anobject to be thought greater than in proportion to its visible extensionbeing either omitted or applied without the usual circumstances, thejudgment depends more entirely on the visible extension, and consequentlythe object must be judged less. Thus in the present case the situation ofthe thing seen being different from what it usually is in those objectswe have occasion to view, and whose magnitude we observe, it follows thatthe very same object, being an hundred feet high, should seem less thanif it was an hundred feet off on (or nearly on) a level with the eye. What has been here set forth seems to me to have no small share incontributing to magnify the appearance of the horizontal moon, anddeserves not to be passed over in the explication of it. 74. If we attentively consider the phenomenon before us, we shall findthe not discerning between the mediate and immediate objects of sight tobe the chief cause of the difficulty that occurs in the explication ofit. The magnitude of the visible moon, or that which is the proper andimmediate object of vision, is not greater when the moon is in thehorizon than when it is in the meridian. How comes it, therefore, to seemgreater in one situation than the other? What is it can put this cheat onthe understanding? It has no other perception of the moon than what itgets by sight: and that which is seen is of the same extent, I say, thevisible appearance hath the same, or rather a less, magnitude when themoon is viewed in the horizontal than when in the meridional position:and yet it is esteemed greater in the former than in the latter. Hereinconsists the difficulty, which doth vanish and admit of a most easysolution, if we consider that as the visible moon is not greater in thehorizon than in the meridian, so neither is it thought to be so. It hathbeen already shown that in any act of vision the visible objectabsolutely, or in itself, is little taken notice of, the mind stillcarrying its view from that to some tangible ideas which have beenobserved to be connected with it, and by that means come to be suggestedby it. So that when a thing is said to appear great or small, or whateverestimate be made of the magnitude of any thing, this is meant not of thevisible but of the tangible object. This duly considered, it will be nohard matter to reconcile the seeming contradiction there is, that themoon should appear of a different bigness, the visible magnitude thereofremaining still the same. For by sect. 56 the very same visibleextension, with a different faintness, shall suggest a different tangibleextension. When therefore the horizontal moon is said to appear greaterthan the meridional moon, this must be understood not of a greatervisible extension, but a of greater tangible or real extension, which byreason of the more than ordinary faintness of the visible appearance, issuggested to the mind along with it. 75. Many attempts have been made by learned men to account for thisappearance. Gassendus, Descartes, Hobbes, and several others haveemployed their thoughts on that subject; but how fruitless andunsatisfactory their endeavours have been is sufficiently shown in THETRANSACTIONS, [Phil. Trans. Num. 187. P. 314] where you maysee their several opinions at large set forth and confuted, not withoutsome surprize at the gross blunders that ingenious men have been forcedinto by endeavouring to reconcile this appearance with the ordinaryPrinciples of optics. Since the writing of which there hath been publishedin the TRANSACTIONS [Numb. 187. P. 323] another paper relating to the sameaffair by the celebrated Dr. Wallis, wherein he attempts to account forthat phenomenon which, though it seems not to contain anything new ordifferent from what had been said before by others, I shall neverthelessconsider in this place. 76. His opinion, in short, is this; we judge not of the magnitude of anobject by the visual angle alone, but by the visual angle in conjunctionwith the distance. Hence, though the angle remain the same, or evenbecome less, yet if withal the distance seem to have been increased, theobject shall appear greater. Now, one way whereby we estimate thedistance of anything is by the number and extent of the intermediateobjects: when therefore the moon is seen in the horizon, the variety offields, houses, etc. , together with the large prospect of the wideextended land or sea that lies between the eye and the utmost limb of thehorizon, suggest unto the mind the idea of greater distance, andconsequently magnify the appearance. And this, according to Dr. Wallis, is the true account of the extraordinary largeness attributed by the mindto the horizontal moon at a time when the angle subtended by its diameteris not one jot greater than it used to be. 77. With reference to this opinion, not to repeat what hath been alreadysaid concerning distance, I shall only observe, FIRST, that if theprospect of interjacent objects be that which suggests the idea offarther distance, and this idea of farther distance be the cause thatbrings into the mind the idea of greater magnitude, it should hencefollow that if one looked at the horizontal moon from behind a wall, itwould appear no bigger than ordinary. For in that case the wallinterposing cuts off all that prospect of sea and land, etc. Which mightotherwise increase the apparent distance, and thereby the apparentmagnitude of the moon. Nor will it suffice to say the memory doth eventhen suggest all that extent of land, etc. , which lies within thehorizon; which suggestion occasions a sudden judgment of sense that themoon is farther off and larger than usual. For ask any man who, from sucha station beholding the horizontal moon, shall think her greater thanusual, whether he hath at that time in his mind any idea of theintermediate objects, or long tract of land that lies between his eye andthe extreme edge of the horizon? And whether it be that idea which is thecause of his making the aforementioned judgment? He will, I suppose, reply in the negative, and declare the horizontal moon shall appeargreater than the meridional, though he never thinks of all or any ofthose things that lie between him and it. SECONDLY, it seems impossibleby this hypothesis to account for the moon's appearing in the very samesituation at one time greater than at another; which nevertheless hasbeen shown to be very agreeable to the principles we have laid down, andreceives a most easy and natural explication from them. For the furtherclearing' up of this point it is to be observed that what we immediatelyand properly see are only lights and colours in sundry situations andshades and degrees of faintness and clearness, confusion anddistinctness. All which visible objects are only in the mind, nor do theysuggest ought external, whether distance or magnitude, otherwise than byhabitual connexion as words do things. We are also to remark that, besidethe straining of the eyes, and beside the vivid and faint, the distinctand confused appearances (which, bearing some proportion to lines andangles, have been substituted instead of them in the foregoing part ofthis treatise), there are other means which suggest both distance andmagnitude; particularly the situation of visible points of objects, asupper or lower; the one suggesting a farther distance and greatermagnitude, the other a nearer distance and lesser magnitude: all which isan effect only of custom and experience; there being really nothingintermediate in the line of distance between the uppermost and lowermost, which are both equidistant, or rather at no distance from the eye, asthere is also nothing in upper or lower, which by necessary connexionshould suggest greater or lesser magnitude. Now, as these customary, experimental means of suggesting distance do likewise suggest magnitude, so they suggest the one as immediately as the other. I say they do not(VIDE sect. 53) first suggest distance, and then leave the mind fromthence to infer or compute magnitude, jut suggest magnitude asimmediately and directly as they suggest distance. 78. This phenomenon of the horizontal moon is a clear instance of theinsufficiency of lines and angles for explaining the way wherein the mindperceives and estimates the magnitude of outward objects. There isnevertheless a use of computation by them in order to determine theapparent magnitude of things, so far as they have a connexion with, andare proportional to, those other ideas or perceptions which are the trueand immediate occasions that suggest to the mind the apparent magnitudeof things. But this in general may, I think, be observed concerningmathematical computation in optics: that it can never be very precise andexact since the judgments we make of the magnitude of external things dooften depend on several circumstances, which are not proportionable to, or capable of being defined by, lines and angles. 79. From what has been said we may safely deduce this consequence; towit, that a man born blind and made to see would, at first opening of hiseyes, make a very different judgment of the magnitude of objectsintromitted by them from what others do. He would not consider the ideasof sight with reference to, or as having any connexion with, the ideas oftouch: his view of them being entirely terminated within themselves, hecan no otherwise judge them great or small than as they contain a greateror lesser number of visible points. Now, it being certain that anyvisible point can cover or exclude from view only one other visiblepoint, it follows that whatever object intercepts the view of anotherhath an equal number of visible points with it; and consequently theyshall both be thought by him to have the same magnitude. Hence it isevident one in those circumstances would judge his thumb, with which hemight hide a tower or hinder its being seen, equal to that tower, or hishand, the interposition whereof might conceal experimental means thefirmament from his view, equal to the firmament: how great an inequalitysoever there may in our apprehensions seem to be betwixt those twothings, because of the customary and close connexion that has grown up inour minds between the objects of sight and touch; whereby the verydifferent and distinct ideas of those two senses are so blended andconfounded together as to be mistaken for one and the same thing; out ofwhich prejudice we cannot easily extricate ourselves. 80. For the better explaining the nature of vision, and setting themanner wherein we perceive magnitudes in a due light, I shall proceed tomake some observations concerning matters relating thereto, whereof thewant of reflexion, and duly separating between tangible and visibleideas, is apt to create in us mistaken and confused notions. And FIRST, Ishall observe that the MINIMUM VISIBILE is exactly equal in all beingswhatsoever that are endowed with the visive faculty. No exquisiteformation of the eye, no peculiar sharpness of sight, can make it less inone creature than in another; for it not being distinguishable intoparts, nor in any wise a consisting of them, it must necessarily be thesame to all. For suppose it otherwise, and that the MINIMUM VISIBILE of amite, for instance, be less than the MINIMUM VISIBILE of a man: thelatter therefore may by detraction of some part be made equal to theformer: it doth therefore consist of parts, which is inconsistent withthe notion of a MINIMUM VISIBILE or point. 81. It will perhaps be objected that the MINIMUM VISIBILE of a man dothreally and in itself contain parts whereby it surpasses that of a mite, though they are not perceivable by the man. To which I answer, theMINIMUM VISIBILE having (in like manner as all other the proper andimmediate objects of sight) been shown not to have any existence withoutthe mind of him who sees it, it follows there cannot be any pan of itthat is not actually perceived, and therefore visible. Now for any objectto contain distinct visible parts, and at the same time to be a MINIMUMVISIBILE, is a manifest contradiction. 82. Of these visible points we see at all times an equal number. It isevery whit as great when our view is contracted and bounded by nearobjects as when it is extended to larger and remoter. For it beingimpossible that one MINIMUM VISIBILE should obscure or keep out of sightmote than one other, it is a plain consequence that when my view is onall sides bounded by the walls of my study see just as many visiblepoints as I could, in case that by the removal of the study-walls and allother obstructions, I had a full prospect of the circumjacent fields, mountains, sea, and open firmament: for so long as I am shut up withinthe walls, by their interposition every point of the external objects iscovered from my view: but each point that is seen being able to cover orexclude from sight one only other corresponding point, it follows thatwhilst my sight is confined to those narrow walls I see as many points, or MINIMA VISIBILIA, as I should were those walls away, by looking on allthe external objects whose prospect is intercepted by them. Whenevertherefore we are said to have a greater prospect at one time thananother, this must be understood with relation, not to the proper andimmediate, but the secondary and mediate objects of vision, which, ashath been shown, properly belong to the touch. 83. The visive faculty considered with reference to its immediate objectsmay be found to labour of two defects. FIRST, in respect of the extent ornumber of visible points that are at once perceivable by it, which isnarrow and limited to a certain degree. It can take in at one view but acertain determinate number of MINIMA VISIBILIA, beyond which it cannotextend its prospect. Secondly, our sight is defective in that its view isnot only narrow, but also for the most part confused: of those thingsthat we take in at one prospect we can see but a few at once clearly andunconfusedly: and the more we fix our sight on any one object, by so muchthe darker and more indistinct shall the rest appear. 84. Corresponding to these two defects of sight, we may imagine as manyperfections, to wit, 1ST, that of comprehending in one view a greaternumber of visible points. 2DLY, of being able to view them all equallyand at once with the utmost clearness and distinction. That thoseperfections are not actually in some intelligences of a different orderand capacity from ours it is impossible for us to know. 85. In neither of those two ways do microscopes contribute to theimprovement of sight; for when we look through a microscope we neithersee more visible points, nor are the collateral points more distinct thanwhen we look with the naked eye at objects placed in a due distance. Amicroscope brings us, as it were, into a new world: it presents us with anew scene of visible objects quite different from what we behold with thenaked eye. But herein consists the most remarkable difference, to wit, that whereas the objects perceived by the eye alone have a certainconnexion with tangible objects, whereby we are taught to foresee whatwill ensue upon the approach or application of distant objects to theparts of our own body, which much conduceth to its preservation, there isnot the like connexion between things tangible and those visible objectsthat are perceived by help of a fine microscope. 86. Hence it is evident that were our eyes turned into the nature ofmicroscopes, we should not be much benefited by the change; we should bedeprived of the forementioned advantage we at present receive by thevisive faculty, and have left us only the empty amusement of seeing, without any other benefit arising from it. But in that case, it willperhaps be said, our sight would be endued with a far greater sharpnessand penetration than it now hath. But it is certain from what we havealready shown that the MINIMUM VISIBILE is never greater or lesser, butin all cases constantly the same: and in the case of microscopical eyes Isee only this difference, to wit, that upon the ceasing of a certainobservable connexion betwixt the divers perceptions of sight and touch, which before enabled us to regulate our actions by the eye, it would nowbe rendered utterly unserviceable to that purpose. 87. Upon the whole it seems that if we consider the use and end of sight, together with the present state and circumstances of our being, we shallnot find any great cause to complain of any defect or imperfection in it, or easily conceive how it could be mended. With such admirable wisdom isthat faculty contrived, both for the pleasure and convenience of life. 88. Having finished what I intended to say concerning the distance andmagnitude of objects, I come now to treat of the manner wherein the mindperceives by sight their situation. Among the discoveries of the lastage, it is reputed none of the least that the manner of vision hath beenmore clearly explained than ever it had been before. There is at this dayno one ignorant that the pictures of external objects are painted on theRETINA, or fund of the eye: that we can see nothing which is not sopainted: and that, according as the picture is more distinct or confused, so also is the perception we have of the object: but then in thisexplication of vision there occurs one mighty difficulty. The objects arepainted in an inverted order on the bottom of the eye: the upper part ofany object being painted on the lower part of the eye, and the lower partof the object on the upper part of the eye: and so also as to right andleft. Since therefore the pictures are thus inverted, it is demanded howit comes to pass that we see the objects erect and in their naturalposture? 89. In answer to this difficulty we are told that the mind, perceiving animpulse of a ray of light on the upper part of the eye, considers thisray as coming in a direct line from the lower part of the object; and inlike manner tracing the ray that strikes on the lower part of the eye, itis directed to the upper part of the object. Thus in the adjacent figure, C, the lower point of the object ABC, is projected on C the upper part ofthe eye. So likewise the highest point A is projected on A the lowestpart of the eye, which makes the representation CBA inverted: but themind considering the stroke that is made on C as coming in the straightline CC from the lower end of the object; and the stroke or impulse on aas coming in the line AA from the upper end of the object, is directed tomake a right judgment of the situation of the object ABC, notwithstandingthe picture of it is inverted. This is illustrated by conceiving a blindman who, holding in his hands two sticks that cross each other, doth withthem touch the extremities of an object, placed in a perpendicularsituation. It is certain this man will judge that to be the upper part ofthe object which he touches with the stick held in the undermost hand, and that to be the lower part of the object which he touches with thestick in his uppermost hand. This is the common explication of the erectappearance of objects, which is generally received and acquiesced in, being (as Mr. Molyneux tells us [Diopt. Par. 2. C. 7. P. 289. ]) 'allowedby all men as satisfactory'. 90. But this account to me does not seem in any degree true. Did Iperceive those impulses, decussations, and directions of the rays oflight in like manner as hath been set forth, then indeed it would not bealtogether void of probability. And there might be some pretence for thecomparison of the blind man and his cross sticks. But the case is farotherwise. I know very well that I perceive no such thing. And ofconsequence I cannot thereby make an estimate of the situation ofobjects. I appeal to anyone's experience, whether he be conscious tohimself that he thinks on the intersection made by the radious [SIC]pencils, or pursues the impulses they give in right lines, whenever heperceives by sight the position of any object? To me it seems evidentthat crossing and tracing of the rays is never thought on by children, idiots, or in truth by any other, save only those who have appliedthemselves to the study of optics. And for the mind to judge of thesituation of objects by those things without perceiving them, or toperceive them without knowing it, is equally beyond my comprehension. Addto this that the explaining the manner of vision by the example of crosssticks and hunting for the object along the axes of the radious pencils, doth suppose the proper objects of sight to be perceived at a distancefrom us, contrary to what hath been demonstrated. 91. It remains, therefore, that we look for some other explication ofthis difficulty: and I believe it not impossible to find one, provided weexamine it to the bottom, and carefully distinguish between the ideas ofsight and touch; which cannot be too oft inculcated in treating ofvision: but more especially throughout the consideration of this affairwe ought to carry that distinction in our thoughts: for that from want ofa right understanding thereof the difficulty of explaining erect visionseems chiefly to arise. 92. In order to disentangle our minds from whatever prejudices we mayentertain with relation to the subject in hand, nothing seems moreapposite than the taking into our thoughts the case of one born blind, and afterwards, when grown up, made to see. And though, perhaps, it maynot be an easy task to divest ourselves entirely of the experiencereceived from sight, so as to be able to put our thoughts exactly in theposture of such a one's, we must, nevertheless, as far as possible, endeavour to frame true conceptions of what might reasonably be supposedto pass in his mind. 93. It is certain that a man actually blind, and who had continued sofrom his birth, would by the sense of feeling attain to have ideas ofupper and lower. By the motion of his hand he might discern the situationof any tangible object placed within his FI reach. That part on which hefelt himself supported, or towards which he perceived his body togravitate, he would term lower, and the contrary to this upper; andaccordingly denominate whatsoever objects he touched. 94. But then, whatever judgments he makes concerning the situation ofobjects are confined to those only that are perceivable by touch. Allthose things that are intangible and of a spiritual nature, his thoughtsand desires, his passions, and in general all the modifications of thesoul, to these he would never apply the terms UPPER and LOWER, exceptonly in a metaphorical sense. He may, perhaps, by way of allusion, speakof high or low thoughts: but those terms in their proper significationwould never be applied to anything that was not conceived to existwithout the mind. For a man born blind, and remaining in the same state, could mean nothing else by the words HIGHER and LOWER than a greater orlesser distance from the earth; which distance he would measure by themotion or application of his hand or some other part of his body. It istherefore evident that all those things which, in respect of each other, would by him be thought higher or lower, must be such as were conceivedto exist without his mind, in the ambient space. 95. Whence it plainly follows that such a one, if we suppose him made tosee, would not at first sight think anything he saw was high or low, erect or inverted; for it hath been already demonstrated in sect. 41 thathe would not think the things he perceived by sight to be at any distancefrom him, or without his mind. The objects to which he had hitherto beenused to apply the terms UP and DOWN, HIGH and LOW, were such only asaffected or were some way perceived by his couch: but the proper objectsof vision make a new set of ideas, perfectly distinct and different fromthe former, and which can in no sort make themselves perceived by touch. There is, therefore, nothing at all that could induce him to think thoseterms applicable to them: nor would he ever think it till such time as hehad observed their connexion with tangible objects, and the sameprejudice began to insinuate itself into his understanding, which fromtheir infancy had grown up in the understandings of other men. 96. To set this matter in a clearer light I shall make use of an example. Suppose the above-mentioned blind person by his touch perceives a man tostand erect. Let us inquire into the manner of this. By the applicationof his hand to the several parts of a human body he had perceiveddifferent tangible ideas, which being collected into sundry complex ones, have distinct names annexed to them. Thus one combination of a certaintangible figure, bulk, and consistency of parts is called the head, another the hand, a third the foot, and so of the rest: all which complexideas could, in his understanding, be made up only of ideas perceivableby touch. He had also by his touch obtained an idea of earth or ground, towards which he perceives the parts of his body to have a naturaltendency. Now, by ERECT nothing more being meant than that perpendicularposition of a man wherein his feet are nearest to the earth, if the blindperson by moving his hand over the parts of the man who stands before himperceives the tangible ideas that compose the head to be farthest from, and those that compose the feet to be nearest to, that other combinationof tangible ideas which he calls earth, he will denominate that manerect. But if we suppose him on a sudden to receive his sight, and thathe behold a man standing before him, it is evident in that case he wouldneither judge the man he sees to be erect nor inverted; for he neverhaving known those terms applied to any other save tangible things, orwhich existed in the space without him, and what he sees neither beingtangible nor perceived as existing without, he could not know that inpropriety of language they were applicable to it. 97. Afterwards, when upon turning his head or eyes up and down to theright and left he shall observe the visible objects to change, and shallalso attain to know that they are called by the same names, and connectedwith the objects perceived by touch; then indeed he will come to speak ofthem and their situation, in the same terms that he has been used toapply to tangible things; and those that he perceives by turning up hiseyes he will call upper, and those that by turning down his eyes he willcall lower. 98. And this seems to me the true reason why he should think thoseobjects uppermost that are painted on the lower part of his eye: for byturning the eye up they shall be distinctly seen; as likewise those thatare painted on the highest part of the eye shall be distinctly seen byturning the eye down, and are for that reason esteemed lowest; for wehave shown that to the immediate objects of sight considered inthemselves, he would not attribute the terms HIGH and LOW. It musttherefore be on account of some circumstances which are observed toattend them: and these, it is plain, are the actions of turning the eyeup and down, which suggest a very obvious reason why the mind shoulddenominate the objects of sight accordingly high or low. And without thismotion of the eye, this turning it up and down in order to discerndifferent objects, doubtless ERECT, INVERSE, and other the like termsrelating to the position of tangible objects, would never have beentransferred, or in any degree apprehended to belong to the ideas ofsight: the mere act of seeing including nothing in it to that purpose;whereas the different situations of the eye naturally direct the mind tomake a suitable judgment of the situation of objects intromitted by it. 99. Farther, when he has by experience learned the connexion there isbetween the several ideas of sight and touch, he will be able, by theperception he has of the situation of visible things in respect of oneanother, to make a sudden and true estimate of the situation of outward, tangible things corresponding to them. And thus it is he shall perceiveby sight the situation of external objects which do not properly fallunder that sense. 100. I know we are very prone to think that, if just made to see, weshould judge of the situation of visible things as we do now: but we arealso as prone to think that, at first sight, we should in the same wayapprehend the distance and magnitude of objects as we do now: which hathbeen shown to be a false and groundless persuasion. And for the likereasons the same censure may be passed on the positive assurance thatmost men, before they have thought sufficiently of the matter, might haveof their being able to determine by the eye at first view, whetherobjects were erect or inverse. 101. It will, perhaps, be objected co our opinion that a man, forinstance, being thought erect when his feet are next the earth, andinverted when his head is next the earth, it doth hence follow that bythe mere act of vision, without any experience or altering the situationof the eye, we should have determined whether he were erect or inverted:for both the earth itself, and the limbs of the man who stands thereon, being equally perceived by sight, one cannot choose seeing what part ofthe man is nearest the earth, and what part farthest from it, i. E. Whether he be erect or inverted. 102. To which I answer, the ideas which constitute the tangible earth andman are entirely different from those which constitute the visible earthand man. Nor was it possible, by virtue of the visive faculty alone, without superadding any experience of touch, or altering the position ofthe eye, ever to have known, or so much as suspected, there had been anyrelation or connexion between them. Hence a man at first view would notdenominate anything he saw earth, or head, or foot; and consequently hecould not tell by the mere act of vision whether the head or feet werenearest the earth: nor, indeed, would we have thereby any thought ofearth or man, erect or inverse, at all: which will be made yet moreevident if we nicely observe, and make a particular comparison between, the ideas of both senses. 103. That which I see is only variety of light and colours. That which Ifeel is hard or soft, hot or cold, rough or smooth. What similitude, whatconnexion have those ideas with these? Or how is it possible that anyoneshould see reason to give one and the same name to combinations of ideasso very different before he had experienced their coexistence? We do notfind there is any necessary connexion betwixt this or that tangiblequality and any colour whatsoever. And we may sometimes perceive colourswhere there is nothing to be felt. All which doth make it manifest thatno man, at first receiving of his sight, would know there was anyagreement between this or that particular object of his sight and anyobject of touch he had been already acquainted with: the colours, therefore, of the head would to him no more suggest the idea of head thanthey would the idea of foot. 104. Farther, we have at large shown (VID. Sect. 63 and 64) there is nodiscoverable necessary connexion between any given visible magnitude andany one particular tangible magnitude; but that it is entirely the resultof custom and experience, and depends on foreign and accidentalcircumstances that we can by the perception of visible extension informourselves what may be the extension of any tangible object connected withit. Hence it is certain that neither the visible magnitude of head orfoot would bring along with them into the mind, at first opening of theeyes, the respective tangible magnitudes of those parts. 105. By the foregoing section it is plain the visible figure of any partof the body hath no necessary connexion with the tangible figure thereof, so as at first sight to suggest it to the mind. For figure is thetermination of magnitude; whence it follows that no visible magnitudehaving in its own nature an aptness to suggest any one particulartangible magnitude, so neither can any visible figure be inseparablyconnected with its corresponding tangible figure: so as of itself and ina way prior to experience, it might suggest it to the understanding. Thiswill be farther evident if we consider that what seems smooth and roundto the touch may to sight, if viewed through a microscope, seem quiteotherwise. 106. From all which laid together and duly considered, we may clearlydeduce this inference. In the first act of vision no idea entering by theeye would have a perceivable connexion with the ideas to which the namesEARTH, MAN, HEAD, FOOT, etc. , were annexed in the understanding of aperson blind from his birth; so as in any sort to introduce them into hismind, or make themselves be called by the same names, and reputed thesame things with them, as afterwards they come to be. 107. There doth, nevertheless, remain one difficulty, which perhaps mayseem to press hard on our opinion, and deserve not to be passed over: forthough it be granted that neither the colour, size, nor figure of thevisible feet have any necessary connexion with the ideas that compose thetangible feet, so as to bring them at first sight into my mind, or makeme in danger of confounding them before I had been used to, and for sometime experienced their connexion: yet thus much seems undeniable, namely, that the number of the visible feet being the same with that of thetangible feet, I may from hence without any experience of sightreasonably conclude that they represent or are connected with the feetrather than the head. I say, it seems the idea of two visible feet willsooner suggest to the mind the idea of two tangible feet than of onehead; so that the blind man upon first reception of the visive facultymight know which were the feet or two, and which the head or one. 108. In order to get clear of this seeming difficulty we need onlyobserve that diversity of visible objects doth not necessarily inferdiversity of tangible objects corresponding to them. A picture paintedwith great variety of colours affects the touch in one uniform manner; itis therefore evident that I do not by any necessary consecution, independent of experience, judge of the number of things tangible fromthe number of things visible. I should not, therefore, at first openingmy eyes conclude that because I see two I shall feel two. How, therefore, can I, before experience teaches me, know that the visible legs, becausetwo, are connected with the tangible legs, or the visible head, becauseone, is connected with the tangible head? The truth is, the things I seeare so very different and heterogeneous from the things I feel that theperception of the one would never have suggested the other to mythoughts, or enabled me to pass the least judgment thereon, until I hadexperienced their connexion. 109. But for a fuller illustration of this matter it ought to beconsidered that number (however some may reckon it amongst the primaryqualities) is nothing fixed and settled, really existing in thingsthemselves. It is entirely the creature of the mind, considering eitheran idea by itself, or any combination of ideas to which it gives onename, and so makes it pass for an unit. According as the mind variouslycombines its ideas the unit varies: and as the unit, so the number, whichis only a collection of units, doth also vary. We call a window one, achimney one, and yet a house in which there are many windows and manychimneys hath an equal right to be called one, and many houses go to themaking of the city. In these and the like, instances it is evident theunit constantly relates to the particular draughts the mind makes of itsideas, to which it affixes names, and wherein it includes more or less asbest suits its own ends and purposes. Whatever, therefore, the mindconsiders as one, that is an unit. Every combination of ideas isconsidered as one thing by the mind, and in token thereof is marked byone name. Now, this naming and combining together of ideas is perfectlyarbitrary, and done by the mind in such sort as experience shows it to bemost convenient: without which our ideas had never been collected intosuch sundry distinct combinations as they now are. 110. Hence it follows that a man born blind and afterwards, when grownup, made to see, would not in the first act of vision parcel out theideas of sight into the same distinct collections that others do, whohave experienced which do regularly coexist and are proper to be bundledup together under one name. He would not, for example, make into onecomplex idea, and thereby esteem an unit, all those particular ideaswhich constitute the visible head or foot. For there can be no reasonassigned why he should do so, barely upon his seeing a man stand uprightbefore him. There crowd into his mind the ideas which compose the visibleman, in company with all the other ideas of sight perceived at the sametime: but all these ideas offered at once to his view, he would notdistribute into sundry distinct combinations till such time as byobserving the motion of the parts of the man and other experiences hecomes to know which are to be separated and which to be collectedtogether. 111. From what hath been premised it is plain the objects of sight andtouch make, if I may so say, two sets of ideas which are widely differentfrom each other. To objects of either kind we indifferently attribute theterms high and low, right and left, and suchlike, denoting the positionor situation of things: but then we must well observe that the positionof any object is determined with respect only to objects of the samesense. We say any object of touch is high or low, according as it is moreor less distant from the tangible earth: and in like manner we denominateany object of sight high or low in proportion as it is more or lessdistant from the visible earth: but to define the situation of visiblethings with relation to the distance they bear from any tangible thing, or VICE VERSA, this were absurd and perfectly unintelligible. For allvisible things are equally in the mind, and take up no part of theexternal space: and consequently are equidistant from any tangible thingwhich exists without the mind. 112. Or rather, to speak truly, the proper objects of sight are at nodistance, neither near nor far, from any tangible thing. For if weinquire narrowly into the matter we shall find that those things only arecompared together in respect of distance which exist after the samemanner, or appertain unto the same sense. For by the distance between anytwo points nothing more is meant than the number of intermediate points:if the given points are visible the distance between them is marked outby the number of the interjacent visible points: if they are tangible, the distance between them is a line consisting of tangible points; but ifthey are one tangible and the other visible, the distance between themdoth neither consist of points perceivable by sight nor by touch, i. E. Itis utterly inconceivable. This, perhaps, will not find an easy admissioninto all men's understanding: however, I should gladly be informedwhether it be not true by anyone who will be at the pains to reflect alittle and apply it home to his thoughts. 113. The not observing what has been delivered in the two last sectionsseems to have occasioned no small part of the difficulty that occurs inthe business of erect appearances. The head, which is painted nearest theearth, seems to be farthest from it: and on the other hand the feet, which are painted farthest from the earth, are thought nearest to it. Herein lies the difficulty, which vanishes if we express the thing moreclearly and free from ambiguity, thus: how comes it that to the eye thevisible head which is nearest the tangible earth seems farthest from theearth, and the visible feet, which are farthest from the tangible earthseem nearest the earth? The question being thus proposed, who sees notthe difficulty is founded on a supposition that the eye, or visivefaculty, or rather the soul by means thereof, should judge of thesituation of visible objects with reference to their distance from thetangible earth? Whereas it is evident the tangible earth is not perceivedby sight: and it hath been shown in the two last preceding sections thatthe location of visible objects is determined only by the distance theybear from one another; and that it is nonsense to talk of distance, faror near, between a visible and tangible thing. 114. If we confine our thoughts to the proper objects of sight, the wholeis plain and easy. The head is painted farthest from, and the feetnearest to, the visible earth; and so they appear to be. What is therestrange or unaccountable in this? Let us suppose the pictures in the fundof the eye to be the immediate objects of the sight. The consequence isthat things should appear in the same posture they are painted in; and isit not so? The head which is seen seems farthest from the earth which isseen; and the feet which are seen seem nearest to the earth, which isseen; and just so they are painted. 115. But, say you, the picture of the man is inverted, and yet theappearance is erect: I ask, what mean you by the picture of the man, or, which is the same thing, the visible man's being inverted? You tell me itis inverted, because the heels are uppermost and the head undermost?Explain me this. You say that by the head's being undermost you mean thatit is nearest to the earth; and by the heels being uppermost that theyare farthest from the earth. I ask again what earth you mean? You cannotmean the earth that is painted on the eye, or the visible earth: for thepicture of the head is farthest from the picture of the earth, and thepicture of the feet nearest to the picture of the earth; and accordinglythe visible head is farthest from the visible earth, and the visible feetnearest to it. It remains, therefore, that you mean the tangible earth, and so determine the situation of visible things with respect to tangiblethings; contrary to what hath been demonstrated in sect. 111 and 112. Thetwo distinct provinces of sight and touch should be considered apart, andas if their objects had no intercourse, no manner of relation one toanother, in point of distance or position. 116. Farther, what greatly contributes to make us mistake in this matteris that when we think of the pictures in the fund of the eye, we imagineourselves looking on the fund of another's eye, or another looking on thefund of our own eye, and beholding the pictures painted thereon. Supposetwo eyes A and B: A from some distance looking on the pictures in B seesthem inverted, and for that reason concludes they are inverted in B: butthis is wrong. There are projected in little on the bottom of A theimages of the pictures of, suppose, man, earth, etc. , which are paintedon B. And besides these the eye B itself, and the objects which environit, together with another earth, are projected in a larger size on A. Now, by the eye A these larger images are deemed the true objects, andthe lesser only pictures in miniature. And it is with respect to thosegreater images that it determines the situation of the smaller images: sothat comparing the little man with the great earth, A judges himinverted, or that the feet are farthest from and the head nearest to thegreat earth. Whereas, if A compare the little man with the little earth, then he will appear erect, i. E. His head shall seem farthest from, andhis feet nearest to, the little earth. But we must consider that B doesnot see two earths as A does: it sees only what is represented by thelittle pictures in A, and consequently shall judge the man erect. For, intruth, the man in B is not inverted, for there the feet are next theearth; but it is the representation of it in A which is inverted, forthere the head of the representation of the picture of the man in B isnext the earth, and the feet farthest from the earth, meaning the earthwhich is without the representation of the pictures in B. For if you takethe little images of the pictures in B, and consider them by themselves, and with respect only to one another, they are all erect and in theirnatural posture. 117. Farther, there lies a mistake in our imagining that the pictures ofexternal objects are painted on the bottom of the eye. It hath been shownthere is no resemblance BETWEEN the ideas of sight and things tangible. It hath likewise been demonstrated that the proper objects of sight donot exist without the mind. Whence it clearly follows that the picturespainted on the bottom of the eye are not the pictures of externalobjects. Let anyone consult his own thoughts, and then say what affinity, what likeness there is between that certain variety and disposition ofcolours which constitute the visible man, or picture of a man, and thatother combination of far different ideas, sensible by touch, whichcompose the tangible man. But if this be the case, how come they to beaccounted pictures or images, since that supposes them to copy orrepresent some originals or other? 118. To which I answer: in the forementioned instance the eye A takes thelittle images, included within the representation of the other eye B, tobe pictures or copies, whereof the archetypes are not things existingwithout, but the larger pictures projected on its own fund: and which byA are not thought pictures, but the originals, or true things themselves. Though if we suppose a third eye C from a due distance to behold the fundof A, then indeed the things projected thereon shall, to C, seem picturesor images in the same sense that those projected on B do to A. 119. Rightly to conceive this point we must carefully distinguish betweenthe ideas of sight and touch, between the visible and tangible eye; forcertainly on the tangible eye nothing either is or seems to be painted. Again, the visible eye, as well as all other visible objects, hath beenshown to exist only in the mind, which perceiving its own ideas, andcomparing them together, calls some PICTURES in respect of others. Whathath been said, being rightly comprehended and laid together, doth, Ithink, afford a full and genuine explication of the erect appearance ofobjects; which phenomenon, I must confess, I do not see how it can beexplained by any theories of vision hitherto made public. 120. In treating of these things the use of language is apt to occasionsome obscurity and confusion, and create in us wrong ideas; for languagebeing accommodated to the common notions and prejudices of men, it isscarce possible to deliver the naked and precise truth without greatcircumlocution, impropriety, and (to an unwary reader) seemingcontradictions; I do therefore once for all desire whoever shall think itworth his while to understand what I have written concerning vision, thathe would not stick in this or that phrase, or manner of expression, butcandidly collect my meaning from the whole sum and tenor of my discourse, and laying aside the words as much as possible, consider the bare notionsthemselves, and then judge whether they are agreeable to truth and hisown experience, or no. 121. We have shown the way wherein the mind by mediation of visible ideasdoth perceive or apprehend the distance, magnitude and situation oftangible objects. We come now to inquire more particularly concerning thedifference between the ideas of sight and touch, which are called by thesame names, and see whether there be any idea common to both senses. Fromwhat we have at large set forth and demonstrated in the foregoing partsof this treatise, it is plain there is no one selfsame numericalextension perceived both by sight and touch; but that the particularfigures and extensions perceived by sight, however they may be called bythe same names and reputed the same things with those perceived by touch, are nevertheless different, and have an existence distinct and separatefrom them: so that the question is not now concerning the same numericalideas, but whether there be any one and the same sort of species of ideasequally perceivable to both senses; or, in other words, whetherextension, figure, and motion perceived by sight are not specificallydistinct from extension, figure, and motion perceived by touch. 122. But before I come more particularly to discuss this matter, I findit proper to consider extension in abstract: for of this there is muchtalk, and I am apt to think that when men speak of extension as being anidea common to two senses, it is with a secret supposition that we cansingle out extension from all other tangible and visible qualities, andform thereof an abstract idea, which idea they will have common both tosight and touch. We are therefore to understand by extension in abstractan idea of extension, for instance, a line or surface entirely strippedof all other sensible qualities and circumstances that might determine itto any particular existence; it is neither black nor white, nor red, norhath it any colour at all, or any tangible quality whatsoever andconsequently it is of no finite determinate magnitude: for that whichbounds or distinguishes one extension from another is some quality orcircumstance wherein they disagree. 123. Now I do not find that I can perceive, imagine, or any wise frame inmy mind such an abstract idea as is here spoken of. A line or surfacewhich is neither black, nor white, nor blue, nor yellow, etc. , nor long, nor short, nor rough, nor smooth, nor square, nor round, etc. , isperfectly incomprehensible. This I am sure of as to myself: how far thefaculties of other men may reach they best can tell. 124. It is commonly said that the object of geometry is abstractextension: but geometry contemplates figures: now, figure is thetermination of magnitude: but we have shown that extension in abstracthath no finite determinate magnitude. Whence it clearly follows that itcan have no figure, and consequently is not the object of geometry. It isindeed a tenet as well of the modern as of the ancient philosophers thatall general truths are concerning universal abstract ideas; withoutwhich, we are told, there could be no science, no demonstration of anygeneral proposition in geometry. But it were no hard matter, did I thinkit necessary to my present purpose, to show that propositions anddemonstrations in geometry might be universal, though they who make themnever think of abstract general ideas of triangles or circles. 125. After reiterated endeavours to apprehend the general idea atriangle, I have found it altogether incomprehensible. And surely ifanyone were able to introduce that idea into my mind, it must be theauthor of the ESSAY CONCERNING HUMAN UNDERSTANDING; he who has so fardistinguished himself from the generality of writers by the clearnessand significancy of what he says. Let us therefore see how thiscelebrated author describes the general or abstract idea of a triangle. 'It must be (says he) neither oblique nor rectangular, neitherequilateral, equicrural, nor scalenum; but all and none of these at once. In effect, it is somewhat imperfect that cannot exist; an idea, whereinsome parts of several different and inconsistent ideas are put together'ESSAY ON HUM. UNDERSTAND. B. Iv. C. 7. S. 9. This is the idea which hethinks needful for the enlargement of knowledge, which is the subject ofmathematical demonstration, and without which we could never come to knowany general proposition concerning triangles. That author acknowledges itdoth 'require some pains and skill to form this general idea of atriangle. ' IBID. But had he called to mind what he says in another place, to wit, 'That ideas of mixed modes wherein any inconsistent ideas are puttogether cannot so much as exist in the mind, i. E. Be conceived. ' VID. B. Iii. C. 10. S. 33. IBID. I say, had this occurred to his thoughts, it isnot improbable he would have owned it above all the pains and skill hewas master of to form the above-mentioned idea of a triangle, which ismade up of manifest, staring contradictions. That a man who laid so greata stress on clear and determinate ideas should nevertheless talk at thisrate seems very surprising. But the wonder will lessen if it beconsidered that the source whence this opinion flows is the prolific wombwhich has brought forth innumerable errors and difficulties in all partsof philosophy and in all the sciences: but this matter, taken in its fullextent, were a subject too comprehensive to be insisted on in this place. And so much for extension in abstract. 126. Some, perhaps, may think pure space, VACUUM, or trine dimension tobe equally the object of sight and touch: but though we have a very greatpropension to think the ideas of outness and space to be the immediateobject of sight, yet, if I mistake not, in the foregoing parts of thisessay that hath been clearly demonstrated to be a mere delusion, arisingfrom the quick and sudden suggestion of fancy, which so closely connectsthe idea of distance with those of sight, that we are apt to think it isitself a proper and immediate object of that sense till reason correctsthe mistake. 127. It having been shown that there are no abstract ideas of figure, andthat it is impossible for us by any precision of thought to frame an ideaof extension separate from all other visible and tangible qualities whichshall be common both to sight and touch: the question now remaining is, whether the particular extensions, figures, and motions perceived bysight be of the same kind with the particular extensions, figures, andmotions perceived by touch? In answer to which I shall venture to laydown the following proposition: THE EXTENSION, FIGURES, AND MOTIONSPERCEIVED BY SIGHT ARE SPECIFICALLY DISTINCT FROM THE IDEAS OF TOUCHCALLED BY THE SAME NAMES, NOR is THERE ANY SUCH THING as ONE IDEA OR KINDOF IDEA COMMON TO BOTH SENSES. This proposition may without muchdifficulty be collected from what hath been said in several places ofthis essay. But because it seems so remote from, and contrary to, thereceived notions and settled opinion of mankind, I shall attempt todemonstrate it more particularly and at large by the following arguments. 128. When upon perception of an idea I range it under this or that sort, it is because it is perceived after the same manner, or because it has alikeness or conformity with, or affects me in the same way as, the ideasof the sort I rank it under. In short, it must not be entirely new, buthave something in it old and already perceived by me. It must, I say, have so much at least in common with the ideas I have before known andnamed as to make me give it the same name with them. But it has been, ifI mistake not, clearly made out that a man born blind would not at firstreception of his sight think the things he saw were of the same naturewith the objects of touch, or had anything in common with them; but thatthey were a new set of ideas, perceived in a new manner, and entirelydifferent from all he had ever perceived before: so that he would notcall them by the same name, nor repute them to be of the same sort withanything he had hitherto known. 129. SECONDLY, light and colours are allowed by all to constitute a sonor species entirely different from the ideas of touch: nor will any man, I presume, say they can make themselves perceived by that sense: butthere is no other immediate object of sight besides light and colours. Itis therefore a direct consequence that there is no idea common to bothsenses. 130. It is a prevailing opinion, even amongst those who have thought andwrit most accurately concerning our ideas and the ways whereby they enterinto the understanding, that something more is perceived by sight thanbarely light and colours with their variations. Mr. Locke termeth sight, 'The most comprehensive of all our senses, conveying to our minds theideas of light and colours, which are peculiar only to that sense; andalso the far different ideas of space, figure, and motion. ESSAY ON HUMANUNDERSTAND. B. Ii. C. 9. S. 9. Space or distance, we have shown, is nototherwise the object of sight than of hearing. VID. Sect. 46. And as forfigure and extension, I leave it to anyone that shall calmly attend tohis own clear and distinct ideas to decide whether he had any ideaintromitted immediately and properly by sight save only light andcolours: or whether it De possible for him to frame in his mind adistinct abstract idea of visible extension or figure exclusive of allcolour: and on the other hand, whether he can conceive colour withoutvisible extension? For my own part, I must confess I am not able toattain so great a nicety of abstraction: in a strict sense, I see nothingbut light and colours, with their several shades and variations. He whobeside these doth also perceive by sight ideas far different and distinctfrom them hath that faculty in a degree more perfect and comprehensivethan I can pretend to. It must be owned that by the mediation of lightand colours other far different ideas are suggested to my mind: but sothey are by hearing, which beside sounds which are peculiar to thatsense, doth by their mediation suggest not only space, figure, andmotion, but also all other ideas whatsoever that can be signified bywords. 131. THIRDLY, it is, I think, an axiom universally received thatquantities of the same kind may be added together and make one entiresum. Mathematicians add lines together: but they do not add a line to asolid, or conceive it as making one sum with a surface: these three kindsof quantity being thought incapable of any such mutual addition, andconsequently of being compared together in the several ways ofproportion, are by then esteemed entirely disparate and heterogeneous. Now let anyone try in his thoughts to add a visible line or surface to atangible line or surface, so as to conceive them making one continued sumor whole. He that can do this may think them homogeneous: but he thatcannot, must by the foregoing axiom think them heterogeneous. A blue anda red line I can conceive added together into one sum and making onecontinued line: but to make in my thoughts one continued line of avisible and tangible line added together is, I find, a task far moredifficult, and even insurmountable: and I leave it to the reflexion andexperience of every particular person to determine for himself. 132. A farther confirmation of our tenet may be drawn from the solutionof Mr. Molyneux's problem, published by Mr. Locke in his ESSAY: which Ishall set down as it there lies, together with Mr. Locke's opinion of it, '"Suppose a man born blind, and now adult, and taught by his touch todistinguish between a cube and a sphere of the same metal, and nighly[SIC] of the same bigness, so as to tell, when he felt one and t'other, which is the cube and which the sphere. Suppose then the cube and sphereplaced on a table, and the blind man to be made to see: QUAERE, whetherby his sight, before he touched them, he could now distinguish and tellwhich is the globe, which the cube?" To which the acute and judiciousproposer answers: "Not. For though he has obtained the experience of howa globe, how a cube, affects his touch, yet he has not yet attained theexperience that what affects his touch so or so must affect his sight soor so: or that a protuberant angle in the cube that pressed his handunequally shall appear to his eye as it doth in the cube. " I agree withthis thinking gentleman, whom I am proud to call my friend, in his answerto this his problem; and am of opinion that the blind man at first sightwould not be able with certainty to say which was the globe, which thecube, whilst he only saw them. ' (ESSAY ON HUMAN UNDERSTANDING, B. Ii. C. 9. S. 8. ) 133. Now, if a square surface perceived by touch be of the same sort witha square surface perceived by sight, it is certain the blind man herementioned might know a square surface as soon as he saw it: it is no morebut introducing into his mind by a new inlet an idea he has been alreadywell acquainted with. Since, therefore, he is supposed to have known byhis touch that a cube is a body terminated by square surfaces, and that asphere is not terminated by square surfaces: upon the supposition that avisible and tangible square differ only IN NUMERO it follows that hemight know, by the unerring mark of the square surfaces, which was thecube, and which not, while he only saw them. We must therefore alloweither that visible extension and figures are specifically distinct fromtangible extension and figures, or else that the solution of this problemgiven by those two thoughtful and ingenious men is wrong. 134. Much more might be laid together in proof of the proposition I haveadvanced: but what has been said is, if I mistake not, sufficient toconvince anyone that shall yield a reasonable attention: and as for thosethat will not be at the pains of a little thought, no multiplication ofwords will ever suffice to make them understand the truth, or rightlyconceive my meaning. 135. I cannot let go the above-mentioned problem without some reflexionon it. It hath been evident that a man blind from his birth would not, atfirst sight, denominate anything he saw by the names he had been used toappropriate to ideas of touch, VID. Sect. 106. Cube, sphere, table arewords he has known applied to things perceivable by touch, but to thingsperfectly intangible he never knew them applied. Those words in theirwonted application always marked out to his mind bodies or solid thingswhich were perceived by the resistance they gave: but there is nosolidity, no resistance or protrusion, perceived by sight. In short, theideas of sight are all new perceptions, to which there be no namesannexed in his mind: he cannot therefore understand what is said to himconcerning them: and to ask of the two bodies he saw placed on the table, which was the sphere, which the cube? were to him a question downrightbantering and unintelligible; nothing he sees being able to suggest tohis thoughts the idea of body, distance, or in general of anything he hadalready known. 136. It is a mistake to think the same thing affects both sight andtouch. If the same angle or square which is the object of touch be alsothe object of vision, what should hinder the blind man at first sightfrom knowing it? For though the manner wherein it affects the sight bedifferent from that wherein it affected his touch, yet, there beingbeside his manner or circumstance, which is new and unknown, the angle orfigure, which is old and known, he cannot choose but discern it. 137. Visible figure and extension having been demonstrated to be of anature entirely different and heterogeneous from tangible figure andextension, it remains that we inquire concerning. Now that visible motionis not of the same sort with tangible motion seems to need no fartherproof, it being an evident corollary from what we have shown concerningthe difference there is between visible and tangible extension: but for amore full and express proof hereof we need only observe that one who hadnot yet experienced vision would not at first sight know motion. Whenceit clearly follows that motion perceivable by sight is of a sort distinctfrom motion perceivable by touch. The antecedent I prove thus: by touchhe could not perceive any motion but what was up or down, to the right orleft, nearer or farther from him; besides these and their severalvarieties or complications, it is impossible he should have any idea ofmotion. He would not therefore think anything to be motion, or give thename motion to any idea which he could not range under some or other ofthose particular kinds thereof. But from sect. 95 it is plain that by themere act of vision he could not know motion upwards or downwards, to theright or left, or in any other possible direction. From which I concludehe would not know motion at all at first sight. As for the idea of motionin abstract, I shall not waste paper about it, but leave it to my readerto make the best he can of it. To me it is perfectly unintelligible. 138. The consideration of motion may furnish a new field for inquiry: butsince the manner wherein the mind apprehends by sight the motion oftangible objects, with the various degrees thereof, may be easilycollected from what hath been said concerning the manner wherein thatsense doth suggest their various distances, magnitudes, and situations, Ishall not enlarge any farther on this subject, but proceed to considerwhat may be alleged, with greatest appearance of reason, against theproposition we have shown to be true. For where there is so muchprejudice to be encountered, a bare and naked demonstration of the truthwill scarce suffice. We must also satisfy the scruples that men may raisein favour of their preconceived notions, show whence the mistake arises, how it came to spread, and carefully disclose and root out those falsepersuasions that an early prejudice might have implanted in the mind. 139. FIRST, therefore, it will be demanded how visible extension andfigures come to be called by the same name with tangible extension andfigures, if they are not of the same kind with them? It must be somethingmore than humour or accident that could occasion a custom so constant anduniversal as this, which has obtained in all ages and nations of theworld, and amongst all ranks of men, the learned as well as theilliterate. 140. To which I answer, we can no more argue a visible and tangiblesquare to be of the same species from their being called by the samename, than we can that a tangible square and the monosyllable consistingof six letters whereby it is marked are of the same species because theyare both called by the same name. It is customary to call written wordsand the things they signify by the same name: for words not beingregarded in their own nature, or otherwise than as they are marks ofthings, it had been superfluous, and beside the design of language, tohave given them names distinct from those of the things marked by them. The same reason holds here also. Visible figures are the marks oftangible figures, and from sect. 59 it is plain that in themselves theyare little regarded, or upon any other score than for their connexionwith tangible figures, which by nature they are ordained to signify. Andbecause this language of nature doth not vary in different ages ornations, hence it is that in all times and places visible figures arecalled by the same names as the respective tangible figures suggested bythem, and not because they are alike or of the same sort with them. 141. But, say you, surely a tangible square is liker to a visible squarethan to a visible circle: it has four angles and as many sides: so alsohas the visible square: but the visible circle has no such thing, beingbounded by one uniform curve without right lines or angles, which makesit unfit to represent the tangible square but very fit to represent thetangible circle. Whence it clearly follows that visible figures arepatterns of, or of the same species with, the respective tangible figuresrepresented by them: that they are like unto them, and of their ownnature fitted to represent them, as being of the same sort: and that theyare in no respect arbitrary signs, as words. 142. I answer, it must be acknowledged the visible square is fitter thanthe visible circle to represent the tangible square, but then it is notbecause it is liker, or more of a species with it, but because thevisible square contains in it several distinct parts, whereby to mark theseveral distinct corresponding parts of a tangible square, whereas thevisible circle doth not. The square perceived by touch hath fourdistinct, equal sides, so also hath it four distinct equal angles. It istherefore necessary that the visible figure which shall be most proper tomark it contain four distinct equal parts corresponding to the four sidesof the tangible square, as likewise four other distinct and equal partswhereby to denote the four equal angles of the tangible square. Andaccordingly we see the visible figures contain in them distinct visibleparts, answering to the distinct tangible parts of the figures signifiedor suggested by them. 143. But it will not hence follow that any visible figure is like unto, or of the same species with, its corresponding tangible figure, unless itbe also shown that not only the number but also the kind of the parts bethe same in both. To illustrate this, I observe that visible figuresrepresent tangible figures much after the same manner that written wordsdo sounds. Now, in this respect words are not arbitrary, it not beingindifferent what written word stands for any sound: but it is requisitethat each word contain in it so many distinct characters as there arevariations in the sound it stands for. Thus the single letter A is properto mark one simple uniform sound; and the word ADULTERY is accommodatedto represent the sound annexed to it, in the formation whereof therebeing eight different collisions or modifications of the air by theorgans of speech, each of which produces a difference of sound, it wasfit the word representing it should consist of as many distinctcharacters, thereby to mark each particular difference or part of thewhole sound. And yet nobody, I presume, will say the single letter a, orthe word ADULTERY, are like unto, or of the same species with, therespective sounds by them represented. It is indeed arbitrary that, ingeneral, letters of any language represent sounds at all: but when thatis once agreed, it is not arbitrary what combination of letters shallrepresent this or that particular sound. I leave this with the reader topursue, and apply it in his own thoughts. 144. It must be confessed that we are not so apt to confound other signswith the things signified, or to think them of the same species, as weare visible and tangible ideas. But a little consideration will show ushow this may be without our supposing them of a like nature. These signsare constant and universal, their connexion with tangible ideas has beenlearnt at our first entrance into the world; and ever since, almost everymoment of our lives, it has been occurring to our thoughts, and fasteningand striking deeper on our minds. When we observe that signs arevariable, and of human institution; when we remember there was a timethey were not connected in our minds with those things they now soreadily suggest; but that their signification was learned by the slowsteps of experience: this preserves us from confounding them. But when wefind the same signs suggest the same things all over the world; when weknow they are not of human institution, and cannot remember that we everlearned their signification, but think that at first sight they wouldhave suggested to us the same things they do now: all this persuades usthey are of the same species as the things respectively represented bythem, and that it is by a natural resemblance they suggest them to ourminds. 145. Add to this that whenever we make a nice survey of any object, successively directing the optic axis to each point thereof, there arecertain lines and figures described by the motion of the head or eye, which being in truth perceived by feeling, do nevertheless so mixthemselves, as it were, with the ideas of sight, that we can scarce thinkbut they appertain to that sense. Again, the ideas of sight enter intothe mind several at once, more distinct and unmingled than is usual inthe other senses beside the touch. Sounds, for example, perceived at thesame instant, are apt to coalesce, if I may so say, into one sound: butwe can perceive at the same time great variety of visible objects, veryseparate and distinct from each other. Now tangible extension being madeup of several distinct coexistent parts, we may hence gather anotherreason that may dispose us to imagine a likeness or an analogy betweenthe immediate objects of sight and touch. But nothing, certainly, dothmore contribute to blend and confound them together than the strict andclose connexion they have with each other. We cannot open our eyes butthe ideas of distance, bodies, and tangible figures are suggested bythem. So swift and sudden and unperceived is the transition from visibleto tangible ideas that we can scarce forbear thinking them equally theimmediate object of vision. 146. The prejudice which is grounded on these, and whatever other causesmay be assigned thereof, sticks so fast that it is impossible withoutobstinate striving and labour of the mind to get entirely clear of it. But then the reluctancy we find in rejecting any opinion can be noargument of its truth to whoever considers what has been already shownwith regard to the prejudices we entertain concerning the distance, magnitude, and situation of objects; prejudices so familiar to our minds, so confirmed and inveterate, as they will hardly give way to the clearestdemonstration. 147. Upon the whole, I think we may fairly conclude that the properobjects of vision constitute an universal language of the Author ofNature, whereby we are instructed how to regulate our actions in order toattain those things that are necessary to the preservation and well-beingof our bodies, as also to avoid whatever may be hurtful and destructiveof them. It is by their information that we are principally guided in allthe transactions and concerns of life. And the manner wherein theysignify and mark unto us the objects which are at a distance is the samewith that of languages and signs of human appointment, which do notsuggest the things signified by any likeness or identity of nature, butonly by an habitual connexion that experience has made us to observebetween them. 148. Suppose one who had always continued blind be told by his guide thatafter he has advanced so many steps he shall come to the brink of aprecipice, or be stopped by a wall; must not this to him seem veryadmirable and surprizing? He cannot conceive how it is possible formortals to frame such predictions as these, which to him would seem asstrange and unaccountable as prophesy doth to others. Even they who areblessed with the visive faculty may (though familiarity make it lessobserved) find therein sufficient cause of admiration. The wonderful artand contrivance wherewith it is adjusted to those ends and purposes forwhich it was apparently designed, the vast extent, number, and variety ofobjects that are at once with so much ease and quickness and pleasuresuggested by it: all these afford subject for much and pleasingspeculation, and may, if anything, give us some glimmering analogousprenotion of things which are placed beyond the certain discovery andcomprehension of our present state. 149. I do not design to trouble myself with drawing corollaries from thedoctrine I have hitherto laid down. If it bears the test others may, sofar as they shall think convenient, employ their thoughts in extending itfarther, and applying it to whatever purposes it may be subservient to:only, I cannot forbear making some inquiry concerning the object ofgeometry, which the subject we have been upon doth naturally lead one to. We have shown there is no such idea as that of extension in abstract, andthat there are two kinds of sensible extension and figures which areentirely distinct and heterogeneous from each other. Now, it is naturalto inquire which of these is the object of geometry. 150. Some things there are which at first sight incline one to thinkgeometry conversant about visible extension. The constant use of theeyes, both in the practical and speculative parts of that science, dothvery much induce us thereto. It would, without doubt, seem odd to amathematician to go about to convince him the diagrams he saw upon paperwere not the figures, or even the likeness of the figures, which make thesubject of the demonstration. The contrary being held an unquestionabletruth, not only by mathematicians, but also by those who apply themselvesmore particularly to the study of logic; I mean, who consider the natureof science, certainty, and demonstration: it being by them assigned asone reason of the extraordinary clearness and evidence of geometry thatin this science the reasonings are free from those inconveniences whichattend the use of arbitrary signs, the very ideas themselves being copiedout and exposed to view upon paper. But, by the bye, how well this agreeswith what they likewise assert of abstract ideas being the object ofgeometrical demonstration I leave to be considered. 151. To come to a resolution in this point we need only observe what hathbeen said in sect. 59, 60, 61, where it is shown that visible extensionsin themselves are little regarded, and have no settled determinablegreatness, and that men measure altogether, by the application oftangible extension to tangible extension. All which makes it evident thatvisible extension and figures are not the object of geometry. 152. It is therefore plain that visible figure are of the same use ingeometry that words are: and the one may as well be accounted the objectof that science as the other, neither of them being otherwise concernedtherein than as they represent or suggest to the mind the particulartangible figures connected with them. There is indeed this differencebetween the signification of tangible figures by visible figures, and ofideas by words: that whereas the latter is variable and uncertain, depending altogether on the arbitrary appointment of men, the former isfixed and immutably the same in all times and places. A visible square, for instance, suggests to the mind the same tangible figure in Europethat it doth in America. Hence it is that the voice of the Author of'Nature which speaks to our eyes, is not liable to that misinterpretationand ambiguity that languages of human contrivance are unavoidably subjectto. 153. Though what has been said may suffice to show what ought to bedetermined with relation to the object of geometry, I shall nevertheless, for the fuller illustration thereof, consider the case of anintelligence, or unbodied spirit, which is supposed to see perfectlywell, i. E. To have a clear perception of the proper and immediate objectsof sight, but to have no sense of touch. Whether there be any such beingin Nature or no is beside my purpose to inquire. It sufficeth that thesupposition contains no contradiction in it. Let us now examine whatproficiency such a one may be able to make in geometry. Which speculationwill lead us more clearly to see whether the ideas of sight can possiblybe the object of that science. 154. FIRST, then, it is certain the aforesaid intelligence could have noidea of a solid, or quantity of three dimensions, which followeth fromits not having any idea of distance. We indeed are prone to think that wehave by sight the ideas of space and solids, which ariseth from ourimagining that we do, strictly speaking, see distance and some parts ofan object at a greater distance than others; which hath been demonstratedto be the effect of the experience we have had, what ideas of touch areconnected with such and such ideas attending vision: but the intelligencehere spoken of is supposed to have no experience of touch. He would not, therefore, judge as we do, nor have any idea of distance, outness, orprofundity, nor consequently of space or body, either immediately or bysuggestion. Whence it is plain he can have no notion of those parts ofgeometry which relate to the mensuration of solids and their convex orconcave surfaces, and contemplate the properties of lines generated bythe section of a solid. The conceiving of any part whereof is beyond thereach of his faculties. 155. Farther, he cannot comprehend the manner wherein geometers describea right line or circle; the rule and compass with their use being thingsof which it is impossible he should have any notion: nor is it an easiermatter for him to conceive the placing of one plane or angle on another, in order to prove their equality: since that supposeth some idea ofdistance or external space. All which makes it evident our pureintelligence could never attain to know so much as the first elements ofplane geometry. And perhaps upon a nice inquiry it will be found hecannot even have an idea of plane figures any more than he can of solids;since some idea of distance is necessary to form the idea of ageometrical plane, as will appear to whoever shall reflect a little onit. 156. All that is properly perceived by the visive faculty amounts to nomore than colours, with their variations and different proportions oflight and shade. But the perpetual mutability and fleetingness of thoseimmediate objects of sight render them incapable of being managed afterthe manner of geometrical figures; nor is it in any degree useful thatthey should. It is true there are divers of them perceived at once, andmore of some and less of others: but accurately to compute theirmagnitude and assign precise determinate proportions between things sovariable and inconstant, if we suppose it possible to be done, must yetbe a very trifling and insignificant labour. 157. I must confess men are tempted to think that flat or plane figuresare immediate objects of sight, though they acknowledge solids are not. And this opinion is grounded on what is observed in painting, wherein (itseems) the ideas immediately imprinted on the mind are only of planesvariously coloured, which by a sudden act of the judgment are changedinto solids. But with a little attention we shall find the planes herementioned as the immediate objects of sight are not visible but tangibleplanes. For when we say that pictures are planes, we mean thereby thatthey appear to the touch smooth and uniform. But then this smoothness anduniformity, or, in other words, this planeness of the picture, is notperceived immediately by vision: for it appeareth to the eye various andmultiform. 158. From all which we may conclude that planes are no more the immediateobject of sight than solids. What we strictly see are not solids, nor yetplanes variously coloured: they are only diversity of colours. And someof these suggest to the mind solids, and other plane figures, just asthey have been experienced to be connected with the one or the other: sothat we see planes in the same way that we see solids, both being equallysuggested by the immediate objects of sight, which accordingly arethemselves denominated planes and solids. But though they are called bythe same names with the things marked by them, they are nevertheless of anature entirely different, as hath been demonstrated. 159. What hath been said is, if I mistake not, sufficient to decide thequestion we proposed to examine, concerning the ability of a pure spirit, such as we have described, to know GEOMETRY. It is, indeed, no easymatter for us to enter precisely into the thoughts of such anintelligence, because we cannot without great pains cleverly separate anddisentangle in our thoughts the proper objects of sight from those oftouch which are connected with them. This, indeed, in a complete degreeseems scarce possible to be performed: which will not seem strange to usif we consider how hard it is for anyone to hear the words of his nativelanguage pronounced in his ears without understanding them. Though heendeavour to disunite the meaning from the sound, it will neverthelessintrude into his thoughts, and he shall find it extreme difficult, if notimpossible, to put himself exactly in the posture of a foreigner thatnever learned the language, so as to be affected barely with the soundsthemselves, and not perceive the signification annexed to them. 160. By this time, I suppose, it is clear that neither abstract norvisible extension makes the object of geometry; the not discerning ofwhich may perhaps have created some difficulty and useless labour inmathematics. Sure I am, that somewhat relating thereto has occurred to mythoughts, which, though after the most anxious and repeated examination Iam forced to think it true, doth, nevertheless, seem so far out of thecommon road of geometry, that I know not whether it may not be thoughtpresumption, if I should make it public in an age, wherein that sciencehath received such mighty improvements by new methods; great part whereof, as well as of the ancient discoveries, may perhaps lose their reputation, and much of that ardour with which men study the abstruse and finegeometry be abated, if what to me, and those few to whom I have impartedit, seems evidently true, should really prove to be so.