134. Much more might be laid together in proof of the proposition I have advanced: but what has been said is, if I mistake not, sufficient to convince anyone that shall yield a reasonable attention: and as for those that will not be at the pains of a little thought, no multiplication of words will ever suffice to make them understand the truth, or rightly conceive my meaning.
135. I cannot let go the above-mentioned problem without some reflexion on it. It hath been evident that a man blind from his birth would not, at first sight, denominate anything he saw by the names he had been used to appropriate to ideas of touch, vid. sect. 106. Cube, sphere, table are words he has known applied to things perceivable by touch, but to things perfectly intangible he never knew them applied. Those words in their wonted application always marked out to his mind bodies or solid things which were perceived by the resistance they gave: but there is no solidity, no resistance or protrusion, perceived by sight. In short, the ideas of sight are all new perceptions, to which there be no names annexed in his mind: he cannot therefore understand what is said to him concerning 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 downright bantering and unintelligible; nothing he sees being able to suggest to his thoughts the idea of body, distance, or in general of anything he had already known.
136. It is a mistake to think the same thing affects both sight and touch. If the same angle or square which is the object of touch be also the object of vision, what should hinder the blind man at first sight from knowing it? For though the manner wherein it affects the sight be different from that wherein it affected his touch, yet, there being beside his manner or circumstance, which is new and unknown, the angle or figure, which is old and known, he cannot choose but discern it.
137. Visible figure and extension having been demonstrated to be of a nature entirely different and heterogeneous from tangible figure and extension, it remains that we inquire concerning. Now that visible motion is not of the same sort with tangible motion seems to need no farther proof, it being an evident corollary from what we have shewn concerning the difference there is between visible and tangible extension: but for a more full and express proof hereof we need only observe that one who had not yet experienced vision would not at first sight know motion. Whence it clearly follows that motion perceivable by sight is of a sort distinct from motion perceivable by touch. The antecedent I prove thus: by touch he could not perceive any motion but what was up or down, to the right or left, nearer or farther from him; besides these and their several varieties or complications, it is impossible he should have any idea of motion. He would not therefore think anything to be motion, or give the name motion to any idea which he could not range under some or other of those particular kinds thereof. But from sect. 95 it is plain that by the mere act of vision he could not know motion upwards or downwards, to the right or left, or in any other possible direction. From which I conclude he would not know motion at all at first sight. As for the idea of motion in abstract, I shall not waste paper about it, but leave it to my reader to 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: but since the manner wherein the mind apprehends by sight the motion of tangible objects, with the various degrees thereof, may be easily collected from what hath been said concerning the manner wherein that sense doth suggest their various distances, magnitudes, and situations, I shall not enlarge any farther on this subject, but proceed to consider what may be alleged, with greatest appearance of reason, against the proposition we have shewn to be true. For where there is so much prejudice to be encountered, a bare and naked demonstration of the truth will scarce suffice. We must also satisfy the scruples that men may raise in favour of their preconceived notions, shew whence the mistake arises, how it came to spread, and carefully disclose and root out those false persuasions that an early prejudice might have implanted in the mind.
139. First, therefore, it will be demanded how visible extension and figures come to be called by the same name with tangible extension and figures, if they are not of the same kind with them? It must be something more than humour or accident that could occasion a custom so constant and universal as this, which has obtained in all ages and nations of the world, and amongst allranks of men, the learned as well as the illiterate.
140. To which I answer, we can no more argue a visible and tangible square to be of the same species from their being called by the same name, than we can that a tangible square and the monosyllable consisting of six letters whereby it is marked are of the same species because they are both called by the same name. It is customary to call written words and the things they signify by the same name: for words not being regarded in their own nature, or otherwise than as they are marks of things, it had been superfluous, and beside the design of language, to have given them names distinct from those of the things marked by them. The same reason holds here also. Visible figures are the marks of tangible figures, and from sect. 59 it is plain that in themselves they are little regarded, or upon any other score than for their connexion with tangible figures, which by nature they are ordained to signify. And because this language of nature doth not vary in different ages or nations, hence it is that in all times and places visible figures are called by the same names as the respective tangible figures suggested by them, 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 square than to a visible circle: it has four angles and as many sides: so also has the visible square: but the visible circle has no such thing, being bounded by one uniform curve without right lines or angles, which makes it unfit to represent the tangible square but very fit to represent the tangible circle. Whence it clearly follows that visible figures are patterns of, or of the same species with, the respective tangible figures represented by them: that they are like unto them, and of their own nature fitted to represent them, as being of the same sort: and that they are in no respect arbitrary signs, as words.
142. I answer, it must be acknowledged the visible square is fitter than the visible circle to represent the tangible square, but then it is not because it is liker, or more of a species with it, but because the visible square contains in it several distinct parts, whereby to mark the several distinct corresponding parts of a tangible square, whereas the visible circle doth not. The square perceived by touch hath four distinct, equal sides, so also hath it four distinct equal angles. It is therefore necessary that the visible figure which shall be most proper to mark it contain four distinct equal parts corresponding to the four sides of the tangible square, as likewise four other distinct and equal parts whereby to denote the four equal angles of the tangible square. And accordingly we see the visible figures contain in them distinct visible parts, answering to the distinct tangible parts of the figures signified or 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 it be also shewn that not only the number but also the kind of the parts be the same in both. To illustrate this, I observe that visible figures represent tangible figures much after the same manner that written words do sounds. Now, in this respect words are not arbitrary, it not being indifferent what written word stands for any sound: but it is requisite that each word contain in it so many distinct characters as there are variations in the sound it stands for. Thus the single letter a is proper to mark one simple uniform sound; and the word adultery is accommodated to represent the sound annexed to it, in the formation whereof there being eight different collisions or modifications of the air by the organs of speech, each of which produces a difference of sound, it was fit the word representing it should consist of as many distinct characters, thereby to mark each particular difference or part of the whole sound. And yet nobody, I presume, will say the single letter a, or the word adultery, are like unto, or of the same species with, the respective sounds by them represented. It is indeed arbitrary that, in general, letters of any language represent sounds at all: but when that is once agreed, it is not arbitrary what combination of letters shall represent this or that particular sound. I leave this with the reader to pursue, and apply it in his own thoughts.
144. It must be confessed that we are not so apt to confound other signs with the things signified, or to think them of the same species, as we are visible and tangible ideas. But a little consideration will shew us how this may be without our supposing them of a like nature. These signs are constant and universal, their connexion with tangible ideas has been learnt at our first entrance into the world; and ever since, almost every moment of our lives, it has been occurring to our thoughts, and fastening and striking deeper on our minds. When we observe that signs are variable, and of human institution; when we remember there was a time they were not connected in our minds with those things they now so readily suggest; but that their signification was learned by the slow steps of experience: this preserves us from confounding them. But when we find the same signs suggest the same things all over the world; when we know they are not of human institution, and cannot remember that we ever learned their signification, but think that at first sight they would have suggested to us the same things they do now: all this persuades us they are of the same species as the things respectively represented by them, and that it is by a natural resemblance they suggest them to our minds.
145. Add to this that whenever we make a nice survey of any object, successively directing the optic axis to each point thereof, there are certain lines and figures described by the motion of the head or eye, which being in truth perceived by feeling, do nevertheless so mix themselves, as it were, with the ideas of sight, that we can scarce think but they appertain to that sense. Again, the ideas of sight enter into the mind several at once, more distinct and unmingled than is usual in the other senses beside the touch. Sounds, for example, perceived at the same instant, are apt to coalesce, if I may so say, into one sound: but we can perceive at the same time great variety of visible objects, very separate and distinct from each other. Now tangible extension being made up of several distinct coexistent parts, we may hence gather another reason that may dispose us to imagine a likeness or an analogy between the immediate objects of sight and touch. But nothing, certainly, doth more contribute to blend and confound them together than the strict and close connexion they have with each other. We cannot open our eyes but the ideas of distance, bodies, and tangible figures are suggested by them. So swift and sudden and unperceived is the transition from visible to tangible ideas that we can scarce forbear thinking them equally the immediate object of vision.
146. The prejudice which is grounded on these, and whatever other causes may be assigned thereof, sticks so fast that it is impossible without obstinate striving and labour of the mind to get entirely clear of it. But then the reluctancy we find in rejecting any opinion can be no argument of its truth to whoever considers what has been already shewn with 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 clearest demonstration.
147. Upon the whole, I think we may fairly conclude that the proper objects of vision constitute an universal language of the Author of Nature, whereby we are instructed how to regulate our actions in order to attain those things that are necessary to the preservation and well-being of our bodies, as also to avoid whatever may be hurtful and destructive of them. It is by their information that we are principally guided in all the transactions and concerns of life. And the manner wherein they signify and mark unto us the objects which are at a distance is the same with that of languages and signs of human appointment, which do not suggest the things signified by any likeness or identity of nature, but only by an habitual connexion that experience has made us to observe between them.
148. Suppose one who had always continued blind be told by his guide that after he has advanced so many steps he shall come to the brink of a precipice, or be stopped by a wall; must not this to him seem very admirable and surprizing? He cannot conceive how it is possible for mortals to frame such predictions as these, which to him would seem as strange and unaccountable as prophesy doth to others. Even they who are blessed with the visive faculty may (though familiarity make it less observed) find therein sufficient cause of admiration. The wonderful art and contrivance wherewith it is adjusted to those ends and purposes for which it was apparently designed, the vast extent, number, and variety of objects that are at once with so much ease and quickness and pleasure suggested by it: all these afford subject for much and pleasing speculation, and may, if anything, give us some glimmering analogous prænotion of things which are placed beyond the certain discovery and comprehension of our present state.
149. I do not design to trouble myself with drawing corollaries from the doctrine I have hitherto laid down. If it bears the test others may, so far as they shall think convenient, employ their thoughts in extending it farther, and applying it to whatever purposes it may be subservient to: only, I cannot forbear making some inquiry concerning the object of geometry, which the subject we have been upon doth naturally lead one to. We have shewn there is no such idea as that of extension in abstract, and that there are two kinds of sensible extension and figures which are entirely distinct and heterogeneous from each other. Now, it is natural to inquire which of these is the object of geometry.
150. Some things there are which at first sight incline one to think geometry conversant about visible extension. The constant use of the eyes, both in the practical and speculative parts of that science, doth very much induce us thereto. It would, without doubt, seem odd to a mathematician to go about to convince him the diagrams he saw upon paper were not the figures, or even the likeness of the figures, which make the subject of the demonstration. The contrary being held an unquestionable truth, not only by mathematicians, but also by those who apply themselves more particularly to the study of logic; I mean, who consider the nature of science, certainty, and demonstration: it being by them assigned as one reason of the extraordinary clearness and evidence of geometry that in this science the reasonings are free from those inconveniences which attend the use of arbitrary signs, the very ideas themselves being copied out and exposed to view upon paper. But, by the bye, how well this agrees with what they likewise assert of abstract ideas being the object of geometrical demonstration I leave to be considered.
151. To come to a resolution in this point we need only observe what hath been said in sect. 59, 60, 61, where it is shewn that visible extensions in themselves are little regarded, and have no settled determinable greatness, and that men measure altogether, by the application of tangible extension to tangible extension. All which makes it evident that visible extension and figures are not the object of geometry.
152. It is therefore plain that visible figure are of the same use in geometry that words are: and the one may as well be accounted the object of that science as the other, neither of them being otherwise concerned therein than as they represent or suggest to the mind the particular tangible figures connected with them. There is indeed this difference between the signification of tangible figures by visible figures, and of ideas by words: that whereas the latter is variable and uncertain, depending altogether on the arbitrary appointment of men, the former is fixed and immutably the same in all times and places. A visible square, for instance, suggests to the mind the same tangible figure in Europe that 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 misinterpretation and ambiguity that languages of human contrivance are unavoidably subject to.
153. Though what has been said may suffice to shew what ought to be determined with relation to the object of geometry, I shall nevertheless, for the fuller illustration thereof, consider the case of an intelligence, or unbodied spirit, which is supposed to see perfectly well, i.e. to have a clear perception of the proper and immediate objects of sight, but to have no sense of touch. Whether there be any such being in Nature or no is beside my purpose to inquire. It sufficeth that the supposition contains no contradiction in it. Let us now examine what proficiency such a one may be able to make in geometry. Which speculation will lead us more clearly to see whether the ideas of sight can possibly be the object of that science.
154. First, then, it is certain the aforesaid intelligence could have no idea of a solid, or quantity of three dimensions, which followeth from its not having any idea of distance. We indeed are prone to think that we have by sight the ideas of space and solids, which ariseth from our imagining that we do, strictly speaking, see distance and some parts of an object at a greater distance than others; which hath been demonstrated to be the effect of the experience we have had, what ideas of touch are connected with such and such ideas attending vision: but the intelligence here 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, or profundity, nor consequently of space or body, either immediately or by suggestion. Whence it is plain he can have no notion of those parts of geometry which relate to the mensuration of solids and their convex or concave surfaces, and contemplate the properties of lines generated by the section of a solid. The conceiving of any part whereof is beyond the reach of his faculties.
155. Farther, he cannot comprehend the manner wherein geometers describe a right line or circle; the rule and compass with their use being things of which it is impossible he should have any notion: nor is it an easier matter for him to conceive the placing of one plane or angle on another, in order to prove their equality: since that supposeth some idea of distance or external space. All which makes it evident our pure intelligence could never attain to know so much as the first elements of plane geometry. And perhaps upon a nice inquiry it will be found he cannot 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 a geometrical plane, as will appear to whoever shall reflect a little on it.
156. All that is properly perceived by the visive faculty amounts to no more than colours, with their variations and different proportions of light and shade. But the perpetual mutability and fleetingness of those immediate objects of sight render them incapable of being managed after the manner of geometrical figures; nor is it in any degree useful that they should. It is true there are divers of them perceived at once, and more of some and less of others: but accurately to compute their magnitude and assign precise determinate proportions between things so variable and inconstant, if we suppose it possible to be done, must yet be a very trifling and insignificant labour.
157. I must confess men are tempted to think that flat or plane figures are immediate objects of sight, though they acknowledge solids are not. And this opinion is grounded on what is observed in painting, wherein (it seems) the ideas immediately imprinted on the mind are only of planes variously coloured, which by a sudden act of the judgment are changed into solids. But with a little attention we shall find the planes here mentioned as the immediate objects of sight are not visible but tangible planes. For when we say that pictures are planes, we mean thereby that they appear to the touch smooth and uniform. But then this smoothness and uniformity, or, in other words, this planeness of the picture, is not perceived immediately by vision: for it appeareth to the eye various and multiform.
158. From all which we may conclude that planes are no more the immediate object of sight than solids. What we strictly see are not solids, nor yet planes variously coloured: they are only diversity of colours. And some of these suggest to the mind solids, and other plane figures, just as they have been experienced to be connected with the one or the other: so that we see planes in the same way that we see solids, both being equally suggested by the immediate objects of sight, which accordingly are themselves denominated planes and solids. But though they are called by the same names with the things marked by them, they are nevertheless of a nature entirely different, as hath been demonstrated.
159. What hath been said is, if I mistake not, sufficient to decide the question we proposed to examine, concerning the ability of a pure spirit, such as we have described, to know geometry. It is, indeed, no easy matter for us to enter precisely into the thoughts of such an intelligence, because we cannot without great pains cleverly separate and disentangle in our thoughts the proper objects of sight from those of touch which are connected with them. This, indeed, in a complete degree seems scarce possible to be performed: which will not seem strange to us if we consider how hard it is for anyone to hear the words of his native language pronounced in his ears without understanding them. Though he endeavour to disunite the meaning from the sound, it will nevertheless intrude into his thoughts, and he shall find it extreme difficult, if not impossible, to put himself exactly in the posture of a foreigner that never learned the language, so as to be affected barely with the sounds themselves, and not perceive the signification annexed to them. By this time, I suppose, it is clear that neither abstract nor visible extension makes the object of geometry; the not discerning of which may perhaps have created some difficulty and useless labour in mathematics.
Appendix [7]
The censures which, I am informed, have been made on the foregoing essay inclined me to think I had not been clear and express enough in some points, and to prevent being misunderstood for the future, I was willing to make any necessary alterations or additions in what I had written. But that was impracticable, the present edition having been almost finished before I received this information. Wherefore I think it proper to consider in this place the principal objections that are come to my notice.
In the first place it's objected that in the beginning of the essay I argue either against all use of lines and angles in optics, and then what I say is false; or against those writers only who will have it that we can perceive by sense the optic axes, angles, etc., and then it's insignificant, this being an absurdity which no one ever held. To which I answer that I argue only against those who are of opinion that we perceive the distance of objects by lines and angles or, as they term it, by a kind of innate geometry. And to shew that this is not fighting with my own shadow, I shall here set down a passage from the celebrated Descartes.
Distantiam praeterea discimus, per mutuam quandam conspirationem oculorum. Ut enim caecus noster duo bacilla tenens AE et CE, de quorum longitudine incercus, solumque intervallum manuum A et C, cum magnitudine angulorum ACE, et CAE exploratum habens, inde, ut ex geometria quadam omnibus innata, scire potest ubi sit punctum E. Sic quum nostri oculi RST et rst ambo, vertuntur ad X, magnitudo lineae Ss, et angulorum XSs et XsS, certos nos redunt ubi sit punctum X. Et idem opera alterutrius possumus indagare, loco illum movendo, ut si versus X illum semper dirigentes, primo sistamus in puncto S, et statim post in puncto s, hoc sufficiet ut magnitudo lineae Ss, et duorum angulorum XSs et XsS nostrae imaginationi simul occurrant, et distantiam puncti X nos edoceant; idque per actionem mentis, quae licet simplex judicium esse videatur, ratiocinationem tamen quandam involutam habet, similem illi, qua geometrae per duas stationes diversas, loca inaccessa dimetiuntur.[8]
I might amass together citations from several authors to the same purpose, but this being so clear in the point, and from an author of so great note, I shall not trouble the reader with any more. What I have said on this head was not for the sake of finding fault with other men, but because I judged it necessary to demonstrate in the first place that we neither see distance immediately, nor yet perceive it by the mediation of anything that hath (as lines and angles) a necessary connexion with it. For on the demonstration of this point the whole theory depends.
Secondly, it is objected that the explication I give of the appearance of the horizontal moon (which may also be applied to the sun) is the same that Gassendus had given before. I answer, there is indeed mention made of the grossness of the atmosphere in both, but then the methods wherein it is applied to solve the : phenomenon are widely different, as will be evident to whoever ,shall compare what I have said on this subject with the following words of Gassendus.
Heinc dici posse videtur: solem humilem oculo speaatum ideo apparere majorem, quam dum altius egreditur, quia dum vicinus est horizonti prolixa est senes vaporum, atque adeo corpusculorum quae solis radios ita retundunt, ut oculus minus conniveat, et pupilla quasi umbrefacta longe magis amplificetur, quam dum sole multum elato rari vapores intercipiuntur, solque ipse ita splendescit, ut pupilla in ipsum speaans contractissima efficiatur. Nempe ex hoc esse videtur, cur visibilis species ex sole procedens, et per pupillam amplificatam intromissa in retinam, ampliorem in illa sedem occupet, majoremque proinde creet solis apparentiam, quam dum per conttactam pupillam eodem intromissa contendit (vid. Epist. I de apparente Magnitudine solis humilis et sublimis, page 6). [9]
This solution of Gassendus proceeds on a false principle, viz., that the pupil's being enlarged augments the species or image on the fund of the eye.
Thirdly, against what is said in sect. 80, it is objected that the me thing which is so small as scarce to be discerned by a man may appear like a mountain to some small insect; from which it follow that the minimum visibile is not equal in respect of all creatures. I answer, if this objection be sounded to the bottom it will be found to mean no more than that the same particle of matter, which is marked to a man by one minimum visibile, exhibits to an insect a great number of minima visibilia. But this does not prove that one minimum visibile of the insect is not equal to one minimum visibile of the man. The not distinguishing between the mediate and immediate objects of sight is, I suspect, a cause of misapprehension in this matter.
Some other misinterpretations and difficulties have been made, but in the points they refer to 1 have endeavoured to be so very plain that I know not how to express myself more clearly. All I shall add is that if they who are pleased to criticise on my essay would but read the whole over with some attention, they might be the better able to comprehend my meaning and consequently to judge of my mistakes.
I am informed that, soon after the first edition of this treatise a man somewhere near London was made to see, who had been born blind, and continued so for about twenty years. Such a one may be supposed a proper judge to decide how far some tenets laid down in several places of the foregoing essay are agreeable to truth, and if any curious person hath the opportunity of making proper interrogatories to him thereon, I should gladly see my notions either amended or confirmed by experience.
Footnotes
[1] See what Decartes and others have written on this subject.
[2] Par. I. Prop. 31, Sect. 9.
[3] Molyneux Dioptr., Par. I. Prop. 5.
[4] Phil. Trans. Num. 187. p. 314
[5] Numb. 187. P. 323
[6] Diopt. par. 2. c. 7. P. 289.
[7] nd edition only (1709).
[8] We apprehend distance, moreover, through a sort of joint activity of the eyes. For in the same way as our blind man, holding two sticks of indeterminate length, AE and CE, and knowing only the distance between his hands, A and C, together with the size of the angles ACE and CAE, can thence determine the position of E by a sort of innate geometrical knowledge shared by all men, so, when both our eyes, RST and rst, are focused on X, the length of the line Ss and the size of the angles XSs and XsS let us know the position of the point X. We can also discover that position by means of either one of our eyes alone, by changing its location. If we keep the eye fixed on X and hold it first at point S and then immediately afterwards at point s, that will be enough for the length of the line Ss and the size of the angles XSs and XsS to be present together in the imagination and thus to inform us of the distance of the point X. They do so in virtue of an act of the mind which, while it may seem to be a simple judgment, nevertheless includes within itself a certain reasoning process like that by which geometers calculate inaccessible positions from two separate given points. [From Descartes' Dioptrics, VI, 13.]
[9] The truth, then, seems to be as follows: the reason why the sun, when it is low, appears to the eye to be larger than when it has climbed higher is because, as long as it is near to the horizon, the [interveningl layer of vapour is deeper, and the atoms so dull the brightness of the sun's rays that the eye blinks less. For the pupil is as if shaded and is far more dilated than when the sun is high in the sky: then a thinner layer of vapour intervenes and the sun itself shines so brightly that, in looking towards it, the pupil closes up and becomes highly contracted. Doubtless this is the explanation why the visible species coming from the sun, when it reaches the retina through a dilated pupil, occupies a larger place on it and so creates the appearance of a larger sun than when it strikes the retina after entering by the same route but through a contracted ed pupil.