I. Deſign.

MY Deſign is to ſhew the man⯑ner, wherein we perceive by Sight the Diſtance, Magm⯑tude, and Situation of Objects. Alſo to conſider the Difference there is be⯑twixt the Ideas of Sight and Touch, and whether there be any Idea com⯑mon to both Senſes. In treating of all which, it ſeems to me, the Writers of Optics have proceeded on wrong Principles.

II. Diſtance of it ſelf In⯑viſible.

It is, I think, agreed by all that Di⯑ſtance of it ſelf, and immediately can⯑not be ſeen. For Diſtance being a Line directed end-wiſe to the Eye, it projects only one Point in the Fund of the Eye. Which Point remains invaria⯑bly the ſame, whether the Diſtance be longer or ſhorter.

III. Remote Di⯑ſtance per⯑ceiv'd ra⯑ther by Ex⯑perience, than by Senſe.

I find it alſo acknowledg'd, that the Eſtimate we make of the Diſtance of Objects conſiderably remote, is ra⯑ther an Act of Judgment grounded on Experience, than of Senſe. For Exam⯑ple, When I perceive a great number of intermediate Objects, ſuch as Houſes, Fields, Rivers, and the like, which I have experienced to take up a conſi⯑derable Space; I thence form a Judg⯑ment or Concluſion, that the Object I ſee beyond them is at a great Diſtance. Again, when an Object appears Faint and Small, which at a near Diſtance I have experienced to make a vigorous and large Appearance; I inſtantly con⯑clude it to be far off. And this, 'tis [3] evident, is the reſult of Experience; without which, from the Faintneſs and Littleneſs, I ſhould not have in⯑fer'd any thing concerning the Di⯑ſtance of Objects.

IV. Near Di⯑ſtance thought to be percei⯑ved by the Angle of the Optic Axes.

But when an Object is placed at ſo near a Diſtance, as that the Interval between the Eyes bears any ſenſible Proportion to it. It is the receiv'd Opinion that the two Optic Axes (the Fancy that we ſee only with one Eye at once being exploded) concurring at the Object do there make an Angle, by means of which, according as it is Greater or Leſſer, the Object is per⯑ceiv'd to be nearer or farther off.

V. Difference between this and the former manner of perceiving Diſtance.

Betwixt which, and the foregoing manner of Eſtimating Diſtance, there is this remarkable Difference. That whereas, there was no apparent, ne⯑ceſſary Connexion between ſmall Di⯑ſtance and a large and ſtrong Ap⯑pearance, or between great Diſtance, and a little and faint Appearance. Yet there appears a very neceſſary Con⯑nexion [4] between an obtuſe Angle and near Diſtance, and an acute Angle and farther Diſtance. It does not in the leaſt depend upon Experience, but may be evidently known by any one before he had experienc'd it, that the nearer the Concurrence of the Optic Axes, the greater the Angle, and the remoter their Concurrence is, the leſſer will be the Angle comprehended by them.

VI. Alſo by Di⯑verging Rays.

There is another way, mention'd by the Optic Writers, whereby they will have us judge of thoſe Diſtan⯑ces, in reſpect of which, the breadth of the Pupil hath any ſenſible bigneſs. And that is the greater or leſſer Di⯑vergency of the Rays, which iſſuing from the viſible Point, do fall on the Pupil: That Point being judged near⯑eſt, which is ſeen by moſt diverging Rays; and that remoter, which is ſeen by leſs diverging Rays. And ſo on, the apparent Diſtance ſtill increaſing, as the Divergency of the Rays decreaſes, till at length it becomes infinite, when the Rays that fall on the Pupil are to [5] Senſe Parallel. And after this manner it is ſaid we perceive Diſtances when we look only with one Eye.

VII. This de⯑pends not on Experi⯑ence.

In this Caſe alſo, 'tis plain we are not beholding to Experience: It be⯑ing a certain, neceſſary Truth, that the nearer the direct Rays falling on the Eye approach to a Paralleliſm, the farther off is the Point of their In⯑terſection, or the viſible Point from whence they flow.

VIII. Theſe the common Accounts, but not ſa⯑tisfactory.

I have here ſet down the common, current Accounts that are given of our perceiving near Diſtances by Sight, which, tho' they are unqueſtionably receiv'd for true by Mathematicians, and accordingly made uſe of by them in determining the apparent Places of Objects, do nevertheleſs ſeem to me very unſatisfactory: And that for theſe following Reaſons.

IX. Some Ideas perceived by the me⯑diation of others.

Firſt, It is evident that when the Mind perceives any Idea, not imme⯑diately and of it ſelf, it muſt be by [6] the means of ſome other Idea. Thus, for Inſtance, the Paſſions which are in the Mind of another, are of them⯑ſelves, to me inviſible. I may never⯑theleſs perceive them by Sight, tho' not immediately yet, by means of the Colours they produce in the Counte⯑nance. We do often ſee Shame or Fear in the Looks of a Man, by per⯑ceiving the Changes of his Counte⯑nance to Red or Pale.

X. No Idea which is not it ſelf per⯑ceived, can be the means of perceiving another.

Moreover it is evident, that no I⯑dea which is not it ſelf perceiv'd, can be to me the means of perceiving any other Idea. If I do not perceive the Redneſs or Paleneſs of a Man's Face themſelves, it is impoſſible I ſhou'd perceive by them the Paſſions which are in his Mind.

XI. Diſtance perceived by means of ſome other Idea.

Now from Sect. II. 'Tis plain that Di⯑ſtance is in it's own nature impercei⯑vable, and yet it is perceiv'd by Sight. It remains therefore, that it be brought into view by means of ſome other Idea, that is it ſelf immediately per⯑ceiv'd in the Act of Viſion.

XII. Thoſe Lines and Angles mentioned in Optics, are not themſelves perceiv'd.

But thoſe Lines and Angles, by means whereof Mathematicians pretend to explain the Perception of Diſtance, are themſelves not at all perceiv'd, nor are they in Truth, ever thought of by thoſe unskilful in Optics. I appeal to any ones Experience, whether up⯑on Sight of an Object, he compute it's Diſtance by the bigneſs of the An⯑gle, made by the meeting of the two Optic Axes? Or whether he ever think of the greater or leſſer Divergency of the Rays, which arrive from any Point to his Pupil. Nay, whether it be not perfectly impoſſible for him to per⯑ceive by Senſe, the various Angles wherewith the Rays according to their greater, or leſſer Divergence do fall on his Eye. Every one is himſelf the beſt Judge of what he perceives, and what not. In vain ſhall all the Ma⯑thematicians in the World tell me, that I perceive certain Lines and An⯑gles which introduce into my Mind the various Ideas of Diſtance; ſo long as I my ſelf am conſcious of no ſuch thing.

XIII, Hence the Mind doth not perceive Diſtance by Lines and Angles

Since therefore thoſe Angles and Lines are not themſelves perceiv'd by Sight, it follows from Sect. X. that the Mind does not by them judge of the Diſtance of Objects.

XIV. Alſo be⯑cauſe they have no re⯑al Exi⯑ſtence.

Secondly, The Truth of this Aſſer⯑tion will be, yet, farther evident to any one that conſiders thoſe Lines and Angles have no real Exiſtence in Na⯑ture, being only an Hypotheſis fram'd by Mathematicians, and by them in⯑troduc'd into Optics, that they might treat of that Science in a Geometrical way.

XV. And be⯑cauſe they are inſuffi⯑cient to ex⯑plain the Phaenome⯑na.

The Third and Laſt Reaſon I ſhall give for my Rejecting that Doctrine, is, that tho' we ſhould grant the real Exiſtence of thoſe Optic Angles, &c. and that it was poſſible for the Mind to perceive them; yet theſe Princi⯑ples wou'd not be found ſufficient to explain the Phaenomena of Diſtance. As ſhall be ſhewn hereafter.

XVI. The Ideas that ſug⯑geſt Di⯑ſtance are 1ſt. the Sen⯑ſation ari⯑ſing from the turn of the Eyes.

Now, It being already ſhewn that Diſtance is ſuggeſted to the Mind, by the Mediation of ſome other Idea which is it ſelf perceiv'd in the Act of Seeing. It remains that we enquire what Idea, or Senſations there be that attend Viſion, unto which we may ſuppoſe the Ideas of Diſtance are connected, and by which they are introduced into the Mind. And Firſt, It is certain by Experience, that when we look at a near Object with both Eyes, according as it approaches, or recedes from us, we alter the Diſpo⯑ſition of our Eyes, by leſſening or widening the Interval between the Pupils. This Diſpoſition or Turn of the Eyes is attended with a Sen⯑ſation, which ſeems to me, to be that which in this Caſe brings the Idea of greater, or leſſer Diſtance into the Mind.

XVII. Betwixt which and Diſtance there is no neceſſary Connexion.

Not, that their is any natural or neceſſary Connexion between the [10] Senſation we perceive by the Turn of the Eyes, and greater or leſſer Diſtance. But becauſe the Mind has by conſtant Experience, found the dif⯑ferent Senſations correſponding to the different Diſpoſitions of the Eyes, to be attended each, with a Different Degree of Diſtance in the Object: There has grown an Habitual or Cu⯑ſtomary Connexion, between thoſe two ſorts of Ideas. So that the Mind no ſooner perceives the Senſation a⯑riſing from the different Turn it gives the Eyes, in order to bring the Pu⯑pils nearer, or farther aſunder; but it withal perceives the different Idea of Diſtance which was wont to be connected with that Senſation. Juſt as upon hearing a certain Sound, the Idea is immediately ſuggeſted to the Underſtanding, which Cuſtom had united with it.

XVIII. Scarce room for Miſtake in this mat⯑ter.

Nor do I ſee, how I can eaſily be miſtaken in this Matter. I know evidently that Diſtance is not per⯑ceived [11] of it ſelf. That by conſequence, it muſt be perceived by means of ſome other Idea which is immediate⯑ly perceiv'd, and varies with the dif⯑ferent Degrees of Diſtance. I know alſo that the Senſation ariſing from the Turn of the Eyes is of it ſelf, im⯑mediately perceiv'd, and various De⯑grees thereof are connected with dif⯑ferent Diſtances; which never fail to accompany them into my Mind, when I view an Object diſtinctly with both Eyes, whoſe Diſtance is ſo ſmall that in reſpect of it, the Interval between the Eyes has any conſiderable Mag⯑nitude.

XIX. No regard had to the Angle of the Optic Axes.

I know it is a receiv'd Opinion, that by altering the diſpoſition of the Eyes, the Mind perceives whether the Angle of the Optic Axes is made greater or leſſer. And that accord⯑ingly by a kind of Natural Geometry, it judges the Point of their Interſecti⯑on to be nearer, or farther off. But that this is not true, I am convinc'd [12] by my own Experience. Since I am not conſcious, that I make any ſuch uſe of the Perception I have by the Turn of my Eyes. And for me to make thoſe Judgments, and draw thoſe Concluſions from it, without knowing that I do ſo, ſeems altogether incomprehen⯑ſible.

XX. Judgment of Diſtance made with both Eyes, the Reſult of Experi⯑ence.

From all which it plainly fol⯑lows, that the Judgment we make of the Diſtance of an Object, view'd with both Eyes, is entirely the Re⯑ſult of Experience. If we had not conſtantly found certain Senſations ariſing from the various Diſpoſiti⯑on of the Eyes, attended with cer⯑tain degrees of Diſtance. We ſhou'd never make thoſe ſudden Judgments from them, concerning the Diſtance of Objects; no more than we wou'd pretend to judge of a Man's Thoughts, by his pronouncing Words we had never heard before.

XXI. 2dly, Con⯑fuſedneſs of Appear⯑ance.

Secondly, An Object placed at a certain Diſtance from the Eye, to which the breadth of the Pupil bears a conſiderable Proportion, being made to approach, is ſeen more con⯑fuſedly. And the nearer it is brought, the more confuſed Appearance it makes. And this being found con⯑ſtantly to be ſo, there ariſes in the Mind an Habitual Connexion be⯑tween the ſeveral Degrees of Confu⯑ſion and Diſtance. The greater Con⯑fuſion ſtill implying the leſſer Di⯑ſtance, and the leſſer Confuſion, the greater Diſtance of the Object.

XXII. This the occaſion of thoſe Judg⯑ments at⯑tributed to diverging Rays.

This confuſed Appearance of the Object, doth therefore ſeem to me to be the Medium, whereby the Mind judges of Diſtance in thoſe Caſes, wherein the moſt approv'd Writers of Optics will have it judge, by the different Divergency, with which the Rays flowing from the Radia⯑ting Point fall on the Pupil. No [14] Man, I believe, will pretend to ſee or feel thoſe imaginary Angles, that the Rays are ſuppoſed to form accor⯑ding to their various Inclinations on his Eye. But he cannot chooſe ſee⯑ing whether the Object appear more, or leſs confuſed. It is therefore a manifeſt Conſequence from what has been Demonſtrated, that inſtead of the greater, or leſſer Divergency of the Rays, the Mind makes uſe of the greater or leſſer Confuſedneſs of the Appearance, thereby to de⯑termine the apparent Place of an Object.

XXIII. Objection anſwer'd.

Nor doth it avail to ſay, there is not any neceſſary Connexion be⯑tween confuſed Viſion, and Diſtance great, or ſmall. For I ask any Man, What neceſſary Connexion he Sees, between the Redneſs of a Bluſh and Shame? And yet no ſooner ſhall he behold that Colour to ariſe in the Face of another. But it brings in⯑to his Mind the Idea of that Paſſion [15] which has been obſerv'd to accom⯑pany it.

XXIV. What de⯑ceives the Writers of Optics in this mat⯑ter.

What ſeems to have miſled the Writers of Optics in this Matter is, that they imagine Men judge of Di⯑ſtance, as they do of a Concluſion in Mathematics; betwixt which and the Premiſes, it is indeed abſolute⯑ly requiſite there be an apparent, neceſſary Connexion. But it is far otherwiſe, in the ſudden Judg⯑ments Men make of Diſtance. We are not to think, that Brutes and Children, or even grown reaſon⯑able Men, whenever they perceive an Object to approach, or depart from them, do it by vertue of Geo⯑metry and Demonſtration.

XXV. The Cauſe, why one I⯑dea may ſuggeſt ano⯑ther.

That one Idea may ſuggeſt ano⯑ther to the Mind, it will ſuffice that they have been obſerv'd to go toge⯑ther; without any demonſtration of the neceſſity of their Coexiſtence, or without ſo much as knowing [16] what it is that makes them ſo to Coexiſt. Of this there are innume⯑rable Inſtances, of which no one can be Ignorant.

XXVI. This apply⯑ed to Con⯑fuſion and Diſtance.

Thus greater Confuſion having been conſtantly attended with near⯑er Diſtance, no ſooner is the for⯑mer Idea perceiv'd, but it ſuggeſts the latter to our Thoughts. And if it had been the ordinary Courſe of Nature, that the farther off an Object were placed, the more Con⯑fuſed it ſhou'd appear. It is certain, the very ſame Perception that now makes us think an Object approaches, would then have made us to ima⯑gine it went farther off. That Per⯑ception, abſtracting from Cuſtom and Experience, being equally fit⯑ted to produce the Idea of great Di⯑ſtance, or ſmall Diſtance, or no Di⯑ſtance at all.

XXVII. 3dly, The ſtraining of the Eye.

Thirdly, an Object being placed at the Diſtance above ſpecified, and [17] brought nearer to the Eye, we may nevertheleſs prevent, at leaſt for ſome time, the Appearance's grow⯑ing more confus'd, by ſtraining the Eye. In which Caſe, that Senſation ſupplys the place of confuſed Viſion, in aiding the Mind to judge of the Di⯑ſtance of the Object. It being eſteem⯑ed ſo much the nearer, by how much the effort, or ſtraining of the Eye in order to diſtinct Viſion, is greater.

XXVIII. The Occa⯑ſions which ſuggeſt Di⯑ſtance, have in their own Nature no Relation to it.

I have here ſet down thoſe Sen⯑ſations or Ideas, that ſeem to me to be the conſtant and general Oc⯑caſions of introducing into the Mind, the different Ideas of near Diſtance. 'Tis true in moſt Caſes, that divers other Circumſtances contribute to frame our Idea of Diſtance, viz. the particular Num⯑ber, Size, Kind, &c. of the things ſeen. Concerning which as well as all other the forementioned Oc⯑caſions which ſuggeſt Diſtance, I [18] ſhall only obſerve, they have none of them, in their own Nature, any Relation or Connexion with it. Nor is it poſſible, they ſhou'd ever ſig⯑nifie the various Degrees thereof, otherwiſe than as by Experience they have been found to be connected with them.

XXIX. A difficult Caſe propo⯑ſed by Dr. Barrow as repugnant to all the known Theories.

I ſhall proceed upon theſe Prin⯑ciples to account for a Phaenome⯑non, which has hitherto ſtrangely puzzled the Writers of Optics, and is ſo far from being accounted for by any of their Theories of Vi⯑ſion, that it is, by their own Con⯑feſſion, plainly repugnant to them. And of Conſequence, if nothing elſe cou'd be objected, were alone ſufficient to bring their Credit in Queſtion. The whole Difficulty I ſhall lay before you in the Words of the Learned Doctor Barrow, with which he concludes his Optic Le⯑ctures.

[24] In Engliſh as follows.

‘I have here delivered what my Thoughts have ſuggeſted to me, concerning that part of Optics which is more properly Mathematical. As for the other parts of that Science (which being rather Phyſical, do conſequently abound with plauſi⯑ble Conjectures, inſtead of certain Principles) there has in them ſcarce any thing occur'd to my Obſerva⯑tion, different from what has been already ſaid by Kepler, Scheinerus, Deſcartes, &c. And, methinks, I had better ſay nothing at all, than repeat that which has been ſo of⯑ten ſaid by others. I think it there⯑fore high time to take my leave of this Subject. But before I quit it for good and all, the fair and ingenuous Dealing that I owe both to You and to Truth, obliges me to acquaint you with a certain un⯑toward Difficulty, which ſeems di⯑rectly oppoſite to the Doctrine I [25] have been hitherto inculcating, at leaſt, admits of no Solution from it. In ſhort it is this. [figure] Before the double Convex Glaſs or Concave Speculum EBF, let the Point A be placed, at ſuch a Diſtance that the Rays proceeding from A, after Re⯑fraction or Reflecti⯑on, be brought to Unite ſomewhere in the Ax AB. And ſuppoſe the Point of Union (i. e. the Image of the Point A, as hath been al⯑ready ſet forth) to be Z; between which and B, the Vertex of the Glaſs or Speculum, conceive the Eye to be any where placed. The Queſti⯑on now is, Where the Point A ought to appear. Experience ſhews that it doth not appear behind at the Point Z, and it were contrary [26] to Nature that it ſhou'd; ſince all the Impreſſion which affects the Senſe comes from towards A. But from our Tenents it ſhou'd ſeem to follow, that it wou'd appear be⯑fore the Eye at a vaſt Diſtance off, ſo great as ſhou'd in ſome Sort, ſur⯑paſs all ſenſible Diſtance. For ſince if we exclude all Anticipations and Prejudices, every Object appears by ſo much the farther off, by how much the Rays it ſends to the Eye are leſs Diverging. And that Object is thought to be moſt remote, from which Parallel Rays proceed unto the Eye. Reaſon wou'd make one think, that Object ſhou'd appear, at yet a greater Diſtance, which is ſeen by converging Rays. More⯑over it may in general be asked con⯑cerning this Caſe, what it is that determines the apparent Place of the Point A, and maketh it to ap⯑pear after a conſtant manner, ſome⯑times nearer, at other times farther off? To which doubt, I ſee no⯑thing [27] that can be anſwer'd agree⯑able to the Principles we have laid down, except only that the Point A ought always to appear extreamly remote. But on the contrary, we are aſſur'd by Experience that the Point A appears variouſly Diſtant, according to the different Situations of the Eye between the Points B and Z. And that it doth almoſt never (if at all) ſeem farther off, than it wou'd if it were beheld by the na⯑ked Eye, but on the contrary, it doth ſometimes appear much near⯑er. Nay, it is even certain, that by how much the Rays falling on the Eye do more converge, by ſo much the nearer does the Object ſeem to approach. For the Eye being placed cloſe to the Point B, the Object A appears nearly in it's own natural Place, if the Point B is taken in the Glaſs, or at the ſame Diſtance, if in the Speculum. The Eye being brought back to O, the Object ſeems to draw near. And [28] being come to P it beholds it ſtill nearer. And ſo on by little and little, till at length the Eye being placed ſomewhere, ſuppoſe at Q, the Object appearing extreamly near, begins to vaniſh into meer Confu⯑ſion. All which doth ſeem Repug⯑nant to our Principles, at leaſt, not rightly to agree with them. Nor is our Tenent alone ſtruck at by this Experiment, but likewiſe all others that ever came to my Know⯑ledge are, every whit as much, en⯑danger'd by it. The ancient one eſpecially (which is moſt common⯑ly receiv'd, and comes neareſt to mine) ſeems to be ſo effectually overthrown thereby, that the moſt learned Tacquet has been forc'd to reject that Principle, as falſe and uncertain, on which alone he had built almoſt his whole Catoptrics, and conſequently by taking away the Foundation, hath himſelf pul⯑led down the Superſtructure he had raiſed on it. Which nevertheleſs, [29] I do not believe he wou'd have done, had he but conſider'd the whole matter more throughly, and examin'd the Difficulty to the bot⯑tom. But as for me, neither this, nor any other Difficulty ſhall have ſo great an Influence on me, as to make me renounce that which I know to be manifeſtly agreeable to Reaſon. Eſpecially when, as it here falls out, the Difficulty is founded in the peculiar Nature of a certain odd and particular Caſe. For in the preſent Caſe ſomething peculiar lies hid, which being involv'd in the Subtilty of Nature will, perhaps, hardly be diſcover'd till ſuch Time, as the manner of Viſion is more per⯑fectly made known. Concerning which, I muſt own, I have hitherto been able to find out nothing that has the leaſt ſhew of Probability, not to mention Certainty. I ſhall there⯑fore, leave this Knot to be united by you, wiſhing you may have bet⯑ter Succeſs in it than I have had.’

XXX. This Caſe contradicts a receiv'd Principle in Catop⯑trics.

The ancient and receiv'd Principle which Dr. Barrow here mentions, as the main Foundation of Tacquet's Catop⯑trics, is that, every viſible Point ſeen by Reflexion from a Speculum, ſhall appear placed at the Interſection of the reflected Ray, and the Perpendicular of Incidence. Which Interſection in the preſent Caſe, happening to be behind the Eye, it greatly ſhakes the Authori⯑ty of that Principle, whereon the aforemention'd Author proceeds throughout his whole Catoptrics, in determining the apparent Place of Objects ſeen by Reflexion from any kind of Speculum.

XXXI. It is ſhewn to agree with the Principles we have laid down.

Let us now ſee how this Phae⯑nomenon agrees with our Tenents. The Eye the nearer it is placed to the Point B in the above Fi⯑gures, the more diſtinct is the Ap⯑pearance of the Object; but as it recedes to O, the Appearance grows more Confuſed; and at P it ſees [31] the Object yet more Confuſed; and ſo on till the Eye being brought back to Z ſees the Object in the greateſt Confuſion of all. Where⯑fore by Sect. XXI. the Object ſhou'd ſeem to approach the Eye gradu⯑ally, as it recedes from the Point B, viz. at O it ſhou'd (in conſe⯑quence of the Principle I have laid down in the aforeſaid Section) ſeem nearer than it did at B, and at P nearer than at O, and at Q nearer than at P; and ſo on, till it quite vaniſhes at Z. Which is the very matter of Fact, as any one that pleaſes may eaſily ſatisfie him⯑ſelf by Experiment.

XXXII. This Phae⯑nomenon Illuſtrated.

This Caſe is much the ſame, as if we ſhou'd ſuppoſe an En⯑gliſh-man to meet a Foreigner, who uſed the ſame Words with the Engliſh, but in a direct contrary Sig⯑nification. The Engliſh-man wou'd not fail to make a wrong Judg⯑ment, of the Ideas annexed to [32] thoſe Sounds, in the Mind of him that uſed them. Juſt ſo, in the preſent Caſe the Object ſpeaks (if I may ſo ſay) with Words that the Eye is well acquainted with, viz. Confuſions of Appearance; but whereas heretofore the great⯑er Confuſions were always wont to ſignifie nearer Diſtances, they have in this Caſe a direct, con⯑trary Signification, being connect⯑ed with the greater Diſtances. Whence it follows, that the Eye muſt unavoidably be miſtaken, ſince it will take the Confuſions in the Senſe it has been uſed to, which is directly oppoſed to the True.

XXXIII. It confirms the Truth of the Principle whereby it is explain⯑ed.

This Phaenomenon as it entirely ſubverts the Opinion of thoſe, who will have us judge of Diſtance by Lines and Angles, on which Sup⯑poſition it is altogether inexplica⯑ble, ſo it ſeems to me no ſmall Confirmation, of the Truth of that Principle whereby it is explain'd. [33] But in order to a more full Ex⯑plication of this Point, and to ſhew how far the Hypotheſis of the Mind's judging, by the various Divergency of Rays, may be of uſe in determining the apparent Place of an Object, it will be ne⯑ceſſary to premiſe ſome few Things, which are already well known to thoſe who have any Skill in Diop⯑trics.

XXXIV. Viſion when Diſtinct, and when Confus'd.

Firſt, Any radiating Point is then diſtinctly ſeen, when the Rays pro⯑ceeding from it are, by the refra⯑ctive Power of the Cryſtalline, ac⯑curately reunited in the Retina, or Fund of the Eye. But if they are reunited, either before they arrive at the Retina, or after they have paſt it, then there is confuſed Vi⯑ſion.

XXXV. The diffe⯑rent Effects of Parallel, Diverging and Con⯑verging Rays.

Secondly, Suppoſe in the adja⯑cent Figures NP repreſent an Eye duly framed, and retaining its na⯑tural [34] Figure. In Fig. 1. the Rays fal⯑ling nearly Parallel on the Eye, are by the Cryſtalline AB refracted, ſo as their Focus, or Point of Union F falls exactly on the Retina. But if

the Rays fall ſenſibly diverging on the Eye, as in Fig. 2. then their Focus falls beyond the Retina: Or if the Rays are made to converge by the Lens QS, before they come at the Eye, as in Fig. 3. their Focus F will fall be⯑fore the Retina. In which two laſt [35] Caſes, 'tis evident from the forego⯑ing Section, that the Appearance of the Point Z is confuſed. And by how much the greater is the Con⯑vergency, or Divergency of the Rays falling on the Pupil, by ſo much the farther will the Point of their reuni⯑on be from the Retina, either be⯑fore or behind it, and conſequent⯑ly the Point Z will appear, by ſo much, the more Confuſed. And this, by the Bye, may ſhew us the difference between Confuſed, and Faint Viſion. Confuſed Viſion is, when the Rays proceedings from each diſtinct Point of the Object, are not accurately recollected in one correſponding Point on the Retina; but take up ſome Space thereon. So that Rays from diffe⯑rent Points become mix'd, and con⯑fuſed together. This is oppoſed to diſtinct Viſion, and attends near Objects. Faint Viſion is, when by reaſon of the Diſtance of the Ob⯑ject, or groſſneſs of the interjacent [36] Medium, few Rays arrive from the Object to the Eye. This is oppos'd to vigorous, or clear Viſion, and attends remote Objects. But to re⯑turn.

XXXVI. How Con⯑verging, and Diver⯑ging Rays come to ſuggeſt the ſame Di⯑ſtance.

The Eye, or (to ſpeak truly) the Mind perceiving only the Confu⯑ſion it ſelf, without ever conſider⯑ing the Cauſe from which it pro⯑ceeds, doth conſtantly annex the ſame Degree of Diſtance, to the ſame Degree of Confuſion. Whe⯑ther that Confuſion be occaſion'd by Converging, or by Diverging Rays, it matters not. Whence it follows, that the Eye viewing the Object Z thro' the Glaſs QS (which by Refraction cauſeth the Rays ZQ, ZS, &c. to converge) ſhou'd judge it to be at ſuch a Nearneſs, at which if it were placed, it wou'd radiate on the Eye with Rays di⯑verging to that Degree, as wou'd produce the ſame Confuſion, which is now produced by Converging [37] Rays, i. e. wou'd cover a Portion of the Retina equal to DC. vid. Fig. 3. Sup. But then this muſt be under⯑ſtood (to uſe Dr. Barrow's Phraſe) Secluſis praenotionibus & praejudiciis, In caſe, we abſtract from all other Circumſtances of Viſion, ſuch as the Figure, Size, Faintneſs, &c. of the viſible Objects; all which do ordina⯑rily concur to form our Idea of Di⯑ſtance; the Mind having, by frequent Experience, obſerved their ſeveral Sorts or Degrees, to be connected with various Diſtances.

XXXVII. A Perſon extream Purblind wou'd judge a⯑right in the fore⯑mention'd Caſe.

It plainly follows from what has been ſaid, that a Perſon perfectly Purblind (i. e. that cou'd not ſee an Object diſtinctly, but when placed cloſe to his Eye) wou'd not make the ſame wrong Judgment that o⯑thers do, in the foremention'd Caſe. For, to him, greater Confuſions con⯑ſtantly ſuggeſting greater Diſtances, he muſt, as he recedes from the Glaſs, and the Object grows more Confus'd, [38] judge it to be at a farther Diſtance, contrary to what they do, who have had the Perception of the Ob⯑ject's growing more Confuſed, con⯑nected with the Idea of Approach.

XXXVIII. Lines and Angles why uſeful in Optics.

Hence alſo it doth appear, there may be good uſe of computation by Lines and Angles in Optics; not, that the Mind judges of Diſtance im⯑mediately by them, but becauſe it judges by ſomewhat which is con⯑nected with them, and to the deter⯑mination whereof, they may be ſub⯑ſervient. Thus the Mind judging of the Diſtance of an Object, by the Confuſedneſs of it's Appearance; and this Confuſedneſs being greater or leſſer to the naked Eye, accord⯑ing as the Object is ſeen by Rays more, or leſs Diverging; it follows, that a Man may make uſe of the Diver⯑gency of the Rays, in computing the apparent Diſtance, tho' not for it's own ſake, yet on account of the Confuſion with which it is connect⯑ed. [39] But, ſo it is, the Confuſion it ſelf is entirely neglected by Mathema⯑ticians, as having no neceſſary rela⯑tion with Diſtance, ſuch as the great⯑er or leſſer Angles of Divergency are conceiv'd to have. And theſe (eſpe⯑cially for that they fall under Ma⯑thematical Computation) are alone regarded, in determining the apparent Places of Objects, as tho' they were the ſole and immediate Cauſe of the Judgments the Mind makes of Di⯑ſtance. Whereas, in Truth, they ſhou'd not at all be regarded in them⯑ſelves, or any otherwiſe, than as they are ſuppoſed to be the Cauſe of Con⯑fuſed Viſion.

XXXIX. The not un⯑derſtand⯑ing this, a cauſe of Miſtake.

The not conſidering of this has been a fundamental and perplexing Overſight. For Proof whereof, we need go no farther than the Caſe before us. It having been obſer⯑ved, that the moſt Diverging Rays brought into the Mind the Idea of neareſt Diſtance, and that ſtill, as [40] the Divergency decreas'd, the Diſt⯑ance increas'd; and it being thought, the connexion between the various Degrees of Divergency, and Diſtance, was immediate; this naturally leads one to conclude, from an ill ground⯑ed Analogy, that Converging Rays ſhall make an Object appear at an immenſe Diſtance: And that, as the Convergency increaſes, the Diſtance (if it were poſſible,) ſhou'd do ſo likewiſe. That this was the Cauſe of Dr. Barrow's Miſtake, is evident from his own Words which we have Quoted. Whereas, had the learn⯑ed Doctor obſerv'd, that Diverging and Converging Rays, how oppo⯑ſite ſoever they may ſeem, do ne⯑vertheleſs agree in producing the ſame effect, viz. Confuſedneſs of Vi⯑ſion, greater Degrees whereof are produced indifferently, either as the Divergency, or Convergency of the Rays increaſeth. And that it is by this effect, which is the ſame in both, that either the Divergency, or Con⯑vergency [41] is perceived by the Eye. I ſay, had he but conſider'd this, 'tis certain he wou'd have made a quite contrary Judgment, and rightly con⯑cluded, that thoſe Rays which fall on the Eye with greater degrees of Convergency ſhou'd make the Ob⯑ject from whence they proceed, appear by ſo much the nearer. But 'tis plain, it was impoſſible for any Man to attain to a right Notion of this Matter, ſo long as he had regard only to Lines and Angles; and did not apprehend the true Nature of Viſion, and how far it was of Mathematical Conſideration.

XL. A Query propos'd by Mr. Moly⯑neux in his Diop⯑trics, con⯑ſider'd.

Before we diſmiſs this this Sub⯑ject, 'tis fit we take Notice of a Query, relating thereto, propo⯑ſed by the Ingenious Mr. Moly⯑neux, in his Treatiſe of Dioptrics, Par. 1. Prop. 31. Sect. 9. where ſpeak⯑ing of the Difficulty we have been explaining, he has theſe Words, ‘[42] And ſo he (i. e. Dr. Barrow) leaves this Difficulty to the Solution of Others, which I (after ſo great an Example) ſhall do likewiſe; but with the Reſolution of the ſame admirable Author of not quitting the evident Doctrine which we have before laid down, for determining the Locus Objecti, on account of being Preſs'd by one Difficulty, which ſeems in⯑explicable till a more intimate Knowledge of the Viſive Facul⯑ty be obtain'd by Mortals. In the mean time, I propoſe it to the Conſideration of the Ingeni⯑ous, Whether the Locus Apparens of an Object placed as in this 9th Section, be not as much be⯑fore the Eye, as the diſtinct Baſe is behind the Eye?’ To which Query we may venture to anſwer in the Negative. For in the pre⯑ſent Caſe, the Rule for determin⯑ing the Diſtance of the diſtinct Baſe, or reſpective Focus from the [43] Glaſs, is this. As the difference be⯑tween the Diſtance of the Object and Focus ∶ is to the Focus or Fo⯑cal Length ∷ So the Diſtance of the Object from the Glaſs ∶ to the Di⯑ſtance of the reſpective Focus or Di⯑ſtinct Baſe from the Glaſs. Vid. Moly⯑neux Dioptr. Par. 1. Prop. 5. Let us now ſuppoſe the Object to be pla⯑ced at the Diſtance of the Focal Length, and one half of the Fo⯑cal Length from the Glaſs, and the Eye cloſe to the Glaſs. Hence it will follow by the Rule, that the Diſtance of the Diſtinct Baſe behind the Eye is double the true Diſtance of the Object before the Eye. If therefore Mr. Molyneux's Con⯑jecture held good, it wou'd follow, that the Eye ſhou'd ſee the Object, twice as far off as it really is. And in other Caſes, at three or four times it's due Diſtance or more. But this manifeſtly contradicts Experience; the Object never appearing, at far⯑theſt, beyond its due Diſtance. What⯑ever [44] therefore is built on this Sup⯑poſition (vid. Corol. 1. Prop. 57. ibid.) comes to the Ground along with it.

XLI. One Born Blind wou'd not at firſt have any Idea of Di⯑ſtance by Sight.

From what hath been premis'd, it is a manifeſt Conſequence, that a Man Born Blind, being made to ſee wou'd at firſt, have no I⯑dea of Diſtance by Sight. The Sun and Stars, the remoteſt Ob⯑jects as well as the nearer wou'd all ſeem to be in his Eye, or rather in his Mind. The Objects intromitted by Sight, wou'd ſeem to him (as in truth they are) no other than a new Set of Thoughts or Senſations, each whereof is as near to him, as the Perceptions of Pain or Pleaſure, or the moſt inward Paſſions of his Soul. For our judging Objects perceiv'd by Sight to be at any Diſtance, or without the Mind, is (vid. Sect. XXVIII.) intirely the effect of Ex⯑perience, which one in thoſe Cir⯑cumſtances [45] cou'd not yet have at⯑tained to.

XLII. This not a⯑greeable to the com⯑mon Prin⯑ciples.

It is indeed otherwiſe upon the common Suppoſition, that Men judge of Diſtance by the Angle of the Optic Axes, juſt as one in the Dark, or a Blind-Man by the Angle comprehended by two Sticks, one whereof he held in each Hand. For if this were true, it wou'd follow that one Blind from his Birth, being made to See, ſhou'd ſtand in need of no new Experience, in order to perceive Diſtance by Sight. But that this is Falſe, has, I think, been ſufficiently demonſtrated.

XLIII. The proper Objects of Sight, not without the Mind, nor the Images of any thing without the Mind.

And perhaps, upon a ſtrict Inqui⯑ry we ſhall not find, that even thoſe, who from their Birth have grown up in a continu'd Habit of See⯑ing, are irrecoverably prejudiced on the other ſide, viz. in thinking what they See to be at a Di⯑ſtance from them. For at this [46] time it ſeems agreed on all Hands, by thoſe who have had any thoughts of that Matter, that Colours, which are the proper and immediate Ob⯑ject of Sight, are not without the Mind. But then ſay you, by Sight we have alſo the Ideas of Exten⯑ſion, and Figure, and Motion; all which may well be thought without, and at ſome Diſtance from the Mind, tho' Colour ſhou'd not. In anſwer to this, I appeal to any Man's Experience, whether the viſible Extenſion of any Ob⯑ject do not appear as near to him, as the Colour of that Ob⯑ject; Nay, whether they do not both ſeem to be in the very ſame Place. Is not the Extenſion we ſee Colour'd, 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 the Motion too. I ſpeak of thoſe which are per⯑ceiv'd by Sight.

XLIV. This more fully ex⯑plain'd.

But for a fuller Explication of this Point, and to ſhew that the immediate Objects of Sight are not ſo much as the Ideas or Reſem⯑blances of things placed at a Di⯑ſtance, 'tis requiſite we look near⯑er into the Matter, and carefully obſerve what is meant in com⯑mon Diſcourſe, when one ſays, that which he ſees is at a Diſtance from him. Suppoſe, for Example, That looking at the Moon I ſhou'd ſay, it were Fifty or Sixty Semi⯑diameters of the Earth diſtant from me. Let us ſee what Moon this is ſpoken of. 'Tis plain it can⯑not be the viſible Moon, or a⯑ny thing like the viſible Moon, or that which I ſee, which is on⯑ly a round, luminous Plain, of a⯑bout Thirty viſible Points in Dia⯑meter. For in caſe I am carry'd, from the place where I ſtand di⯑rectly towards the Moon; 'tis ma⯑nifeſt the Object varies, ſtill as I [48] go on; and by the time that I am advanced Fifty or Sixty Se⯑midiameters of the Earth, I ſhall be ſo far from being near a ſmall, round, luminous Flat, that I ſhall perceive nothing like it; this Ob-ject having long ſince diſappear'd, and if I wou'd recover it, it muſt be by going back to the Earth from whence I ſet out. Again, Suppoſe I perceive by Sight the faint and obſcure Idea of ſome⯑thing, which I doubt whether it be a Man, or a Tree, or a Tow⯑er; but judge it to be at the Di⯑ſtance of about a Mile. 'Tis plain I cannot mean, that what I ſee is a Mile off, or that it is the Image or Likeneſs of any thing which is a Mile off. Since that every Step I take towards it, the Appearance alters, and from be⯑ing Obſcure, Small, and Faint grows, Clear, Large, and Vigo⯑rous. And when I come to the Mile's end, that which I ſaw [49] firſt is quite loſt, neither do I find any thing in the likeneſs of it.

XLV. In what Senſe we muſt be un⯑derſtood to ſee Diſtance and exter⯑nal Things.

In theſe, and the like Inſtances, the truth of the Matter, I find, ſtands thus. Having of a long time, expe⯑rienced certain Ideas, perceivable by Touch, as Diſtance, Tangible Figure, and Solidity to have been con⯑nected with certain Ideas of Sight, I do upon perceiving theſe Ideas of Sight, forthwith conclude what Tangible Ideas are, by the won⯑ted, ordinary courſe of Nature like to follow. Looking at an Object I perceive a certain Viſible Figure, and Colour with ſome degree of Faint⯑neſs and other Circumſtances; which, from what I have formerly obſerv'd, determin me to think, that if I ad⯑vance forward ſo many Paces, Miles, &c. I ſhall be affected with ſuch, and ſuch Ideas of Touch. So that in truth, and ſtrictneſs of Speech, I neither ſee Diſtance it ſelf, nor any [50] thing that I take to be at a Diſtance. I ſay, neither Diſtance, nor things placed at a Diſtance are themſelves, or their Ideas, truly perceiv'd by Sight. This I am perſwaded of, as to what concerns my ſelf. And I believe whoever will look narrowly into his own Thoughts, and examin what he means by ſaying, he ſees this, or that thing at a Diſtance, will agree with me that, what he ſees only ſuggeſts to his Under⯑ſtanding, that after having paſſed a certain Diſtance, to be meaſur'd by the Motion of his Body, which is perceivable by Touch, he ſhall come to perceive ſuch, and ſuch Tangible Ideas which have been uſually connected with ſuch and ſuch Viſible Ideas. But that one might be deceived by theſe ſug⯑geſtions of Senſe, and that there is no neceſſary Connexion, between Viſible, and Tangible Ideas ſuggeſted by them, we need go no farther than the next Looking-Glaſs or Pi⯑cture, [51] to be convinced. Note, that when I ſpeak of Tangible Ideas, I take the Word Idea for any the im⯑mediate Object of Senſe, or Under⯑ſtanding, in which large Significati⯑on it is commonly uſed by the Mo⯑derns.

XLVI. Diſtance and Things placed at a Diſtance, not other⯑wiſe per⯑ceived by the Eye than by the Ear.

From what we have ſhewn it is a manifeſt Conſequence, that the I⯑deas of Space, Outneſs, and things placed at a Diſtance are not, ſtrictly ſpeaking, the Object of Sight. They are no otherwiſe perceived by the Eye, than by the Ear. Sitting in my Study I hear a Coach drive along the Streets. I look through the Caſe⯑ment and ſee it. I walk out and enter into it. Thus, common Speech wou'd incline one to think, I heard, ſaw, and touch'd the ſame Thing, viz. the Coach. It is, nevertheleſs, certain, the Ideas intromitted by each Senſe are widely different, and diſtinct from each other; but ha⯑ving been obſerved conſtantly to go [52] together, they are ſpoken of as one and the ſame thing. By the varia⯑tion of the Noiſe, I perceive the different Diſtances of the Coach, and know that it approaches before I look out. Thus by the Ear I per⯑ceive Diſtance, juſt after the ſame manner, as I do by the Eye.

XLVII. The Ideas of Sight more apt to be confoun⯑ded with the Ideas of Touch than thoſe of Hearing are.

I do not, nevertheleſs, ſay I hear Diſtance, in like manner as I ſay that I ſee it, the Ideas perceiv'd by Hear⯑ing not being ſo apt to be confound⯑ed with the Ideas of Touch, as thoſe of Sight are. So likewiſe, a Man is eaſily convinced that Bodies, and external Things are not properly the Object of Hearing, but only Sounds, by the Mediation whereof the Idea of this or that Body, or Diſtance is ſuggeſted to his Thoughts. But then one is with more difficulty, brought to diſcern the difference there is, betwixt the Ideas of Sight and Touch: Tho' it be certain, a Man no more Sees and Feels the ſame [53] Thing, than he Hears and Feels the ſame Thing.

XLVIII. How this comes to paſs.

One Reaſon of which ſeems to be this. It is thought a great Ab⯑ſurdity to imagine that one, and the ſame thing, ſhou'd have any more than one Extenſion, and one Figure. But the Extenſion and Figure of a Body, being let into the Mind two ways, and that indifferently, either by Sight, or Touch, it ſeems to fol⯑low that we ſee the ſame Extenſi⯑on, and the ſame Figure which we Feel.

XLIX. Strictly ſpeaking, we never ſee and feel the ſame thing.

But if we take a cloſe and ac⯑curate View of the Matter, it muſt be acknowledg'd, that we never See and Feel one and the ſame thing. That which is Seen is one thing, and that which is felt is another. If the Viſible Figure and Extenſion be not the ſame, with the Tangi⯑ble Figure and Extenſion, we are not to infer, that one and the ſame [54] thing has divers Extenſions. The true Conſequence is, that the Ob⯑jects of Sight and Touch are two diſtinct things. It may perhaps, re⯑quire ſome Thought, rightly to con⯑ceive this Diſtinction. And the dif⯑ficulty ſeems not a little increas'd, becauſe the Combination of Viſi⯑ble Ideas hath conſtantly the ſame Name, as the Combination of Tan⯑gible Ideas wherewith it is con⯑nected. Which does of neceſſity ariſe from the uſe, and end of Language.

L. Objects of Sight twofold Mediate and Imme⯑diate.

In order therefore to treat ac⯑curately, and unconfuſedly of Vi⯑ſion, we muſt bear in Mind, that there are two ſorts of Objects ap⯑prehended by the Eye: The one, pri⯑marily and immediately, the other, ſecondarily and by intervention of the former. Thoſe of the firſt ſort neither are, nor appear to be with⯑out the Mind, or at any diſtance off. They may, indeed, grow Great⯑er, [55] or Smaller, more Confuſed, or more Clear, or more Faint. But, they do not, cannot Approach, or even ſeem to Approach, or Re⯑cede from us. Whenever we ſay an Object is at a Diſtance, when⯑ever we ſay, it draws near, or goes farther off; we muſt always mean it of the latter ſort, which proper⯑ly belong to the Touch, and are not ſo truly perceived, as ſuggeſt⯑ed, by the Eye, in like manner as Thoughts by the Ear.

LI. Theſe hard to ſeparate, in our Thoughts.

No ſooner do we hear the Words of a familiar Language pronoun⯑ced in our Ears, but the Ideas correſponding thereto preſent them⯑ſelves to our Minds. In the very ſame inſtant, the Sound and the Meaning enter the Underſtanding. So cloſely are they United, that 'tis not in our Power to keep out the one, except we exclude the o⯑ther alſo. We even act in all re⯑ſpects, as tho' we heard the very [56] Thoughts themſelves. So likewiſe, the Secondary Objects, or thoſe which are only ſuggeſted by Sight, do often more ſtrongly affect us, and are more regarded than the pro⯑per Objects of that Senſe; along with which they enter into the Mind, and with which they have a far more ſtrict and near Con⯑nexion, than Ideas have with Words. Hence it is, we find it ſo difficult to diſcriminate, between the im⯑mediate and mediate Objects of Sight, and are ſo prone to at⯑tribute to the former, what be⯑longs only to the latter. They are, as it were, moſt cloſely twiſted, blended, and incorporated together. And the Prejudice is confirm'd, and riveted in our Thoughts, by a long tract of Time, by the uſe of Language, and want of Reflexi⯑on. However, I doubt not, but any one that ſhall attentively con⯑ſider what we have already ſaid, and ſhall ſay upon this Subject be⯑fore [57] we have done, (eſpecially if he purſue it in his own Thoughts) may be able to deliver himſelf from that Prejudice. Sure I am, 'tis worth ſome Attention, to whoever wou'd underſtand the true nature of Vi⯑ſion.

LII. The recei⯑ved Ac⯑counts of our percei⯑ving Mag⯑nitude by Sight falſe

I have now done with Diſtance, and proceed to ſhew, how it is, that we perceive by Sight, the Magni⯑tude of Objects. It is the Opinion of ſome, that we do it by Angles, or by Angles in Conjuction with Diſtance. But neither Angles, nor Diſtance being perceivable by Sight: And the things we ſee being, in truth, at no Diſtance from us; it follows, that as we have demonſtra⯑ted Lines and Angles not to be the Medium, the Mind makes uſe of in apprehending the Apparent Place, ſo neither are they, the Medium where⯑by it apprehends the Apparent Mag⯑nitude of Objects.

LIII. Magnitude perceiv'd as imme⯑diately, as Diſtance.

It is well known that the ſame Extenſion, at a near Diſtance, ſhall ſubtend a greater Angle, and at a farther Diſtance, a leſſer Angle. And by this Principle (we are told) the Mind eſtimates the Magnitude of an Object, comparing the Angle under which it is ſeen, with its Diſtance, and thence infering the Magnitude thereof. What inclines Men to this Miſtake (beſide the Humour of ma⯑king one ſee by Geometry) is, that the ſame Perceptions or Ideas which ſug⯑geſt Diſtance, do alſo ſuggeſt Mag⯑nitude. But if we examine it, we ſhall find they ſuggeſt the latter, as immediately as the former. I ſay, they do not firſt ſuggeſt Diſtance, and then leave it to the Judgment to uſe that as a Medium, whereby to collect the Magnitude; but they have as cloſe, and immediate a Con⯑nexion with the Magnitude, as with the Diſtance; and ſuggeſt Magni⯑tude as independently of Diſtance, [59] as they do Diſtance independently of Magnitude. All which will be evident, to whoever conſiders what⯑has been already ſaid, and what fol⯑lows.

LIV. Two kinds of ſenſible Extenſion, neither of which is infinitely Diviſible.

It has been ſhewn, there are two ſorts of Objects apprehended by Sight; each whereof hath its diſtinct Mag⯑nitude, or Extenſion. The one, pro⯑perly Tangible, i. e. to be perceiv'd and meaſur'd by Touch, and not immediately falling under the Senſe of Seeing. The other, properly and immediately Viſible, by Mediation of which, the former is brought in View. Each of theſe Magnitudes are greater or leſſer, according as they contain in 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 ſenſible Extenſion is not in⯑finitely Diviſible. There is a Mini⯑mum Tangibile, and a Minimum Viſi⯑bile, beyond which Senſe cannot per⯑ceive. [60] This, every ones Experience will inform him.

LV. The Tangi⯑ble Magni⯑tude of an Object ſteddy, the Viſible not.

The Magnitude of the Object which exiſts without the Mind, and is at a Diſtance, continues always invariably the ſame. But the Viſi⯑ble Object ſtill changing as you approach to, or recede from the Tangible Object, it hath no fixed and determinate Greatneſs. When⯑ever therefore, we ſpeak of the Mag⯑nitude of any thing, for Inſtance a Tree or a Houſe, we muſt mean the Tangible Magnitude, otherwiſe there can be nothing ſteddy, and free from Ambiguity ſpoken of it. Now, tho' the Tangible and Viſi⯑ble Magnitude do, in truth, belong to two diſtinct Objects: I ſhall ne⯑vertheleſs (eſpecially ſince thoſe Ob⯑jects are called by the ſame Name, and are obſerv'd to coexiſt) to a⯑void tediouſneſs and ſingularity of Speech, ſometimes ſpeak of them, as belonging to one and the ſame thing.

LVI. By what means, Tan⯑gible Mag⯑nitude is perceiv'd by Sight.

Now in order to diſcover by what means, the Magnitude of Tan⯑gible Objects is perceived by Sight; I need only reflect on what Paſſes in my own Mind. And obſerve what thoſe things be, which in⯑troduce the Ideas of greater or leſ⯑ſer into my Thoughts, when I look on any Object. And theſe I find to be, Firſt, the Magnitude or Ex⯑tenſion of the Viſible Object, which being immediately perceived by Sight, is connected with that other which is Tangible, and placed at a Diſtance. Secondly, The Confu⯑ſion or Diſtinctneſs. And, Thirdly, The Vigorouſneſs or Faintneſs of the aforeſaid Viſible Appearance. Caeteris paribus, by how much the greater or leſ⯑ſer, do I conclude the Tangible Object to be. But, be the Idea im⯑mediately perceived by Sight never ſo large, yet if it be withal Con⯑fuſed, [62] I judge the Magnitude of the thing to be but ſmall. If it be Diſtinct and Clear, I judge it greater. And if it be Faint, I ap⯑prehend it to be yet greater. What is here meant, by Confuſion and Faintneſs, has been Explain'd in Sect. XXXV.

LVII. This far⯑ther en⯑larged on.

Moreover, the Judgments we make of Greatneſs do, in like man⯑ner as thoſe of Diſtance, depend on the Diſpoſition of the Eyes, al⯑ſo on the Figure, Number of in⯑termediate Objects, and other Cir⯑cumſtances that have been obſerv'd to attend great, or ſmall Tangi⯑ble Magnitudes. Thus, for Inſtance, The very ſame Quantity of Viſi⯑ble Extenſion, which in the Figure of a Tower, doth ſuggeſt the Idea of great Magnitude, ſhall, in the Figure of a Man, ſuggeſt the Idea of much ſmaller Magnitude. That this is owing to the Experience we have had, of the uſual Bigneſs of [63] a Tower and a Man, no one, I ſup⯑poſe, need be told.

LVIII. No neceſſa⯑ry Connexi⯑on between, Confuſion or Faintneſs of Appear⯑ance, and ſmall or great Mag⯑nitude.

It is alſo evident, that Confuſion, Faintneſs, &c. have no more a neceſ⯑ſary Connexion with little or great Magnitude, than they have with little or great Diſtance. As they ſuggeſt the latter, ſo they ſuggeſt the former to our Minds. And, by Conſequence, if it were not for Experience, we ſhou'd no more judge a faint or confuſed Appear⯑ance to be connected, with great or little Magnitude, than we ſhou'd that it was connected with great or little Diſtance.

LIX. The Tangi⯑ble Magni⯑tude of an Object, more heed⯑ed than the Viſible; and why.

Nor will it be found, that great or ſmall Viſible Magnitude hath any neceſſary Relation to great or ſmall Tangible Magnitude: So that the one may certainly, and infallibly be infer'd from the other. But, before we come to the Proof of this, 'tis fit we conſider the dif⯑ference [64] there is, betwixt the Ex⯑tenſion and Figure which is the proper Object of Touch, and that other which is termed Viſible; and how the former is principally, tho' not immediately, taken notice of, when we look at any Object. This has been before mention'd, but we ſhall here enquire into the Cauſe thereof. We regard the Ob⯑jects that environ us, in propor⯑tion as they are adapted to be⯑nefit, or injure our own Bodies, and thereby, produce in our Minds the Senſations of Pleaſure, or Pain. Now Bodies operating on our Or⯑gans, by an immediate Applicati⯑on: And the Hurt and Advantage ariſing there-from, depending alto⯑gether on the Tangible, ang not at all on the Viſible, Qualities of any Object. This is a plain Rea⯑ſon, why thoſe ſhou'd be regard⯑ed by us much more than theſe. And for this End, chiefly, the Vi⯑ſive Senſe ſeems to have been be⯑ſtowed [65] on Animals, viz. that by the Perception of Viſible Ideas (which in themſelves are not ca⯑pable of affecting, or any wiſe alter⯑ing the Frame of their Bodies) they may be able to foreſee (from the Experience they have had, what Tan⯑gible Ideas are connected with ſuch, and ſuch Viſible Ideas) the Damage or Benefit which is like to enſue, upon the Application of their own Bodies to this, or that Body which is at a Diſtance. Which Foreſight, how neceſſary it is to the preſer⯑vation of an Animal, every ones Experience can inform him. Hence it is, that when we look at an Object, the Tangible Figure and Extenſion thereof are principally attended to; whilſt there is ſmall heed taken of the Viſible Figure and Magnitude, which, tho' more immediately perceiv'd, do leſs ſen⯑ſibly affect us, and are not fitted to produce any Alteration in our Bodies.

LX. An Inſtance of this.

That the Matter of Fact is true, will be evident to any one, who conſiders that a Man placed at Ten Foot Diſtance, is thought as great, as if he were placed at the Diſtance only of Five Foot; which is true, not with Relation to the Viſible, but Tangible great⯑neſs of the Object. The Viſible Magnitude being far greater, at one Station, than it is at the o⯑ther.

LXI. Men do not Meaſure by Viſible Feet or Inches.

Inches, Feet, &c. are ſettled, ſta⯑ted Lengths, whereby we meaſure Objects, and eſtimate their Mag⯑nitude, we ſay, for Example, an Object appears to be Six Inches, or Six Foot long. Now, that this cannot be meant of Viſible Inch⯑ches, &c. is evident, becauſe a Vi⯑ſible Inch is it ſelf no conſtant, de⯑terminate Magnitude, and cannot, therefore, ſerve to mark out, and determin the Magnitude of any o⯑ther [67] thing. Take an Inch mark'd upon a Ruler; view it, ſucceſſive⯑ly, at the Diſtance of Half a Foot, a Foot, a Foot and a Half, &c. from the Eye; at each of which, and at all the intermediate Diſtances, the Inch ſhall have a different Vi⯑ſible Extenſion, i. e. there ſhall be more or fewer Points diſcerned in it. Now I ask which of all theſe various Extenſions, is that Stated, determinate one, that is agreed on, for a common Meaſure of other Magnitudes? No reaſon can be aſ⯑ſign'd, why we ſhou'd pitch on one, more than another. And ex⯑cept there be ſome invariable, de⯑terminate Extenſion fixed on, to be mark'd by the Word Inch, 'tis plain, it can be uſed to little Pur⯑poſe; and to ſay, a Thing con⯑tains this or that Number of Inch⯑es, ſhall imply no more than that it is extended, without bringing any particular Idea of that Exten⯑ſion into the Mind. Farther, an [68] Inch and a Foot, from different Diſtances, ſhall both exhibit the ſame Viſible Magnitude, and yet at the ſame time, you ſhall ſay, that one ſeems ſeveral times great⯑er than the other. From all which it is manifeſt, that the Judgments we make of the Magnitude of Ob⯑jects by Sight, are altogether in re⯑ference to their Tangible Extenſi⯑on. Whenever we ſay an Object is Great, or Small, of this or that determinate Meaſure, I ſay, it muſt be meant of the Tangible, and not the Viſible Extenſion, which, tho' immediately perceiv'd, is neverthe⯑leſs little taken Notice of.

LXII. No neceſſa⯑ry Conexi⯑on between Viſible and Tangible Extenſion.

Now, that there is no neceſſa⯑ry Connexion, between theſe two Diſtinct Extenſions is evident from hence. Becauſe our Eyes might have been framed in ſuch a man⯑ner, as to be able to ſee nothing but what were leſs than the Mini⯑mum Tangibile. In which Caſe, it's not [69] impoſſible we might have perceived all the Immediate Objects of Sight, the very ſame that we do now. But unto thoſe Viſible Appearances, there wou'd not be Connected thoſe different Tangible Magnitudes, that are now. Which ſhews, the Judg⯑ments we make of the Magnitude of Things placed at a Diſtance, from the various Greatneſs of the Immediate Objects of Sight, do not ariſe from any Eſſential or Neceſſary, but only a Cuſtomary Tye, which has been obſerv'd be⯑twixt them.

LXIII. Greater Vi⯑ſible Mag⯑nitude might ſig⯑nifie Leſſer Tangible Magnitude

Moreover, it is not only certain, that any Idea of Sight might not have been Connected, with this or that Idea of Touch, we now ob⯑ſerve to accompany it: But alſo, that the greater Viſible Magnitudes might have been Connected with, and In⯑troduced into our Minds, leſſer Tangible Magnitudes, and Vice Ver⯑ſa. Nay, that it often is ſo, we [70] have daily Experience; that Object which makes a ſtrong and large Appearance, not ſeeming near ſo great, as another the Viſible Mag⯑nitude whereof is much leſs, but more faint.

LXIV. The Judg⯑ments we make of Magnitude depend al⯑together on Experience

From which, and from Sect. LVII, and LVIII. it is manifeſt, that as we do not perceive the Magnitude of Objects immediate⯑ly by Sight, ſo neither do we per⯑ceive them, by the Mediation of any thing which has a neceſſary Connexion with them. Thoſe Ideas that now ſuggeſt unto us, the va⯑rious Magnitudes of External Ob⯑jects, before we touch them, might poſſibly have ſuggeſted no ſuch thing: Or they might have ſignified them, in a direct, contrary manner, ſo that the very ſame Ideas, on the Perception whereof we judge an Object to be ſmall, might as well have ſerv'd to make us conclude it great. Thoſe Ideas being in their [71] own Nature, equally fitted to bring into our Minds the Idea of Small, or Great, or no Size at all of outward Objects. Juſt as the Words of any Language are in their own Nature, indifferent to ſignifie this, or that thing, or nothing at all.

LXV. Diſtance and Mag⯑nitude ſeen as Shame or Anger.

As we ſee Diſtance, ſo we ſee Magnitude. And we ſee both, in the ſame way that we ſee Shame or Anger, in the Looks of a Man. Thoſe Paſſions are themſelves In⯑viſible, they are nevertheleſs let in by the Eye along with Colours, and alterations of Countenance, which are the immediate Object of Viſion: And which ſignifie them for no other Reaſon, than barely becauſe they have been obſerv'd to accompany them. Without which Experience, we ſhou'd no more have taken Bluſhing for a Sign of Shame, than of Gladneſs.

LXVI. But we are prone to think o⯑therwiſe, and why.

We are nevertheleſs exceeding Prone to imagine, thoſe things which are perceived only by the Mediation of others, to be them⯑ſelves the immediate Objects of Sight: Or, at leaſt, to have in their own Nature a Fitneſs to be ſuggeſt⯑ed by them, before ever they had been experienced to Coexiſt with them. From which prejudice eve⯑ry one, perhaps, will not find it eaſy to emanicipate himſelf, by a⯑ny the cleareſt Convictions of Rea⯑ſon. And there are ſome Grounds to think, that if there was one only invariable, and univerſal Lan⯑guage in the World, and that Men were born with the Faculty of ſpeaking it; it wou'd be the O⯑pinion of ſome, that the Ideas in other Mens Minds were properly perceived by the Ear, or had at leaſt a neceſſary and inſeparable Tye with the Sounds that were affix⯑ed to them. All which ſeems to [73] ariſe, from want of a due Appli⯑cation of our Diſcerning Faculty, thereby to Diſcriminate between the Ideas that are in our Under⯑ſtandings, and conſider them apart from each other; which wou'd preſerve us from confounding thoſe that are different, and make us to ſee what Ideas do, and what do not include, or imply this or that other Idea.

LXVII. The Moon ſeems greater in the Hori⯑zon than in the Me⯑ridian.

There is a Celebrated Phaeno⯑menon, the Solution whereof I ſhall attempt to give, by the Principles that have been laid down, in re⯑ference to the manner wherein we apprehend by Sight, the Magnitude of Objects. It is as follows. The apparent Magnitude of the Moon when placed in the Horizon, is much greater than when it is in the Meridian. Tho' the Angle un⯑der which the Diameter of the Moon is ſeen, be not obſerv'd greater in the former Caſe, than [74] in the latter. Moreover, the Ho⯑rizontal Moon doth not conſtant⯑ly appear of the ſame Bigneſs, but at ſome times ſeemeth far great⯑er than at others.

LXVIII. The cauſe of this Phaenome⯑non, aſſign⯑ed.

Now in order to explicate the reaſon, of the Moon's appearing greater than ordinary in the Ho⯑rizon; it muſt be obſerv'd, that the Particles which compoſe our Atmoſphaere, do intercept the Rays of Light, proceeding from any Ob⯑ject to the Eye; and by how much the greater is the Portion of Atmoſphaere, interjacent between the Object and the Eye, by ſo much the more are the Rays intercept⯑ed; and by conſequence, the Ap⯑pearance of the Object render'd more Faint: Every Object appearing more Vigorous or more Faint, in Proportion as it ſendeth more or fewer Rays unto the Eye. Now, be⯑tween the Eye, and the Moon, when ſituated in the Horizon, there lies [75] a far greater Quantity of Atmo⯑ſphaere, than there does when the Moon is in the Meridian. Whence it comes paſs, that the Appearance of the Horizontal Moon is fain⯑ter, and therefore by Sect. LVI, it ſhou'd be thought bigger in that Situation, than in the Meridian, or in any other Elevation above the Horizon.

LXIX. The Hori⯑zontal Moon, why greater at one time than ano⯑ther.

Farther, The Air being variouſly impregnated, ſometimes more and ſometimes leſs, with Vapours and Exhalations fitted to retund and intercept the Rays of Light; it follows, that the Appearance of the Horizontal Moon hath not always an equal Faintneſs; and by Conſe⯑quence, that Luminary, tho' in the very ſame Situation, is at one time judged greater than at another.

LXX. The Ac⯑count we have gi⯑ven, prov'd to be true.

That we have here given the true Account of the Phaenomena of the Horizontal Moon, will, I ſup⯑poſe, [76] be farther Evident to any one from the following Conſide⯑rations. Firſt, 'Tis plain, that which in this Caſe ſuggeſts the Idea of greater Magnitude, muſt be ſome⯑thing which is it ſelf perceiv'd; for, that which is unperceiv'd can⯑not ſuggeſt to our Perception a⯑ny other thing. Secondly, It muſt be ſomething that does not con⯑ſtantly remain the ſame, but is ſubject to ſome Change or Va⯑riation, ſince the Appearance of the Horizontal Moon varies, be⯑ing at one time greater than at another. Thirdly, It muſt not lie in the External Circumjacent or Intermediate Objects but be an Affection of the very Viſible Moon it ſelf: Since by looking thro' a Tube, when all other Objects are excluded from Sight, the Appear⯑ance is as great as ever. And yet, Fourthly, It cannot be the Vi⯑ſible Figure or Magnitude, ſince that remains the ſame, or is ra⯑ther [77] leſſer, by how much the Moon is nearer to the Horizon. It re⯑mains therefore, that the true Cauſe is that Affection or Alteration of the Viſible Appearance, which pro⯑ceeds from the greater Paucity of Rays arriving at the Eye, and which I term Faintneſs: Since this anſwers all the foremention'd Conditions, and I am not conſcious of any other Perception that does.

LXXI. And con⯑firmed, by the Moon's appearing greater in a Miſt.

Add to this, that in miſty Wea⯑ther it is a common Obſervation, that the Appearance of the Hori⯑zontal Moon is far larger than u⯑ſual, which greatly conſpires with, and ſtrengthens our Opinion. Nei⯑ther wou'd it prove, in the leaſt, Ir⯑reconcilable with what we have ſaid: If the Horizontal Moon ſhou'd chance ſometime to ſeem enlarged beyond its uſual Extent, even in more Serene Weather. For we muſt not only have regard to the Miſt, which happens to be in [78] the place where we ſtand; we ought alſo to take into our Thoughts, the whole Sum of Vapours and Ex⯑halations, which lie betwixt the Eye and the Moon: All which cooperating to render the Appear⯑ance of the Moon more Faint, and thereby increaſe it's Magni⯑tude, it may chance to appear greater than it uſually does, even in the Horizontal Poſition, at a time when, tho' there be no ex⯑traordinary Fog or Hazineſs, juſt in the place where we ſtand, yet, the Air between the Eye and the Moon, taken all together, may be loaded with a greater quantity of interſperſed Vapours and Exhalati⯑ons, than at other times.

LXXII. Objection anſwer'd.

It may be Objected, That in Conſequence of our Principles, the Interpoſition of a Body in ſome degree Opaque, which may Inter⯑cept a great Part of the Rays of Light, ſhou'd render the Appear⯑ance [79] of the Moon in the Meridi⯑an as large, as when it is viewed in the Horizon. To which I an⯑ſwer, 'tis not Faintneſs any how apply'd, that ſuggeſts greater Mag⯑nitude. There being no neceſſary, but only an experimental Connexi⯑on between thoſe two things: It follows, that the Faintneſs, which enlarges the Appearance, muſt be applied in ſuch Sort, and with ſuch Circumſtances, as have been ob⯑ſerved to attend the Viſion of great Magnitudes. When from a Diſtance (I ſpeak with the Vulgar) we be⯑hold great Objects, the Particles of the intermediate Air and Va⯑pours, which are themſelves unper⯑ceivable, do interrupt the Rays of Light, and thereby render the Ap⯑pearance leſs Strong and Vivid; now, Faintneſs of Appearance cau⯑ſed in this Sort, hath been ex⯑perienced to coexiſt with great Magnitude. But, when it is cau⯑ſed by the Interpoſition of an Opa⯑que, [80] ſenſible Body, this Circum⯑ſtance alters the Caſe; ſo that a Faint Appearance this way cauſed, does not ſuggeſt greater Magni⯑tude, becauſe it hath not been ex⯑perienced to coexiſt with it.

LXXIII. The way wherein Faintneſs ſuggeſts greater Magnitude Illuſtrated.

Faintneſs, as well as all other Ideas or Perceptions, which ſug⯑geſt Magnitude or Diſtance, does it in the ſame way, that Words ſug⯑geſt the Notions to which they are annexed. Now, it is known, a Word pronounced with certain Circum⯑ſtances, or in a certain Context with other Words, hath not always the ſame Import and Signification, that it hath when pronounced in ſome other Circumſtances, or dif⯑ferent Context of Words. This well conſider'd may, perhaps, pre⯑vent ſome Objections that might otherwiſe be made, againſt what we have offer'd as the true Ex⯑plication of the Appearance of the Horizontal Moon.

LXXIV. Appear⯑ance of the Horizontal Moon, why thought difficult to explain.

If we attentively conſider the Phae⯑nomenon before us, we ſhall find the not diſcerning between the Mediate, and Immediate Objects of Sight, to be the chief Cauſe of the Difficulty that occurs in the Explication of it. The Magnitude of the Viſible Moon, or that which is the proper and immediate Ob⯑ject of Viſion, is no greater when the Moon is in the Horizon, than when it is in the Meridian. How comes it, therefore, to ſeem great⯑er in one Situation than the o⯑ther? What is it can put this Cheat on the Underſtanding? It has no other Perception of the Moon, than what it gets by Sight: And that which is ſeen is of the ſame Extent, I ſay, the Viſible Appearance hath the very ſame, or, rather, a leſſer Magnitude when the Moon is view'd in the Ho⯑rizontal, than when in the Meri⯑dional Poſition: And yet it is E⯑ſteemed [82] greater in the former, than in the latter. Herein conſiſts the Difficulty; which doth Vaniſh, and admit of a moſt eaſy Solution, if we conſider that, as the Viſible Moon is not greater in the Ho⯑rizon, than in the Meridian, ſo nei⯑ther is it thought to be ſo. It hath been already ſhewn, that in any act of Viſion, the Viſible Ob⯑ject abſolutely, or in it ſelf, is lit⯑tle taken notice of, the Mind ſtill carrying its View from that to ſome Tangible Ideas, which have been obſerv'd to be Connected with it, and by that means, come to be ſuggeſted by it. So that when a thing is ſaid to appear Great, or Small, or whatever Eſtimate be made of the Magnitude of any Thing; this is meant, not of the Viſible, but, of the Tangible Ob⯑ject. This duly conſider'd, it will be no hard matter to reconcile, the ſeeming Contradiction there is, that the Moon ſhou'd appear of [83] a different Bigneſs, the viſible Mag⯑nitude thereof remaining ſtill the ſame. For by Sect. LVI. the very ſame viſible Extenſion, with a dif⯑ferent Faintneſs, ſhall ſuggeſt a dif⯑ferent Tangible Extenſion. When, therefore, the Horizontal Moon is ſaid to appear greater than the Me⯑ridional Moon; this muſt be un⯑derſtood, not of a greater Viſi⯑ble Extenſion, but of a greater Tangible Extenſion; which, by reaſon of the more than ordinary Faintneſs of the Viſible Appear⯑ance, is ſuggeſted to the Mind a⯑long with it.

LXXV. Attempts towards the Soluti⯑on of it made by ſeveral, but in vain.

Many Attempts have been made by Learned Men, to account for this Appearance. Gaſſendus, Deſ⯑cartes, Hobbs, and ſeveral others, have employ'd their Thoughts on that Subject: But how fruitleſs and unſatisfactory their Endeavours have been, is ſufficiently ſhewn by Mr. Molyneux, vid. Philoſ. Tranſ. [84] Numb. 187, p. 314. where you may ſee their ſeveral Opinions at large ſet forth and confuted, not with⯑out ſome Surprize at the groſs Blunders, that Ingenious Men have been forced into, by endeavour⯑ing to reconcile this Appearance with the ordinary Principles of Optics. Since the Writing of which Diſcourſe, there hath been Publiſh'd in the Tranſactions, Numb. 187, p. 323. another Paper rela⯑ting to the ſame Affair, by the Celebrated Dr. Wallis, wherein he pretends to account for that Phae⯑nomenon; which, tho' it ſeems not to contain any thing new, or different from what had been ſaid before by others, I ſhall ne⯑vertheleſs conſider in this place.

LXXVI. The Opini⯑on of Dr. Wallis.

His Opinion in ſhort is this. We judge not of the Magni⯑tude of an Object by the Optic Angle alone, but by the Optic Angle in Conjunction with the [85] Diſtance, Hence, tho' the An⯑gle remain the ſame, or even becomes leſs; yet if withal the Diſtance ſeem to have been in⯑creas'd, the Object ſhall appear greater. Now, one way whereby we eſtimate the Diſtance of any thing, is by the Number and Ex⯑tent of the intermediate Objects: When therefore the Moon is ſeen in the Horizon, the Variety of Fields, Houſes, &c. together with the large Proſpect of the wide-extended Land, or Sea, that lies between the Eye and the utmoſt Limb of the Horizon, ſuggeſt unto the Mind the Idea of greater Di⯑ſtance, and conſequently magnify the Appearance. And this, accord⯑ing to Dr. Wallis, is the true Ac⯑count of the extraordinary Large⯑neſs attributed by the Mind to the Horizontal Moon, at a time when the Angle ſubtended by its Diameter, is not one jot greater than it us'd to be.

LXXVII. It is ſhewn to be unſa⯑tisfactory.

With reference to this Opinion, not to repeat what has been al⯑ready ſaid concerning Diſtance, I ſhall only obſerve, Firſt, That if the Proſpect of interjacent Ob⯑jects be that which ſuggeſts the Idea of farther Diſtance, and this Idea of farther Diſtance be the Cauſe, that brings into the Mind the Idea of greater Magnitude; it ſhould hence follow, that if one look'd at the Horizontal Moon from behind a Wall, it would appear no bigger than or⯑dinary. For in that Caſe, the Wall interpoſing, cuts off all that Proſpect of Sea and Land, &c. which might otherwiſe increaſe the apparent Diſtance, and there⯑by the apparent Magnitude of the Moon. Nor will it ſuffice to ſay, the Memory doth even then ſuggeſt all that Extent of Land, &c. which lies within the Hori⯑zon; which Suggeſtion occaſions [87] a ſudden Judgment of Senſe, that the Moon is farther off, and lar⯑ger than uſual. For ask any Man, who from ſuch a Station behold⯑ing the Horizontal Moon, ſhall think her greater than uſual, whe⯑ther he have at that time in his Mind any Idea of the intermedi⯑ate Objects, or long Tract of Land that lies between his Eye and the extream Edge of the Horizon? And whether it be that Idea which is the Cauſe of his making the aforemention'd Judg⯑ment? He will, without doubt, reply in the Negative, and de⯑clare the Horizontal Moon ſhall appear greater than the Meridio⯑nal, tho' he never thinks of all or any of thoſe things that lie between him and it. And as for the Abſurdity of any Idea's intro⯑ducing into the Mind another, whilſt it ſelf is not perceiv'd, this has already fallen under our Ob⯑ſervation, and is too evident to [88] need any farther Enlargement on it. Secondly, It ſeems impoſſible by this Hypotheſis, to account for the Moon's appearing in the ve⯑ry ſame Situation, at one time greater than at another. Which, nevertheleſs, has been ſhewn to be very agreeable to the Principles we have laid down, and receives a moſt eaſie and natural Explica⯑tion from them.

LXXVIII. How Lines and Angles may be of uſe in com⯑puting ap⯑parent Magni⯑tudes.

This Phaenomenon of the Hori⯑zontal Moon is a clear Inſtance of the Inſufficiency of Lines and Angles, for explaining the way wherein the Mind perceives, and eſtimates the Magnitude of out⯑ward Objects. There is, never⯑theleſs, a uſe of Computation by them, in order to determin the apparent Magnitude of things, ſo far as they have a Connexion with, and are Proportional to thoſe other Ideas, or Perceptions which are the true and immedi⯑ate [89] Occaſions that ſuggeſt to the Mind the apparent Magnitude of Things. But this in general may, I think, be obſerv'd concerning Mathematical Computation in Op⯑tics: That it can hardly be very Preciſe and Exact, ſince the Judgments we make of the Mag⯑nitude of External Things, do often depend on ſeveral Circum⯑ſtances, which are not Proportio⯑nal to, or capable of being defin'd by Lines and Angles.

LXXIX. One born Blind, be⯑ing made to See, what Judgment he'd make of Magni⯑tude.

From what has been ſaid we may ſafely deduce this Conſe⯑quence, viz. That a Man born Blind, and made to See, wou'd, at firſt opening of his Eyes, make a very different Judgment of the Magnitude of Objects in⯑tromitted by them, from what others do. He wou'd not con⯑ſider the Ideas of Sight with re⯑ference to, or as having any Connexion with the Ideas of [90] Touch. His View of them be⯑ing intirely terminated within them⯑ſelves, he can no otherwiſe judge them Great or Small, than as they contain a greater or leſſer Num⯑ber of Viſible Points. Now, it being certain, that any Viſible Point can cover or exclude from View, only one other Viſible Point, it follows, that whatever Object intercepts the View of another, hath an equal Number of Viſible Points with it; and conſequently they ſhall both, by him, be thought to have the ſame Magnitude. Hence, it's e⯑vident, one in thoſe Circumſtan⯑ces would judge his Thumb, with which he might hide a Tower, or hinder its being ſeen, e⯑qual to that Tower, or his Hand, the Interpoſition whereof might con⯑ceal the Firmament from his View, equal to the Firmament. How great an Inequality ſoever there may, in our Apprehenſions, ſeem [91] to be betwixt thoſe two things: becauſe of the cuſtomary and cloſe Connexion, that has grown up in our Minds between the Objects of Sight and Touch, whereby the very different and diſtinct Ideas of thoſe two Senſes, are ſo blended and confounded together, as to be miſtaken for one and the ſame thing; out of which Pre⯑judice, we cannot totally extricate our ſelves, without ſome Labour and Striving of Thought.

LXXX. The Mini⯑mum Vi⯑ſibile the ſame to all Creatures.

For the better clearing up the Nature of Viſion, and ſetting the manner wherein we perceive Mag⯑nitudes in a due Light, I ſhall proceed to make ſome Obſerva⯑tions concerning Matters relating thereto, whereof the want of Re⯑flexion, and duly ſeparating be⯑tween Tangible and Viſible Ideas, is apt to create in us miſtaken and confuſed Notions. And, Firſt, I ſhall obſerve that the Minimum [92] Viſibile is exactly equal in all Be⯑ings whatſoever, that are endow'd with the Viſive Faculty. No ex⯑quiſite Formation of the Eye, no peculiar Sharpneſs of Sight, can make it leſs in one Creature, than in another. For it not be⯑ing diſtinguiſhable into Parts, nor in any wiſe conſiſting of them, it muſt neceſſarily be the ſame to all. For ſuppoſe it otherwiſe, and that the Minimum Viſibile of a Mite, for Inſtance, be leſs than the Minimum Viſibile of a Man; the latter, therefore, may by Detracti⯑on of ſome part be made equal to the former: It doth, therefore, con⯑ſiſt of Parts: Which is inconſiſtent with the Notion of a Minimum Viſi⯑bile, or Point.

LXXXI. Objection anſwer'd.

It will, perhaps, be objected, that the Minimum Viſibile of a Man doth really, and in it ſelf, contain Parts whereby it ſurpaſſes that of a Mite, tho' they are not [93] perceivable by the Man. To which I anſwer, the Minimum Vi⯑ſibile having (in like manner as all other the Proper and Imme⯑diate Objects of Sight) been ſhewn not to have any Exiſtence with⯑out the Mind of him who ſees it, it follows, there cannot be any part of it that is not actu⯑ally perceiv'd, and therefore Viſi⯑ble. Now, for any Object to con⯑tain ſeveral diſtinct, viſible Parts, and at the ſame time to be a Minimum Viſibile, is a manifeſt Contradiction.

LXXXII. The Eye at all times, perceives the ſame number of viſible Points.

Of theſe Viſible Points we ſee at all times an equal Number. It is every whit as great when our View is contracted, and bound⯑ed by near Objects, as when it is extended to larger and remoter ones. For it being impoſſible, that one Minimum Viſibile ſhould obſcure, or keep out of Sight, more than one other; it's a plain [94] Conſequence, that when my View is on all ſides bounded by the Walls of my Study, I ſee juſt as many viſible Points, as I cou'd, in caſe that by the Removal of the Study-Walls, and all other Obſtructions, I had a full Proſ⯑pect of the circumjacent Fields, Mountains, Sea, and open Firma⯑ment. For, ſo long as I am ſhut up within the Walls, by their Interpoſition every Point of the External Object is cover'd from my View. But each Point that is ſeen, being able to cover or exclude from Sight, one only o⯑ther correſponding Point: It fol⯑lows, that whilſt my Sight is confin'd to thoſe narrow Walls, I ſee as many Points, or Minima Viſibilia, as I ſhould, were thoſe Walls away, by looking on all the External Objects, whoſe Pro⯑ſpect is intercepted by them. Whenever, therefore, we are ſaid to have a greater Proſpect at one [95] time than another; this muſt be underſtood with relation, not to the proper and immediate, but the ſecondary and mediate Ob⯑jects of Viſion, which, as hath been ſhewn, do properly belong to the Touch.

LXXXIII Two Im⯑perfections in the Vi⯑ſive Fa⯑culty.

The Viſive Faculty conſider'd, with reference to it's immediate Objects, may be found to La⯑bour of two Defects. Firſt, In reſpect of the Extent or Number of viſible Points that are at once perceivable by it, which is nar⯑row and limited to a certain De⯑gree. It can take in at one View but a certain, determinate Num⯑ber of Minima Viſibilia, beyond which it cannot extend it's Pro⯑ſpect. Secondly, Our Sight is de⯑fective in that its View is not only narrow, but alſo, for the moſt part, confus'd. Of thoſe things that we take in at one Proſpect, we can ſee but a few [96] at once clearly and unconfuſedly. And the more we fix our Sight on any one Object, by ſo much the Darker and more Indiſtinct ſhall the reſt appear.

LXXXIV Anſwering to which, we may conceive two Per⯑fections.

Correſponding to theſe two De⯑fects of Sight, we may imagine as many Perfections, viz. 1ſt. That of comprehending in one View, a greater number of Viſible Points. 2dly, Of being able to View them all equally, and at once, with the utmoſt Clearneſs and Diſtinction. That theſe Perfections are not actu⯑ally in ſome Intelligences, of a different Order and Capacity from ours, it is impoſſible for us to know.

LXXXV. In neither of theſe two Ways do Microſcopes improve the Sight.

In neither of theſe two Ways, do Microſcopes contribute to the improvement of Sight. For, when we look thro' a Microſcope, we nei⯑ther ſee more Viſible Points, nor are the Collateral Points more Di⯑ſtinct, [97] than when we look with the naked Eye, at Objects placed in a due Diſtance. A Microſcope brings us, as it were, into a new World: It preſents us with a new Scene of Viſible Objects, quite dif⯑ferent from what we behold with the naked Eye. But herein con⯑ſiſts the moſt remarkable Difference, viz. That whereas the Objects per⯑ceived by the Eye alone have a certain Connexion with Tangible Objects, whereby we are taught to Foreſee what will enſue, upon the Approach or Application of di⯑ſtant Objects to the Parts of our own Body, which much condu⯑ceth to it's Preſervation; there is not the like Connexion between things Tangible and thoſe Viſible Objects, that are perceiv'd by help of a fine Microſcope.

LXXXVI The Caſe of Microſcopi⯑cal Eyes, conſider'd.

Hence it's evident, that were our Eyes turned into the Nature of Mi⯑croſcopes, we ſhou'd not be much [98] benefited by the Change. We ſhou'd be depriv'd of the fore⯑mention'd Advantage we at pre⯑ſent receive by the Viſive Faculty; and have left us only the empty Amuſement of Seeing, without any other benefit ariſing from it. But in that Caſe, it will perhaps be ſaid, our Sight wou'd be endued with a far greater Sharpneſs and Pene⯑tration than it now hath. But I wou'd fain know wherein con⯑ſiſts that Sharpneſs, which is e⯑ſteem'd ſo great an Excellency of Sight. It is certain from what we have already ſhewn, that the Mi⯑nimum Viſibile is never Greater, or Leſſer, but in all Caſes conſtant⯑ly the ſame. And in the Caſe of Microſcopical Eyes, I ſee only this difference, viz. that upon the Ceaſing of a certain obſervable Connexion, betwixt the divers Per⯑ceptions of Sight and Touch, which before enabled us to regulate our Actions by the Eye: It wou'd [99] now be render'd utterly unſervi⯑ceable to that Purpoſe. Which whether it be a deſirable Perfecti⯑on, or no, I leave it to any one to determin.

LXXXVII The Sight, admirably adapted to the ends of Seeing.

Upon the whole, my Opinion is, That if we conſider the Uſe and End of Sight, together with the preſent State and Circumſtances of our Being, we ſhall not find any great Cauſe, to complain of any Defect or Imperfection in it, or eaſily conceive how it cou'd be mended. With ſuch admirable Wiſdom is that Faculty contriv'd, both for the Pleaſure and Con⯑veniency of Life.

LXXXVIII Difficulty concerning Erect Vi⯑ſion.

Having finiſh'd what I intend⯑ed to ſay, concerning the Diſtance and Magnitude of Objects, I come now to treat of the Manner, where⯑in the Mind perceives by Sight their Situation. Among the Diſcoveries of the laſt Age, it is reputed none of the [100] leaſt, that the manner of Viſion has been more clearly Explain'd, than ever it had been before. There is, at this Day, no one Ignorant, that the Pictures of External Ob⯑jects are Painted on the Retina, or Fund of the Eye. That we can ſee no thing which is not ſo Paint⯑ed. And that, according as the Picture is more Diſtinct or Con⯑fuſed, ſo alſo is the Perception we have of the Object. But then in this Explication of Viſion, there occurs one mighty Difficulty. The Objects are Painted in an inverted Order on the Bottom of the Eye: The upper part of any Object be⯑ing Painted on the lower part of the Eye, and the lower part of the Object, on the upper part of the Eye. And ſo alſo as to Right and Left. Since therefore the Pictures are thus in⯑verted, it is demanded how it comes to paſs, that we ſee the Ob⯑jects erect and in their natural Poſture?

LXXXIX The com⯑mon way of explaining it.

In anſwer to this Difficulty, we are told, that the Mind perceiving an impulſe of a Ray of Light, on the upper part of the Eye, con⯑ſiders this Ray as coming in a direct Line, from the lower part of the Object; and in like man⯑ner tracing the Ray that ſtrikes on the lower part of the Eye, it is directed to the upper part of the Object. Thus in the adjacent Fi⯑gure, C the lower Point of the Object ABC is projected on c the upper part of the Eye. So like⯑wiſe,

the higheſt Point A is pro⯑jected on a the loweſt part of the Eye; which makes the Repre⯑ſentation cba inverted. But the Mind conſidering the Stroak that is made on c as coming in the [102] ſtraight Line C c from the lower End of the Object; and the Stroak or Impulſe on a, as coming in the Line Aa from the upper End of the Object, is directed to make a right Judgement of the Situa⯑tion of the Object ABC, notwith⯑ſtanding the Picture of it be in⯑verted. Moreover, this is illuſtra⯑ted by conceiving a Blind Man, who holding in his Hands two Sticks that croſs each other, doth with them touch the extremities of an Object, placed in a perpen⯑dicular Situation. It is certain, this Man will judge that to be the upper part of the Object, which he touches with the Stick held in the undermoſt Hand, and that to be the lower part of the Ob⯑ject, which he touches with the Stick in his uppermoſt Hand. This is the common Explication of the erect Appearance of Objects, which is generally receiv'd and acquieſed in, being (as Mr. Molyneux tells us, [103] Dioptr. par. 2. c. 7. p. 289.) allow⯑ed by all Men as Satisfactory.

XC. The ſame ſhewn to be falſe.

But how reaſonable and ſatis⯑factory ſoever, this account may be thought by others, to me cer⯑tainly it does not ſeem, in any degree, True. Did I perceive thoſe Impulſes, Decuſſations, and Directi⯑ons of the Rays of Light, in like manner as hath been ſet forth, then, indeed, it wou'd not at firſt view be altogether void of Pro⯑bability. And there might be ſome Pretence for the Compariſon of the Blind-Man and his croſs Sticks. But the Caſe is far otherwiſe. I know very well that I perceive no ſuch thing. And of Conſequence, I cannot thereby make an Eſti⯑mate of the Situation of Objects. Moreover I appeal to any one's Experience, whether he be conſci⯑ous to himſelf, that he thinks on the Interſection made by the Ra⯑dious Pencils, or purſue the Im⯑pulſes [104] they give in right Lines, whenever he perceives by Sight the Poſition of any Object? To me it ſeems evident, that Croſſing and Tracing of the Rays, &c. is ne⯑ver thought on by Children, Idi⯑ots, or in Truth by any other, ſave only thoſe who have apply⯑ed themſelves to the Study of Op⯑tics. And for the Mind to judge of the Situation of Objects, by thoſe things, without perceiving them, or to perceive them with⯑out knowing it, take which you pleaſe, 'tis Perfectly beyond my Comprehenſion. Add to this, that the explaining the manner of Vi⯑ſion by the Example of croſs Sticks, and Hunting for the Object along the Axes of the Radious Pencils, doth ſuppoſe the proper Objects of Sight to be perceived at a Di⯑ſtance from us, contrary to what hath been Demonſtrated. We may therefore, venture to pronounce this Opinion concerning the way where⯑in [105] the Mind perceives the Erect Appearance of Objects, to be of a Piece with thoſe other Tenents of Writers in Optics, which in the foregoing Parts of this Treatiſe, we have had occaſion to Examine and Refute.

XCI. Not diſtin⯑guiſhing between I⯑deas of Sight and Touch, Cauſe of Miſtake, in this Mat⯑ter.

It remains, therefore, that we look for ſome other Explication of this Difficulty. And I believe it not impoſſible to find one, pro⯑vided we Examine it to the Bot⯑tom, and carefully diſtinguiſh be⯑tween the Ideas of Sight and Touch; which cannot be too oft incul⯑cated in treating of Viſion. But more eſpecially throughout the con⯑ſideration of this Affair, we ought to carry that Diſtinction in our Thoughts. For that from want of a right Underſtanding thereof, the Difficulty of Explaining Erect Viſion ſeems chiefly to ariſe.

XCII. The Caſe of one Born Blind, pro⯑per to be conſider'd.

But in order to Diſentangle our Minds, from whatever Prejudices we may entertain with relation to the Subject in hand: Nothing ſeems more appoſite, than the ta⯑king into our Thoughts the Caſe of one Born Blind, and afterwards, when grown up, made to ſee. And tho', perhaps, it may not be a Task altogether eaſy, and famili⯑ar to us, to diveſt our ſelves in⯑tirely of the Experiences receiv'd from Sight. So as to be able to put our Thoughts exactly in the Poſture of ſuch a one's. We muſt, nevertheleſs, as far as poſſible, en⯑deavour to frame true Concepti⯑ons, of what might reaſonably be ſuppoſed to paſs in his Mind.

XCIII. Such a one might by Touch, at⯑tain to have Ideas of Upper and Low⯑er.

It is certain, that a Man actu⯑ally Blind, and who had conti⯑nued ſo from his Birth, wou'd by the Senſe of Feeling attain to have Ideas of Upper and Lower. By [107] the Motion of his Hand he might diſcern the Situation of any Tangi⯑ble Object placed within his Reach. That part on which he felt him⯑ſelf ſupported, or towards which he perceiv'd his Body to gravitate, he wou'd term Lower, and the con⯑trary to this Upper. And accor⯑dingly denominate whatſoever Ob⯑jects he touch'd.

XCIV. Which Modes of Situation he'd attri⯑bute only to things Tangible.

But then, whatever Judgments he makes concerning the Situati⯑on of Objects, are confin'd to thoſe only that are perceivable by Touch. All thoſe things that are intangi⯑ble, and of a ſpiritual Nature, his Thoughts and Deſires, his Paſſi⯑ons, and in general all the Mo⯑difications of his Soul, to theſe he wou'd never apply the Terms Upper and Lower, except only in a Metaphorical Senſe. He may, perhaps, by way of Alluſion, ſpeak of High or Low Thoughts. But thoſe Terms in their proper Sig⯑nification, [108] wou'd never be apply⯑ed to any thing, that was not conceiv'd to exiſt without the Mind. For a Man Born Blind, and re⯑maining in the ſame State, cou'd mean nothing elſe by the Words Higher and Lower, than a great⯑er or leſſer Diſtance from the Earth: Which Diſtance he wou'd meaſure by the Motion or Appli⯑cation of his Hand, or ſome o⯑ther Part of his Body. It is, there⯑fore, evident, that all thoſe things which, in reſpect of each other, wou'd by him be thought Higher or Lower, muſt be ſuch as were conceiv'd to exiſt without his Mind, in the ambient Space.

XCV. He'd not at firſt Sight think any thing he ſaw, High or Low, E⯑rect or In⯑verted.

Whence it plainly follows, that ſuch a one, if we ſuppoſe him made to See, wou'd not at firſt Sight think, that any thing he ſaw was High or Low, Erect or In⯑verted; for it hath been already Demonſtrated in Sect. XLI, that [109] he wou'd not think the Things he perceived by Sight to be at any Diſtance from him, or without his Mind. The Objects to which he had hitherto been uſed to ap⯑ply the Terms Up and Down, High and Low, were ſuch only as affect⯑ed, or were ſome way perceiv'd by his Touch. But the proper Objects of Viſion make a new Set of Ideas, perfectly diſtinct and dif⯑ferent from the former, and which can in no ſort make themſelves perceiv'd by Touch. There is, there⯑fore, nothing at all that cou'd in⯑duce him to think thoſe Terms applicable to them. Nor wou'd he ever think it, till ſuch time as he had obſerv'd their Connexion with Tangible Objects, and the ſame Prejudice begin to inſinuate it ſelf into his Underſtanding, which from their Infancy had grown up in the Underſtandings of other Men.

XCVI. This Illuſ⯑trated by an Exam⯑ple.

To ſet this Matter in a clearer Light, I ſhall make uſe of an Ex⯑ample. Suppoſe the above-men⯑tioned Blind Perſon do, by his Touch, perceive a Man to ſtand Erect. Let us enquire into the manner of this. By the applica⯑tion of his Hand to the ſeveral Parts of a Human Body, he had perceiv'd different Tangible Ideas, which being collected into ſundry complex ones have diſtinct Names annexed to them. Thus one Com⯑bination of a certain Tangible Fi⯑gure, Bulk, and Conſiſtency of Parts is called the Head, another the Hand, a Third the Foot, and ſo of the reſt. All which Com⯑plex Ideas cou'd, in his Underſtand⯑ing, be made up only of Ideas perceivable by Touch. He had al⯑ſo by his Touch obtain'd an Idea of Earth or Ground, towards which he perceives the Parts of his Bo⯑dy to have a natural Tendency. [111] Now, by Erect nothing more be⯑ing meant, than that perpendicu⯑lar Poſition of a Man, wherein his Feet are neareſt to the Earth: If the Blind Perſon by moving his Hand, over the Parts of the Man who ſtands before him, do perceive the Tangible Ideas that compoſe the Head, to be fartheſt from, and thoſe that compoſe the Feet to be neareſt to, that other Combination of Tangible Ideas which he calls Earth: He will de⯑nominate that Man Erect. But if we ſuppoſe him on a ſudden to re⯑ceive his Sight, and that he behold a Man ſtanding before him: It's evident, in that Caſe, he wou'd neither judge the Man he ſees, to be Erect nor Inverted; for he never having known thoſe Terms applied to any other, ſave Tangible Things, or which exiſted in the Space without him, and what he ſees neither being Tangible, nor per⯑ceived as exiſting without, he cou'd [112] not know that in propriety of Lan⯑guage, they were applicable to it.

XCVII. By what means he'd come to de⯑nominate Viſible Ob⯑jects high or low, &c.

Afterwards, when upon turning his Head or Eyes, up and down, to the right and left, he ſhall ob⯑ſerve the Viſible Objects to change, and ſhall alſo attain to know, that they are call'd by the ſame Names, and Connected with the Ob⯑jects perceiv'd by Touch; then, indeed, he will come to ſpeak of them, and their Situation, in the the ſame Terms that he has been us'd to apply to Tangible Things. And thoſe that he perceives by turning up his Eyes, he will call Upper, and thoſe that by turning down his Eyes, he will call Lower.

XCVIII. Why he ſhou'd think thoſe Objects higheſt, which are Painted on the loweſt part of his Eye, and vice ver⯑ſa.

And this ſeems to me the true Reaſon, why he ſhou'd think thoſe Objects uppermoſt that are Pain⯑ted on the lower part of his Eye. For, by turning the Eye up they ſhall be diſtinctly ſeen; as likewiſe, [113] they that are Painted on the high⯑eſt part of the Eye ſhall be di⯑ſtinctly ſeen, by turning the Eye down, and are for that Reaſon e⯑ſteemed loweſt. For we have ſhewn that to the immediate Objects of Sight, conſider'd in themſelves, he'd not attribute the Terms High and Low. It muſt therefore be on ac⯑count of ſome Circumſtances, which are obſerv'd to attend them. And theſe, 'tis plain, are the Actions of turning the Eye up and down, which ſuggeſt a very obvious Rea⯑ſon, why the Mind ſhou'd deno⯑minate the Objects of Sight ac⯑cordingly High or Low. And with⯑out this Motion of the Eye, this turning it up and down in or⯑der to diſcern different Objects, doubtleſs Erect, Inverſe, and other the like Terms relating to the Poſition of Tangible Objects, wou'd never have been transfer'd, or in any degree apprehended to belong to the Ideas of Sight: The meer [114] act of Seeing including nothing in it to that Purpoſe, whereas the different Situations of the Eye, na⯑turally direct the Mind to make a ſuitable Judgement, of the Si⯑tuation of Objects intromitted by it.

XCIX. How he wou'd per⯑ceive by Sight the Situation of Exter⯑nal Objects.

Farther, when he has by Experi⯑ence learn'd the Connexion there is, between the ſeveral Ideas of Sight and Touch, he will be able, by the Perception he has of the Si⯑tuation of Viſible Things in re⯑ſpect of one another, to make a ſudden and true Eſtimate, of the Situation of Outward, Tangible things correſponding to them. And thus it is, he ſhall perceive by Sight the Situation of External Objects, which do not properly fall under that Senſe.

C. Our propen⯑ſion to think the contrary, no Argu⯑ment a⯑gainſt what hath been ſaid.

I know we are very prone to think, that if juſt made to ſee, we ſhou'd judge of the Situation of Viſible Things as we do now. [115] But, we are alſo as prone to think, that at firſt Sight, we ſhou'd in the ſame way apprehend the Diſtance and Magnitude of Objects, as we do now. Which hath been ſhewn to be a falſe and groundleſs Perſwaſion. And for the like Reaſons, the ſame Cenſure may be paſt on the poſitive Aſſurance, that moſt Men, before they have thought ſuffici⯑ently of the Matter, might have of their being able to determine by the Eye, at firſt view, whe⯑ther Objects were Erect or Inverſe.

CI. Objection.

It will, perhaps, be objected to our Opinion, that a Man, for in⯑ſtance, being thought Erect, when his Feet are next the Earth, and inverted, when his Head is next the Earth, it doth hence follow, that by the meer act of Viſion, without any Experience or alter⯑ing the Situation of the Eye, we ſhou'd have determined whether he were Erect or Inverted. For [116] both the Earth it ſelf, and the Limbs of the Man who ſtands thereon, being equally perceiv'd by Sight: One cannot chuſe ſeeing, what part of the Man is neareſt the Earth, and what part fartheſt from it, i. e. whether he be Erect or Inverted.

CII. Anſwer.

To which I anſwer, the Ideas which conſtitute the Tangible Earth and Man, are intirely different from thoſe which conſtitute the Viſible Earth and Man. Nor was it poſ⯑ſible, by virtue of the Viſive Fa⯑culty alone, without ſuper-adding any Experience of Touch, or al⯑tering the Poſition of the Eye, e⯑ver to have known, or ſo much as ſuſpected, there had been any Relation or Connexion between them. Hence, a Man at firſt view wou'd not denominate any thing he ſaw Earth, or Head, or Foot. And conſequently, he cou'd not tell by the meer act of Viſion, whe⯑ther [117] the Head or Feet were near⯑eſt the Earth. Nor, indeed, wou'd he have thereby any thought of Earth or Man, Erect or Inverſe, at all. Which will be made yet more evident, if we nicely obſerve, and make a particular Compariſon be⯑tween the Ideas of both Senſes.

CIII. An Object cou'd not be known at firſt Sight by the Co⯑lour.

That which I ſee is only varie⯑ty of Light and Colours. That which I feel, is Hard or Soft, Hot or Cold, Rough or Smooth. What Similitude, what Connexion have thoſe Ideas with theſe? Or how is it poſſible, that any one ſhou'd ſee reaſon, to give one and the ſame Name, to combina⯑tions of Ideas ſo very different, before ever he had experienced their Coexiſtence? We do not find there is any neceſſary Connexion, betwixt this or that Tangible Quality, and any Colour whatſoever. And we may ſometimes perceive Colours, where there is nothing to be felt. [118] All which doth make it manifeſt, that no Man at firſt receiving of his Sight, wou'd know there was any Agreement between this or that particular Object of his Sight, and any Object of Touch he had been already acquainted with. The Colours therefore of the Head, wou'd to him no more ſuggeſt the Idea of Head, than they wou'd the Idea of Feet.

CIV. Nor by the Magnitude thereof.

Farther, we have at large ſhewn (vid. Sect. LXIII and LXIV.) there is no diſcoverable, neceſſary Con⯑nexion, between any given Viſi⯑ble Magnitude, and any one par⯑ticular Tangible Magnitude. But that it is intirely the reſult of Cuſtom and Experience, and de⯑pends on foreign and accidental Circumſtances, that we can by the Perception of Viſible Extenſi⯑on inform our ſelves, what may be the Extenſion of any Tangible Object connected therewith. Hence, [119] 'tis certain that neither the Viſi⯑ble Magnitude of Head or Foot, wou'd bring along with them in⯑to the Mind, at firſt opening of the Eyes, the reſpective Tangible Magnitudes of thoſe Parts.

CV. Nor by the Figure

By the foregoing Section 'tis plain, the Viſible Figure of any Part of the Body, hath no neceſſary Con⯑nexion with the Tangible Figure thereof, ſo as at firſt Sight to ſug⯑geſt it to the Mind. For Figure is the Termination of Magnitude. Whence it follows, that no Vi⯑ſible Magnitude having, in it's own Nature, an aptneſs to ſuggeſt any one particular Tangible Magnitude, ſo neither can any Viſible Figure, be inſeparably Connected with its correſponding Tangible Figure: So as of it ſelf, and in a way prior to Experience it might ſuggeſt it to the Underſtanding. This will be farther evident, if we conſider that what ſeems Smooth and Round [120] to the Touch, may to Sight, if view'd thro' a Microſcope, ſeem quite otherwiſe.

CVI. In the firſt act of Viſi⯑on, no Tan⯑gible Thing wou'd be ſuggeſted by Sight.

From all which laid together, and duly conſider'd, we may clear⯑ly deduce this Inference, viz. In the firſt act of Viſion, no Idea entering by the Eye, wou'd have a perceivable Connexion with the I⯑deas to which the Names Earth, Man, Head, Foot, &c. were annex⯑ed, in the Underſtanding of a Per⯑ſon Blind from his Birth: So as in any ſort to introduce them in⯑to his Mind, or make themſelves be called by the ſame Names, and reputed the ſame things with them, as afterwards they come to be.

CVII. Difficulty propoſed concerning Number.

There doth, nevertheleſs, remain one Difficulty, which to ſome per⯑haps, may ſeem to preſs hard on our Opinion, and deſerve not to be paſs'd over. For tho' it be granted, that neither the Colour, [121] Size, nor Figure of the Viſible Feet, have any neceſſary Connexion with the Ideas that compoſe the Tangi⯑ble Feet, ſo as to bring them at firſt ſight, into my Mind, or make me in danger of confounding them, before I had been us'd to, and for ſome time experienced their Con⯑nexion. Yet thus much ſeems un⯑deniable. Namely, that the Num⯑ber of the Viſible Feet, being the ſame with that of the Tangible Feet: I may from hence, without any Ex⯑perience of Sight, reaſonably con⯑clude that they repreſent, or are connected with the Feet rather than the Head. I ſay, it ſeems the I⯑dea of Two Viſible Feet will ſoon⯑er ſuggeſt to the Mind, the Idea of Two Tangible Feet than of one Head. So that the Blind Man up⯑on firſt reception of the Viſive Fa⯑culty might know, which were the Feet or Two, and which, the Head or One.

CVIII. Number of things Vi⯑ſible, wou'd not, at firſt Sight, ſug⯑geſt the like number of things Tan⯑gible.

In order to get clear of this ſeeming Difficulty, we need only obſerve, that Diverſity of Viſible Objects does not neceſſarily infer, Diverſity of Tangible Objects, cor⯑reſponding to them. A Picture Painted with great variety of Co⯑lours, affects the Touch in one uniform manner. It is therefore evident, that I do not by any neceſſary Conſecution, independent of Experience, judge of the num⯑ber of things Tangible, from the number of things Viſible. I ſhou'd not therefore at firſt open⯑ing my Eyes conclude, that be⯑cauſe I ſee Two, I ſhall feel Two. How therefore can I, before Ex⯑perience teaches me, know that the Viſible Legs, becauſe Two, are connected with the Tangible Legs: Or the Viſible Head, becauſe One, connected with the Tangible Head? The Truth on't is, the things I ſee are ſo very different, and he⯑terogeneous [123] from the things I feel: That the Perception of the one, wou'd never have ſuggeſted the other to my Thoughts, or enabled me to paſs the leaſt Judgment thereon, until I had Experienced their Connexion.

CIX. Number the Crea⯑ture of the Mind.

But for a fuller Illuſtration of this Matter, it ought to be con⯑ſider'd, that Number (however ſome may reckon it amongſt the Prima⯑ry Qualities) is nothing fix'd, and ſettled, really exiſting in things them⯑ſelves. It is intirely the Creature of the Mind, conſidering, either a Simple Idea by it ſelf, or any Com⯑bination of Simple Ideas to which it gives one Name, and ſo makes it paſs for an Unite. According as the Mind variouſly Combines it's Ideas, the Unite varies. And as the Unite, ſo the Number, which is only a Collection of Unites, doth alſo vary. We call a Window one, a Chimney one; and yet a Houſe [124] in which there are many Win⯑dows, and many Chimneys, has an equal right to be called one. And many Houſes go to the ma⯑king of one City. In theſe and the like Inſtances, it's evident the Unite conſtantly relates to the particu⯑lar Draughts the Mind makes of it's Ideas, to which it affixes Names, and wherein it includes more or leſs, as beſt ſuits it's own Ends and Purpoſes. Whatever therefore the Mind conſiders as one, that is an Unite. Every Combination of Ideas is conſider'd as one thing by the Mind, and in token there⯑of, is mark'd by one Name. Now, this Naming and Combining to⯑gether of Ideas is perfectly Arbi⯑trary, and done by the Mind in ſuch ſort, as Experience ſhews it to be moſt convenient. Without which, our Ideas had never been collected into ſuch ſundry, diſtinct Combinations, as they now are.

CX. One Born Blind wou'd not at firſt Sight, num⯑ber Viſible Things as others do.

Hence it follows, that a Man Born Blind, and afterwards, when grown up, made to ſee, wou'd not in the firſt act of Viſion, par⯑cel out the Ideas of Sight, into the ſame diſtinct Collections that others do, who have experienced which do regularly coexiſt and are proper to be bundled up toge⯑ther under one Name. He wou'd not, for Example, make into one Complex Idea, and thereby eſteem an unite all thoſe particular Ideas which conſtitute the Viſible Head, or Foot. For there can be no Reaſon aſſign'd why he ſhou'd do ſo, barely upon his ſeeing a Man ſtand upright before him. There croud into his Mind, the Ideas which compoſe the Viſible Man, in company with all the other Ideas of Sight perceiv'd at the ſame time. But all theſe Ideas offer'd at once to his View, he'd not diſtribute into ſundry, diſtinct [126] Combinations: till ſuch time, as by obſerving the Motion of the Parts of the Man, and other Ex⯑periences he comes to know, which are to be ſeparated, and which to be collected together.

CXI. The Situa⯑tion of any Object, de⯑termin'd with re⯑ſpect only to Objects of the ſame Senſe.

From what hath been premiſed, 'tis plain the Objects of Sight and Touch make, if I may ſo ſay, two Sets of Ideas, which are widely different from each other. To Ob⯑jects of either Kind, we indiffe⯑rently attribute the Terms High and Low, Right and Left, and ſuch like, denoting the Poſition or Si⯑tuation of things. But then we muſt well obſerve, that the Po⯑ſition of any Object is determin'd, with reſpect only to Objects of the ſame Senſe. We ſay any Object of Touch is High or Low, accor⯑ding as it is more or leſs di⯑ſtant from the Tangible Earth. And in like manner, we denomi⯑nate any Object of Sight High or [127] Low, in proportion as it is more or leſs Diſtant, from the Viſible Earth. But to define the Situa⯑tion of Viſible Things, with rela⯑tion to the Diſtance they bear from any Tangible Thing, or vi⯑ce verſa: This were abſurd and perfectly unintelligible. For all Vi⯑ſible Things are equally in the Mind, and take up no part of the Exter⯑nal Space: And, conſequently, are Equidiſtant from any Tangi⯑ble Thing which exiſts without the Mind.

CXII. No Di⯑ſtance great or ſmall, between a Viſible and Tangible Thing.

Or rather, to ſpeak truly, the pro⯑per Objects of Sight are at no Di⯑ſtance, neither near nor far, from any Tangible Thing. For if we inquire narrowly into the Matter, we ſhall find, that thoſe things only are compar'd together in re⯑ſpect of Diſtance, which exiſt af⯑ter the ſame manner, or apper⯑tain unto the ſame Senſe. For by the Diſtance between any Two [128] Points, nothing more is meant than the Number of intermediate Points. If the given Points are Viſible, the Diſtance between them is mark'd out, by the Number of the interjacent Viſible Points: If they are Tangible, the Diſtance between them is a Line conſiſting of Tangible Points. But if they are one Tangible, and the other Viſible, the Diſtance between them doth neither conſiſt of Points per⯑ceivable by Sight, nor by Touch, i. e. it is utterly inconceivable. This, perhaps, will not find an eaſy Admiſſion into all Men's Un⯑derſtandings: However, I ſhou'd gladly be informed whether it be not True, by any one who will be at the pains to Reflect a lit⯑tle, and apply it home to his Thoughts.

CXII. The not ob⯑ſerving this, cauſe of difficul⯑ty in Erect Viſion,

The not obſerving what has been deliver'd in the two laſt Sections, ſeems to have occaſion'd no ſmall [129] part of the Difficulty that occurs in the Buſineſs of Erect Appear⯑ances. The Head, which is Paint⯑ed neareſt the Earth, ſeems to be fartheſt from it; and on the o⯑ther Hand, the Feet, which are Painted fartheſt from the Earth, are thought neareſt to it. Here⯑in lies the Difficulty, which va⯑niſhes if we expreſs the thing more clearly, and free from Ambigui⯑ty, thus. How comes it that to the Eye, the Viſible Head which is neareſt the Tangible Earth, ſeems fartheſt from the Earth, and the Viſible Feet, which are fartheſt from the Tangible Earth, ſeem neareſt the Earth? The Queſtion being thus propos'd, who ſees not, the Difficulty is founded on a Sup⯑poſition, that the Eye or Viſive Fa⯑culty, or rather the Soul by means thereof, ſhou'd judge of the Situ⯑ation of Viſible Objects, with Re⯑ference to their Diſtance from the Tangible Earth? Whereas it's e⯑vident, [130] the Tangible Earth is not perceiv'd by Sight: And it hath been ſhewn in the two laſt pre⯑ceding Sections, that the Location of Viſible Objects is determin'd only, by the Diſtance they bear from one another; and that it is Nonſenſe to talk of Diſtance, far or near, between a Viſible and Tangible Thing.

CXIV. Which o⯑therwiſe includes nothing un⯑accounta⯑ble.

If we confine our Thoughts to the proper Objects of Sight, the whole is plain and eaſy. The Head is Painted fartheſt from, and the Feet neareſt to the Viſible Earth: And ſo they appear to be. What is there ſtrange or unaccountable in this? Let us ſuppoſe the Pic⯑tures in the Fund of the Eye, to be the immediate Objects of Sight. The Conſequence is, that things ſhou'd appear in the ſame Poſture they are Painted in. And is it not ſo? The Head which is ſeen, ſeems fartheſt from the Earth which [131] is ſeen; and the Feet, which are ſeen, ſeem neareſt to the Earth which is ſeen. And juſt ſo they are Painted.

CXV. What is meant by the Pictures being in⯑verted.

But, ſay you, the Picture of the Man is inverted, and yet the Ap⯑pearance 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 'tis inverted, becauſe the Heels are uppermoſt, and the Head undermoſt? Explain me this. You ſay, that by the Head's being un⯑dermoſt, you mean that it is near⯑eſt to the Earth; and by the Heels being uppermoſt, that they are fartheſt from the Earth. I ask a⯑gain, what Earth you mean? You cannot mean the Earth that is Painted on the Eye, or the Vi⯑ſible Earth. For the Picture of the Head is fartheſt from the Pic⯑ture of the Earth; and the Pic⯑ture of the Feet neareſt to the Pic⯑ture [132] of the Earth; and accordingly, the Viſible Head is fartheſt from the Viſible Earth, and the Viſible Feet, neareſt to it. It remains, there⯑fore, that you mean the Tangible Earth: And ſo determine the Si⯑tuation of Viſible Things, with re⯑ſpect to Tangible Things; contra⯑ry to what hath been demonſtra⯑ted in Sect. CXI. and CXII. The two diſtinct Provinces of Sight and Touch ſhou'd be conſider'd apart, and as tho' their Objects had no Intercourſe, no manner of Rela⯑tion to one another, in point of Diſtance or Poſition.

CXVI. Cauſe of Miſtake in this Mat⯑ter.

Farther, What greatly contributes to make us miſtake in this Mat⯑ter is, that when we think of the Pictures in the Fund of the Eye, we imagine our ſelves looking on the Fund of another's Eye, or a⯑nother looking on the Fund of our own Eye, and beholding the Pictures Painted thereon. Suppoſe [133] two Eyes A and B: A from ſome diſtance looking on the Pictures in B ſees them inverted, and for that reaſon concludes they are in⯑verted in B. But this is wrong. There are projected in little on the Bot⯑tom of A, the Images of the Pictures of, ſuppoſe, Man, Earth, &c. which are Painted on B. And beſides theſe, the Eye B it ſelf, and the Objects which environ it, together with another Earth are projected in a larger Size on A. Now, by the Eye A, theſe lar⯑ger Images are deemed the true Objects, and the leſſer only Pict⯑ures in miniature. And it is with reſpect to thoſe greater Images, that it determines the Situation of the ſmaller Images. So that com⯑paring the little Man with the great Earth, A judges him inver⯑ted, or that the Feet are fartheſt from, and the Head neareſt to the great Earth. Whereas, if A compare the little Man with the [134] little Earth, then he will appear Erect, i. e. his Head ſhall ſeem far⯑theſt from, and his Feet neareſt to the little Earth. But we muſt conſider that B does not ſee two Earths, as A does: It ſees only what is repreſented by the little Pictures in A, and conſequently ſhall judge the Man Erect. For, in truth, the Man in B is not inverted, for there the Feet are next the Earth. But it is the Re⯑preſentation of it in A which is inverted, for there, the Head of the Repreſentation of the Picture of the Man in B, is next the Earth, and the Feet fartheſt from the Earth, meaning the Earth which is without the Repreſentation of the Pictures in B. For if you take the little Images of the Pictures in B, and conſider them by them⯑ſelves, and with reſpect only to one another, they are all Erect and in their natural Poſture.

CXVII. Images in the Eye, not Pictures of external Objects.

Farther, there lies a Miſtake, in our imagining that the Pictures of External Objects are Painted on the Bottom of the Eye. It hath been ſhewn, there is no reſemblance be⯑tween the Ideas of Sight, and things Tangible. It hath likewiſe been de⯑monſtrated, that the proper Objects of Sight do not exiſt without the Mind. Whence it clearly follows, that the Pictures Painted on the Bottom of the Eye, are not the Pictures of External Objects. Let any one conſult his own Thoughts, and then tell me, what Affinity, what Likeneſs there is, between that certain Variety and Diſpoſi⯑tion of Colours, which conſtitute the Viſible Man, or Picture of a Man, and that other Combinati⯑on of far different Ideas, ſenſible by Touch, which compoſe the Tan⯑gible Man. But if this be the Caſe, how come they to be ac⯑counted Pictures or Images, ſince [136] that ſuppoſes them to copy or repreſent ſome Originals or o⯑ther?

CXVIII. In what Senſe they are Pictures

To which I anſwer. In the foremention'd Inſtance, the Eye A takes the little Images, inclu⯑ded within the Repreſentation of the other Eye B, to be Pictures or Copies, whereof the Archetypes are not things exiſting with⯑out but, the larger Pictures pro⯑jected on it's own Fund: And which by A are not thought Pic⯑tures, but the Originals or true Things themſelves. Tho' if we ſuppoſe a third Eye C, from a due diſtance to behold the Fund of A: Then, indeed, the things project⯑ed thereon ſhall, to C, ſeem Pic⯑tures or Images, in the ſame Senſe that thoſe projected on B do to A.

CXIX. In this Af⯑fair we muſt care⯑fully di⯑ſtinguiſh between Ideas of Sight and Touch.

Rightly to conceive the Buſi⯑neſs in hand, we muſt carefully diſtinguiſh between the Ideas of [137] Sight and Touch, between the Vi⯑ſible and Tangible Eye, for cer⯑tainly on the Tangible Eye, no⯑thing either is or ſeems to be Painted. Again, the Viſible Eye, as well as all other Viſible Ob⯑jects, hath been ſhewn to exiſt only in the Mind, which perceiv⯑ing its own Ideas, and compa⯑ring them together, doth call ſome Pictures in reſpect of others. What hath been ſaid being rightly com⯑prehended and laid together, does, I think, afford a full and genu⯑ine Explication of the Erect Ap⯑pearance of Objects, which Phaeno⯑menon, I muſt confeſs, I do not ſee how it can be explain'd, by any Theories of Viſion hitherto made publick.

CXX. Difficult to explain by Words the true The⯑ory of Vi⯑ſion.

In treating of theſe things, the uſe of Language is apt to occa⯑ſion ſome Obſcurity and Confu⯑ſion, and create in us wrong Ideas. For Language being accomodated [138] to the common Notions and Prejudices of Men, it is ſcarce poſſible to deliver the naked and preciſe Truth, without great Cir⯑cumlocution, Impropriety, and (to an unwary Reader) ſeeming Con⯑tradictions. I do therefore, once for all, deſire whoever ſhall think it worth his while, to underſtand what I have written concerning Viſion, that he'd not ſtick in this or that Phraſe, or manner of Ex⯑preſſion; but candidly collect my meaning from the whole Sum and Tenor of my Diſcourſe; and laying aſide the Words, as much as poſſible, conſider the bare Notions themſelves, and then judge whether they are agreeable to Truth and his own Experience, or no.

CXXI. The Que⯑ſtion, whe⯑ther there is any Idea common to Sight and Touch, ſtated.

We have ſhewn the way where⯑in the Mind by Mediation of Viſible Ideas, doth perceive or apprehend the Diſtance, Magnitude [139] and Situation of Tangible Ob⯑jects. I come now to enquire more particularly, concerning the Difference betwixt the Ideas of Sight and Touch, which are call'd by the ſame Names; and ſee whether there be any Idea com⯑mon to both Senſes. From what we have at large ſet forth and demonſtrated in the foregoing parts of this Treatiſe, 'tis plain there's no one ſelf-ſame numeri⯑cal Extenſion, perceiv'd both by Sight and Touch. But that the particular Figures and Extenſions perceiv'd by Sight, however they may be called by the ſame Names, and reputed the ſame Things, with thoſe perceiv'd by Touch, are ne⯑vertheleſs different, and have an Exiſtence very diſtinct and Sepa⯑rate from them. So that the Que⯑ſtion is not now concerning the ſame numerical Ideas, but whether there be any one and the ſame ſort or Species of Ideas equally [140] perceivable to both Senſes? Or, in other Words, whether Exten⯑ſion, Figure, and Motion perceiv'd by Sight, are not ſpecifically di⯑ſtinct from Extenſion, Figure and Motion perceived by Touch.

CXXII. Abſtract Extenſion enquir'd into.

But, before I come more par⯑ticularly to Diſcuſs this Matter, I find it proper to take into my Thoughts Extenſion in Abſtract: For of this there is much talk, and I am apt to think, that when Men ſpeak of Extenſion as being an Idea common to Two Senſes, it is with a ſecret Suppoſition, that we can ſingle out Extenſi⯑on from all other Tangible and Viſible Qualities, and frame there⯑of an Abſtract Idea, which Idea they will have common both to Sight and Touch. We are there⯑fore to underſtand by Extenſion in Abſtract, an Idea of Extenſi⯑on, v. g. a Line or Surface, in⯑tirely ſtript of all other ſenſible [141] Qualities and Circumſtances that might determine it to any particular Exiſtence. It is neither Black, nor White, nor Red, nor hath it a⯑ny Colour at all, or any Tan⯑gible Quality whatſoever. And conſequently it is of no finite, determinate Magnitude. For, that which bounds or diſtinguiſhes one Extenſion from another, is ſome Quality or Circumſtance wherein they diſagree.

CXXIII. It is incom⯑prehenſible.

Now I do not find that I can perceive, imagine, or any wiſe frame in my Mind ſuch an ab⯑ſtract Idea, as is here ſpoken of. A Line, or Surface which is nei⯑ther Black, nor White, nor Blue, nor Yellow, &c. Nor Long, nor Short, nor Rough, nor Smooth, nor Square, nor Round, &c. is perfectly incomprehenſible. This I am ſure of as to my ſelf, how far the Faculties of other Men may reach, they beſt can tell.

CXXIV. Abſtract Extenſion not the Ob⯑ject of Geo⯑metry.

I know 'tis commonly ſaid, that the Object of Geometry is Abſtract Extenſion. To this I cannot agree, for Geometry contemplates Figures: Now, Figure is the Termination of Magnitude, but we have ſhewn that Extenſion in Abſtract hath no finite, determinate Magnitude, whence it clearly follows that it can have no Figure, and conſe⯑quently is not the Object of Geo⯑metry. I know it is a Tenent as well of the Modern as the An⯑cient Philoſophers, that all gene⯑ral Truths are concerning Uni⯑verſal, Abſtract Ideas, without which, we are told, there cou'd be no Science, no Demonſtrati⯑on of any general Propoſition in Geometry. But it were no hard matter, did I think it neceſſary to my preſent Purpoſe, to ſhew that Propoſitions and Demonſtra⯑tions in Geometry might be Uni⯑verſal, tho' they who make 'em, [143] never think of Abſtract general I⯑deas of Triangles or Circles.

CXV. The gene⯑ral Idea of a Triangle, conſider'd.

After reiterated Efforts and pangs of Thought, in order to appre⯑hend the general Idea of v. g. a Triangle, I have found it alto⯑gether incomprehenſible. And ſure⯑ly if any one were able to let that Idea into my Mind, it muſt be the deſervedly admir'd Author of the Eſſay concerning Human Un⯑derſtanding: He, who has ſo far diſtinguiſh'd himſelf from the ge⯑nerality of Writers, by the Clear⯑neſs and Significancy of what he Says. Let us therefore ſee how that great Man deſcribes the ge⯑neral, or, which is the ſame thing, the Abſtract Idea of a Triangle. ‘It muſt be, (ſays he) neither Ob⯑lique, nor Rectangle, neither E⯑quilateral, Equicrural, nor Sca⯑lenon; but all and none of theſe at once. In effect it is ſome⯑what imperfect that cannot exiſt; [144] an Idea, wherein ſome 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 he thinks needful, for the enlargement of Knowledge, which is the Subject of Mathematical Demonſtration, and without which we cou'd ne⯑ver come to know any general Propoſition concerning Triangles. Sure I am, if this be the Caſe, 'tis impoſſible for me to attain to know even the firſt Elements of Geometry: Since I have not the Faculty to frame in my Mind ſuch an Idea as is here deſcrib'd. That Author acknowledges it doth ‘re⯑quire ſome Pains and Skill to Form this general Idea of a Tri⯑angle,’ ibid. But had he call'd to mind what he ſays in another place, viz. that ‘Ideas of mix'd Modes wherein any inconſiſtent Ideas are put together, cannot ſo much as exiſt in the Mind,’ i. e. be con⯑ceiv'd, [145]

I ſay, had this occur'd to his Thoughts, 'tis not improbable he'd have own'd it above all the Pains and Skill he was Maſter of, to form the above-mention'd Idea of a Triangle, which is made up of ma⯑nifeſt, ſtaring Contradictions. That a Man of ſuch a clear Underſtanding, who thought ſo much, and ſo well, and laid ſo great a Streſs on Clear and Determinate Ideas, ſhou'd never⯑theleſs talk at this rate, ſeems very ſurpriſing. But my Wonder is leſ⯑ſen'd when I conſider, that the Source whence this Opinion of Abſtract Figures and Extenſion flows, is the prolific Womb which has brought forth innumerable Errors and Difficulties, in all Parts of Philoſophy, and in all the Scien⯑ces. But this Matter, taken in its full Extent, were a Subject too vaſt and comprehenſive to be in⯑ſiſted on in this place. I ſhall on⯑ly obſerve that your Metaphyſici⯑ans, [146] and Men of Speculation, ſeem to have Faculties diſtinct from thoſe of ordinary Men; when they talk of General or Abſtracted Triangles and Circles, &c. and ſo perempto⯑rily declare them to be the Subject, of all the Eternal, Immutable, Uni⯑verſal Truths, in Geometry. And ſo much for Extenſion in Abſtract.

CXXVI. Vacuum or pure Space, not com⯑mon to Sight and Touch.

Some, perhaps, may think pure Space, Vacuum, or Trine Dimen⯑ſion to be equally the Object of Sight and Touch. But tho' we have a very great Propenſion, to think the Ideas of Outneſs and Space to be the immediate Object of Sight; yet, if I miſtake not, in the fore-going Parts of this Eſſay, That hath been clearly Demonſtra⯑ted to be a meer Deluſion, ari⯑ſing from the quick and ſudden Suggeſtion of Fancy, which ſo cloſely Connects the Idea of Di⯑ſtance with thoſe of Sight, that we are apt to think it is it ſelf [147] a proper and immediate Object of that Senſe, till Reaſon corrects the Miſtake.

CXXVII. There is no Idea or kind of I⯑dea, com⯑mon to both Senſes.

It having been ſhewn, that there are no Abſtract Ideas of Figure, and that it is impoſſible for us, by any Preciſion of Thought, to frame an Idea of Extenſion ſe⯑parate from all other Viſible and Tangible Qualities, which ſhall be common both to Sight and Touch: The Queſtion now remaining is, whether the particular Extenſions, Figures, and Motions perceiv'd by Sight be of the ſame Kind, with the particular Extenſions, Figures, and Motions perceiv'd by Touch? In anſwer to which, I ſhall ven⯑ture to lay down the following Propoſition, viz. The Extenſion, Fi⯑gures, and Motions perceiv'd by Sight are ſpecifically Diſtinct from the Ideas of Touch, called by the ſame Names, nor is there any ſuch thing as an Idea, or kind of Idea common to [148] both Senſes. This Propoſition may, without much Difficulty, be col⯑lected from what hath been ſaid in ſeveral Places of this Eſſay. But, becauſe it ſeems ſo remote from, and contrary to, the receiv'd No⯑tions and ſettled Opinion of Man⯑kind; I ſhall attempt to demon⯑ſtrate it more particularly, and at large, by the following Arguments.

CXXVIII. Firſt Ar⯑gument in Proof here⯑of.

Firſt, When upon Perception of an Idea, I range it under this or that ſort; it is becauſe it's per⯑ceiv'd after the ſame manner, or becauſe it has a Likeneſs or Con⯑formity with, or affects me in the ſame way as the Ideas of the ſort I rank it under. In ſhort, it muſt not be intirely new, but have ſomething in it Old, and already perceiv'd by me: It muſt, I ſay, have ſo much, at leaſt, in com⯑mon with the Ideas I have before known and nam'd, as to make me give it the ſame Name with them. [149] But it has been, if I miſtake not, clearly made out, that a Man Born Blind wou'd not, at firſt reception of his Sight, think the things he ſaw were of the ſame Nature with the Objects of Touch, or had any thing in common with them; but that they were a new Set of Ideas, perceiv'd in a new manner, and intirely different from all he had ever perceiv'd before. So that he wou'd not call them by the ſame Name, nor repute them to be of the ſame Sort, with any thing he had hitherto known. And ſurely, the Judgment of ſuch an unprejudic'd Perſon is more to be relied on in this Caſe, than the Sentiments of the generality of Men: Who in this, as in almoſt every thing elſe, ſuffer themſelves to be guided by Cuſtom, and the erroneous Suggeſtions of Prejudice, rather than Reaſon and ſedate Re⯑flexion.

CXXIX. Second Ar⯑gument.

Secondly, Light and Colours are allow'd by all to conſtitute a Sort or Species, intirely different from the Ideas of Touch: Nor will any Man, I preſume, ſay they can make themſelves perceiv'd by that Senſe. But there is no other immediate Object of Sight, beſides Light and Colours. It is there⯑fore a direct Conſequence, that there is no Idea common to both Senſes.

CXXX. Viſible Fi⯑gure and Extenſion, not diſtinct Ideas from Colour.

It is, I know, a prevailing O⯑pinion, even amongſt thoſe who have Thought and Writ moſt Ac⯑curately concerning our Ideas, and the Ways whereby they enter in⯑to the Underſtanding, that ſome⯑thing more is perciev'd by Sight, than barely Light and Colours with their Variations. The Excellent Mr. Locke termeth Sight ‘The moſt Comprehenſive of all our Senſes, conveying to our Minds the I⯑deas [151] of Light and Colours, which are peculiar only to that Senſe; and alſo the far different Ideas of Space, Figure, and Motion.’ Eſſay on Hum. Underſtand. b. ii. c. 9. ſ. 9. Space or Diſtance, we have ſhewn, is no otherwiſe the Object of Sight than of Hearing. vid. Sect. XLVI. And as for Figure and Extenſion, I leave it to any one, that ſhall calmly attend to his own clear and diſtinct Ideas, to decide whether he has any I⯑dea intromitted immediately and properly by Sight, ſave only Light and Colours. Or whether it be poſſible for him, to frame in his Mind a diſtinct Abſtract Idea of Viſible Extenſion, or Figure, ex⯑cluſive of all Colour; and on the other hand, whether he can conceive Colour without Viſible Extenſion. For my own part, I muſt con⯑feſs, I am not able to attain ſo great a nicety of Abſtraction. I know very well that, in a ſtrict [152] Senſe, I ſee nothing but Light and Colours, with their ſeveral Shades and Variations. He who beſide theſe, doth alſo perceive by Sight Ideas far different and diſtinct from them, hath that Faculty in a de⯑gree more perfect and compre⯑henſive than I can pretend to. I own indeed, that by the media⯑tion of Light and Colours, other far different Ideas are ſuggeſted to my Mind. But then, upon this Score, I ſee no reaſon why the Sight ſhou'd be thought more Com⯑prehenſive than the Hearing: Which beſide Sounds, which are pecu⯑liar to that Senſe, doth by their Mediation ſuggeſt, not only Space, Figure, and Motion, but alſo, all other Ideas whatſoever that can be ſignified by Words.

CXXXI. Third Ar⯑gument.

Thirdly, It is, I think, an Axi⯑om univerſally receiv'd, that Quan⯑tities of the ſame Kind may be ad⯑ded together, and make one intire [153] Sum. Mathematicians add Lines together; but they do not add a Line to a Solid, or conceive it as making one Sum with a Sur⯑face. Theſe three Kinds of Quan⯑tity being thought incapable of any ſuch mutual Addition, and conſequently of being compa⯑red together, in the ſeveral ways of Proportion, are by them, for that reaſon, eſteem'd intirely Diſ⯑parate and Heterogeneous. Now let any one try in his Thoughts, to add a Viſible Line or Surface to a Tangible Line or Surface. So as to conceive them making one continu'd Sum or Whole. He that can do this, may think 'em Homogenuous; but he that cannot muſt, by the foregoing Anxiom, think them Heterogene⯑ous. I acknowledge my ſelf to be of the latter Sort. A Blue, and and a Red Line I can conceive ad⯑ded together into one Sum, and making one continu'd Line; but [154] to make, in my Thoughts, one continu'd Line of a Viſible and Tangible Line added together is, I find, a Task far more difficult, and even inſurmountable by me: And I leave it to the Reflexion and Experience of every particu⯑lar Perſon, to determine for him⯑ſelf.

CXXXII. Confirma⯑tion drawn from Mr. Moly⯑neux's Problem of a Sphere and a Cube, publiſh'd by Mr. Locke.

A further Confirmation of our Tenent may be drawn from the Solution of Mr. Molyneux's Pro⯑blem, publiſh'd by Mr. Locke in his Eſſay. Which I ſhall ſet down as it there lies, together with Mr. Locke's Opinion of it. ‘Sup⯑poſe a Man Born Blind, and now Adult, and taught by his Touch to di⯑ſtinguiſh between a Cube, and a Sphere of the ſame Metal, and nighly of the ſame Bigneſs, ſo as to tell, when he felt one and t'other, which is the Cube, and which the Sphere. Sup⯑poſe then the Cube and Sphere pla⯑ced on a Table, and the Blind Man [155] to be made to See: Quaere, Whether by his Sight, before he Touch'd them, he could now diſtinguiſh, and tell, which is the Globe, which the Cube. To which the acute and judicious Propoſer Anſwers: Not. For though he has obtain'd the experience of, how a Globe, how a Cube affects his Touch; yet he has not yet attain⯑ed the Experience, that what af⯑fects his Touch ſo or ſo, muſt affect his Sight ſo or ſo: Or that a pro⯑tuberant Angle in the Cube, that preſſed his Hand unequally, ſhall appear to his Eye, as it doth in the Cube. I agree with this think⯑ing Gentleman, whom I am proud to call my Friend, in his Anſwer to this his Problem; and am of opinion, that the Blind Man, at firſt Sight, would not be able with certainty to ſay, which was the Globe, which the Cube, whilſt he only ſaw them.’ Eſſay on Hu⯑man Underſtand. b. ii. c. 9. ſ. 8.

CXXXIII. Which is falſly ſol⯑ved, if the common Suppoſition be true.

Now, if a Square Surface per⯑ceiv'd by Touch be of the ſame Sort, with a Square Surface percei⯑ved by Sight: It is certain the Blind Man here mention'd might know a Square Surface, as ſoon as he ſaw it. It is no more but introducing into his Mind, by a new Inlet, an Idea he has been already well acquainted with. Since therefore he is ſuppos'd to have known by his Touch, that a Cube is a Body terminated by Square Surfaces; and that a Sphere is not terminated by Square Surfa⯑ces: Upon the Suppoſition that a Viſible and Tangible Square dif⯑fer only in Numero, it follows, that he might know, by the unerring Mark of the Square Surfaces, which was the Cube, and which not, whilſt he only ſaw them. We muſt therefore allow, either that Viſible Extenſion and Figures are Specifically diſtinct, from Tangi⯑ble [157] Extenſion and Figures, or elſe, that the Solution of this Problem, given by thoſe two very thought⯑ful and ingenious Men, is wrong.

CXXXIV. More might be ſaid in proof of our Tenent, but this ſuffices.

Much more might be laid to⯑gether in Proof of the Propoſiti⯑on I have advanced. But what has been ſaid is, if I miſtake not, ſufficient to convince any one that ſhall yield a reaſonable Attenti⯑on. And, as for thoſe that will not be at the Pains of a lit⯑tle Thought, no Multiplication of Words will ever ſuffice to make them underſtand the Truth, or rightly conceive my Meaning.

CXXXV. Farther Reflexion, on the fore⯑going Pro⯑blem.

I cannot let go the above-men⯑tion'd Problem, without ſome Re⯑flexion on it. It hath been made evident, that a Man Blind from his Birth wou'd not, at firſt Sight, denominate any thing he ſaw by the Names, he had been us'd to appropriate to Ideas of Touch. [158] vid. Sect. CVI. Cube, Sphere, Table, are Words he has known applied to Things perceivable by Touch, but to Things perfectly Intangi⯑ble he never knew them apply'd. Thoſe Words, in their wonted ap⯑plication, always mark'd out to his Mind Bodies, or Solid Things which were perceiv'd by the Re⯑ſiſtance they gave. But there is no Solidity, no Reſiſtance or Pro⯑truſion perceiv'd by Sight. In ſhort, the Ideas of Sight are all new Perceptions, to which there be no Names annex'd 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 down right Bantering and Unintelligible: Nothing he ſees being able to ſug⯑geſt to his Thoughts, the Idea of Body, Diſtance, or, in general, of any thing he had already known.

CXXXVI The ſame thing doth not affect both Sight and Touch.

'Tis 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 ſhou'd hinder the Blind Man, at firſt Sight, from knowing it? For tho' the manner wherein it affects the Sight, be different from that wherein it affected his Touch; yet, there be⯑ing, beſide this Manner or Circum⯑ſtance, which is new and unknown, the Angle or Figure which is old and known, he cannot chuſe but diſcern it.

CXXXVII Tho ſame Idea of Mo⯑tion not common to Sight and Touch.

Viſible Figure and Extenſion ha⯑ving been demonſtrated, to be of a Nature intirely Different and He⯑terogeneous, from Tangible Fi⯑gure and Extenſion, it remains that we inquire concerning Motion. Now, that Viſible Motion is not of the ſame Sort with Tangible Motion, ſeems to need no farther Proof, [150] it being an evident Corollary from what we have ſhewn, concerning the Difference there is betwixt Vi⯑ſible and Tangible Extenſion. But for a more full and expreſs Proof hereof, we need only obſerve, that one who had not yet experien⯑ced Viſion, wou'd not, at firſt Sight, know Motion. Whence it clear⯑ly follows, that Motion perceiva⯑ble by Sight is of a Sort diſtinct from Motion perceivable by Touch. The Antecedent I prove thus. By Touch he cou'd not perceive a⯑ny Motion, but what was up or down, to the right or left, near⯑er or farther from him; beſides theſe, and their ſeveral Varieties or Complications, it's impoſſible he ſhou'd have any Idea of Motion. He wou'd not therefore think a⯑ny thing to be Motion, or give the name Motion to any Idea, which he cou'd not range under ſome or other, of thoſe particular Kinds thereof. But from Sect. XCV. it's [161] plain that by the meer act of Viſi⯑on, he cou'd not know Motion upwards or downwards, to the right or left, or in any other poſ⯑ſible Direction. From which I con⯑clude, he'd not know Motion at all at firſt Sight. As for the I⯑dea of Motion in Abſtract, I ſhall not waſte Paper about it, but leave it to my Reader, to make the beſt he can on't. To me 'tis perfect⯑ly Unintelligible.

CXXXVIII The way wherein we apprehend Motion by Sight, eaſi⯑ly collected from what hath been ſaid.

The Conſideration of Motion, may furniſh a new Field for In⯑quiry. But ſince the manner where⯑in the Mind apprehends by Sight, the Motion of Tangible Objects, with the various Degrees thereof, may be eaſily collected, from what has been ſaid concerning the man⯑ner, wherein that Senſe doth ſug⯑geſt their various Diſtances, Mag⯑nitudes, and Situations; I ſhall not enlarge any farther on this Sub⯑ject: But proceed to enquire what [150] [...] [161] [...] [162] may be alleg'd, with greateſt ap⯑pearance of Reaſon, againſt the Propoſition we have Demonſtra⯑ted to be true. For where there is ſo much Prejudice to be en⯑counter'd, a bare and naked De⯑monſtration of the Truth will ſcarce ſuffice. We muſt alſo, ſatisfie the Scruples that Men may Start, in favour of their preconceiv'd No⯑tions, ſhew whence the Miſtake ariſes, how it came to ſpread, and carefully diſcloſe and root out thoſe falſe Perſwaſions, that an early Pre⯑judice might have implanted in the Mind.

CXXXIX. Qu. How Viſible and Tangible Ideas came to have the ſame Name if not of the ſame Kind.

Firſt, Therefore, it will be de⯑manded, how Viſible Extenſion and Figures come to be call'd by the ſame Name, with Tangible Ex⯑tenſion and Figures, if they are not of the ſame Kind with them? It muſt be ſomething more than Humour or Accident, that cou'd occaſion a Cuſtom ſo conſtant and uni⯑verſal [163] as this, which has obtain'd in all Ages and Nations of the World, and amongſt all Ranks of Men, the Learned as well as the Illiterate.

CXL. This ac⯑counted for without ſuppoſing them of the ſame Kind.

To which I Anſwer, we can no more Argue e. g. a Viſible and Tangible Square to be of the ſame Species, from their being call'd by the ſame Name; than we can, that a Tangible Square and the Monoſyllable conſiſting of Six Let⯑ters, whereby it is mark'd, are of the ſame Species, becauſe they are both call'd by the ſame Name. It is cuſtomary to call written Words, and the Things they ſignify, by the ſame Name: For Words not be⯑ing regarded in their own Nature, or otherwiſe than as they are marks of Things, it had been ſuperflu⯑ous, and beſide the deſign of Lan⯑guage, to have given them Names diſtinct from thoſe of the Things marked by them. The ſame Rea⯑ſon [164] holds here alſo. Viſible Fi⯑gures are the marks of Tangible Figures, and from Sect. LIX, it is plain, that in themſelves they are lit⯑tle regarded, or upon any other Score than for their Connexion with Tan⯑gible Figures, which by Nature they are ordain'd to ſignifie. And becauſe this Language of Nature does not vary, in different Ages or Nations, hence it is that, in all Times and Places, Viſible Figures are call'd by the ſame Names, as the re⯑ſpective Tangible Figures ſuggeſt⯑ed by them: And not becauſe they are alike, or of the ſame ſort with them.

CXLI. Obj. That a Tangible Square is liker to a Viſible Square than to a Viſible Cir⯑cle.

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 An⯑gles; [165] which makes it unfit to repreſent the Tangible Square, but very fit to repreſent the Tan⯑gible Circle. Whence it clearly follows, that Viſible Figures are Patterns of, or of the ſame Spe⯑cies with, the reſpective Tangible Figures repreſented by them; that they are like unto them, and of their own Nature fitted to re⯑preſent them as being of the ſame ſort; and that they are in no reſpect arbitrary Signs, as Words.

CXLII. Anſ. That a Viſible Square is fitter than a Viſible Circle, to repreſent a Tangible Square.

I Anſwer it muſt be acknow⯑ledg'd, the Viſible Square is fit⯑ter than the Viſible Circle to re⯑preſent the Tangible Square, but then it is not becauſe it's 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 [166] doth not. The Square perceiv'd by Touch hath four diſtinct, equal Sides, ſo alſo hath it four diſtinct, equal Angles. It is therefore ne⯑ceſſary, 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 like⯑wiſe four other diſtinct and equal Parts, whereby to denote the four equal Angles of the Tangible Square. And accordingly we ſee the Vi⯑ſible Figures contain in them di⯑ſtinct Viſible Parts anſwering to the diſtinct Tangible Parts of the Figures ſignify'd, or ſuggeſted by them.

CXLIII. But it doth not hence follow, that a Viſible Square is like a Tan⯑gible Square.

But it will not hence follow, that any Viſible Figure is like un⯑to, 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. [167] To Illuſtrate this, I obſerve that Viſible Figures repreſent Tangible Figures, much after the ſame man⯑ner that written Words do Sounds. Now, in this reſpect, Words are not Arbitrary, it not being indif⯑ferent, what written Word ſtands for any Sound. But it is requi⯑ſite, that each Word contain in it as 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 annext 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 ſhou'd conſiſt of as many di⯑ſtinct Characters, thereby to mark each particular Difference or Part of the whole Sound. And yet [168] no Body, I preſume, will ſay, the ſingle Letter a or the Word A⯑dultery are like unto, or of the ſame Species with, the reſpective Sounds by them Repreſented. It is indeed Arbitrary that, in ge⯑neral, Letters of any Language repreſent Sounds at all; but when that is once agreed, it is not Ar⯑bitrary what Combination of Let⯑ters ſhall repreſent this or that par⯑ticular Sound. I leave this with the Reader to purſue, and ap⯑ply it in his own Thoughts.

CXLIV. Why we are more apt to confound Viſible with Tan⯑gible I⯑deas, than other Signs with the Things ſig⯑nify'd.

It muſt be confeſt, 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 well be, without our ſuppoſing them of a like Nature. Theſe Signs are conſtant and univerſal, this Con⯑nexion with Tangible Ideas has been [169] learnt, at our firſt Entrance into the World, and ever ſince, almoſt eve⯑ry 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 Hu⯑man Inſtitution, when we re⯑member, 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 learn'd their Signifi⯑cation; but think that at firſt Sight they would have ſuggeſted to us, the ſame Things they do now: All this perſwades us they are of the ſame Species as the [170] Things reſpectively repreſented by them, and that is by a natural Re⯑ſemblance they ſuggeſt them to our Minds.

CXLV. Several o⯑ther Rea⯑ſons hereof, aſſign'd.

Add to this, that whenever we make a nice Survey of any Ob⯑ject, ſucceſſively directing the Op⯑tic Axis to each Point thereof; there are certain Lines and Fi⯑gures deſcrib'd by the Motion of the Head or Eye; which, being in Truth perceiv'd 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 be⯑ſide the Touch. Sounds, for Ex⯑ample, perceiv'd at the ſame Inſtant, are apt to coaleſce, if I may ſo ſay, into one Sound. But we can perceive at the ſame [171] time great variety of Viſible Ob⯑jects, very ſeparate and diſtinct from each other. Now Tangible Extenſion being made up, of ſe⯑veral diſtinct coexiſtent parts, we may hence gather another Reaſon, that may diſpoſe us to imagine a Likeneſs, or Analogy, between the immediate Objects of Sight and Touch. But nothing, certainly, does 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 Tan⯑gible Figures are ſuggeſted by them. So ſwift, and ſudden, and unper⯑ceiv'd is the Tranſit from Viſible to Tangible Ideas; that we can ſcarce forbear thinking 'em equally the immediate Object of Viſion.

CXLVI. Reluctancy in reject⯑ing any O⯑pinion, no Argument of its Truth.

The Prejudice which is ground⯑ed on theſe, and whatever other Cauſes may be aſſign'd thereof, [172] ſticks ſo faſt on our Underſtand⯑ings, that it is impoſſible without obſtinate Striving, and Labour of the Mind, to get intirely 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, Magni⯑tude, and Situation of Objects: Prejudices ſo familiar to our Minds, ſo confirm'd and inveterate, as they will hardly give way to the cleareſt Demonſtration.

CXLVII. Proper Ob⯑jects of Vi⯑ſion, the Language of Nature.

Upon the whole, I think we may fairly conclude, that the pro⯑per Objects of Viſion conſtitute the Univerſal Language of Nature, whereby we are inſtructed how to regulate our Actions, in or⯑der to attain thoſe things, that are neceſſary to the Preſervation and Well-being of our Bodies, as [173] alſo to avoid whatever may be hurtful and deſtructive of them. It's by their Information that we are principally guided in all the Tranſactions and Concerns of Life. And the manner wherein they ſig⯑nify, and mark out unto us the Objects which are at a diſtance, is the ſame with that of Lan⯑guages and Signs of Human Ap⯑pointment; which do not ſug⯑geſt the things ſignify'd, by any Likeneſs or Identity of Nature, but only by an Habitual Con⯑nexion, that Experience has made us to obſerve between 'em.

CXLVIII In it there is much ad⯑mirable, and deſer⯑ving our attention.

Suppoſe one who had always continu'd Blind, be told by his Guide, that after he has advan⯑ced ſo many Steps, he ſhall come to the Brink of a Precipice, or be ſtopt by a Wall; muſt not this to him ſeem very admirable and ſurprizing? He can't con⯑ceive how 'tis poſſible for Mor⯑tals, [174] to frame ſuch Predictions as theſe, which to him would ſeem as ſtrange and unaccountable, as Propheſy does to others. Even they who are Bleſſed with the Viſive Faculty, may (tho' Fami⯑liarity make it leſs obſerv'd) find therein ſufficient Cauſe of Admi⯑ration. The wonderful Art and Contrivance wherewith it is ad⯑juſted, to thoſe Ends and Purpo⯑ſes for which it was apparently deſign'd, the vaſt Extent, Num⯑ber, and Variety of Objects that are, at once, with ſo much Eaſe, and Quickneſs, and Pleaſure, ſug⯑geſted by it: All theſe afford Subject for much and pleaſing Speculation; and may, if any thing, give us ſome Glimmer⯑ing, Analogous, Praenotion of Things, that are placed beyond the certain Diſcovery, and Com⯑prehenſion of our preſent State.

CXLIX. Queſtion propos'd, concerning the Object of Geome⯑try.

I do not deſign to trouble my ſelf much with drawing Corollaries, from the Doctrine I have hither⯑to 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 whate⯑ver Purpoſes it may be ſubſer⯑vient to. Only, I cannot forbear making ſome Inquiry concerning the Object of Geometry, which the Subject we have been upon does naturally lead one to. We have ſhewn there's no ſuch Idea, as that of Extenſion in Abſtract, and that there are two kinds of ſenſible Extenſion and Figures, which are intirely Diſtinct and Heteroge⯑neous from each other. Now, it is natural to enquire which of theſe is the Object of Geometry.

CL. At firſt View, we are apt to think Viſi⯑ble Exten⯑ſion the Ob⯑ject of Geo⯑metry.

Some things there are which, at firſt ſight, incline one to think [176] Geometry converſant about Viſi⯑ble Extenſion. The conſtant uſe of the Eyes, both in the Practi⯑cal and Speculative Parts of that Science, doth very much induce us thereto. It would, without doubt, ſeem odd to a Mathema⯑tician, 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 be⯑ing held an unqueſtionable Truth, not only by Mathematicians, but alſo by thoſe who apply them⯑ſelves more particularly to the Study of Logick; I mean, who conſider the Nature of Science, Certainty, and Demonſtration: It being by them aſſign'd as one Reaſon, of the extraordinary Clear⯑neſs and Evidence of Geometry, that in that Science the Reaſon⯑ings are free from thoſe Incon⯑veniences, which attend the uſe of [177] 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 Demon⯑ſtration, I leave to be conſi⯑der'd.

CLI. Viſible Ex⯑tenſion ſhewn not to be the Ob⯑ject of Geo⯑metry.

To come to a Reſolution in this Point, we need only ob⯑ſerve what has been ſaid in Sect. LIX, LX, LXI; where it is ſhewn, that Viſible Extenſions in themſelves are little regarded, and have no ſettled determinate Great⯑neſs; and that Men meaſure al⯑together, by the Application of Tangible Extenſion to Tangible Extenſion. All which makes it evident, that Viſible Extenſion and Figures are not the Object of Geo⯑metry.

CLII. Words may as well be thought the Object of Geometry, as Viſible Extenſion.

It is, therefore, plain that Vi⯑ſible Figures are of the ſame Uſe in Geometry, that Words are. And the one may as well be ac⯑counted the Object of that Science, as the other; neither of them being any otherwiſe concern'd therein, than as they repreſent or ſuggeſt to the Mind the particu⯑lar Tangible Figures connected with them. There is, indeed, this Difference betwixt the Significa⯑tion of Tangible Figures by Vi⯑ſible Figures, and of Ideas by Words. That whereas the Latter is variable and uncertain, depend⯑ing altogether on the Arbitrary Appointment of Men; the For⯑mer is fix'd, 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 Nature, which [179] ſpeaks to our Eyes, is not liable to that Miſinterpretation and Am⯑biguity, that Languages of Hu⯑man Contrivance are unavoidably ſubjected to. From which may, in ſome meaſure, be derived that peculiar Evidence and Clearneſs of Geometrical Demonſtrations.

CLIII. It is pro⯑pos'd to en⯑quire, what Progreſs an Intelligence that cou'd ſee, but not feel, might make in Geometry.

Tho' what has been ſaid may ſuffice to ſhew what ought to be determin'd, with relation to the Object of Geometry; I ſhall ne⯑vertheleſs, for the fuller Illuſtra⯑tion thereof, take into my Thoughts the Caſe of an Intelligence, or Unbody'd Spirit, which is ſup⯑pos'd 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 enquire. It ſuffices, that the Suppoſition con⯑tains no Contradiction in it. Let [180] 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 Sci⯑ence.

CLIV. He cannot underſtand thoſe parts which re⯑late to So⯑lids, and their Sur⯑faces and Lines ge⯑nerated by their Secti⯑on.

Firſt, then 'tis certain, the a⯑foreſaid Intelligence could have no Idea of a Solid, or Quantity of three Dimenſions; which follows 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 ariſes from our imagining that we do, ſtrictly ſpeaking, ſee Diſtance, and ſome parts of an Object at a greater Diſtance than others, which has been demon⯑ſtrated to be the Effect of the Experience we have had, what I⯑deas of Touch are connected with ſuch and ſuch Ideas attending Vi⯑ſion. But the Intelligence here [181] ſpoken of is ſuppos'd to have no Experience of Touch. He wou'd not, therefore, judge as we do, nor have any Idea of Diſtance, Outneſs, or Profundity, nor con⯑ſequently of Space or Body, ei⯑ther immediately or by Suggeſtion. Whence it is plain, he can have no Notion of thoſe parts of Geo⯑metry, which relate to the Men⯑ſuration of Solids, and their Con⯑vex or Concave Surfaces, and contemplate the Properties of Lines generated by the Section of a Solid. The conceiving of any part where⯑of, is beyond the Reach of his Fa⯑culties.

CLV. Nor even the Ele⯑ments of plain Geo⯑metry.

Farther, he cannot comprehend the manner wherein Geometers de⯑ſcribe a right Line or Circle: The Rule and Compaſs with their Uſe, being things of which it's impoſ⯑ſible he ſhould have any Notion. Nor is it an eaſier matter for him, to conceive the placing of [182] one Plain or Angle on another, in order to prove their Equality. Since that ſuppoſes 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 plain Geometry. And, perhaps, upon a nice Enquiry, it will be found, he cannot even have an Idea of Plain Figures, any more than he can of Solids. Since ſome Idea of Diſtance is neceſſary, to form the Idea of a Geometrical Plain, as will appear to whoever ſhall reflect a little on it.

CLVI. The proper Objects of Sight inca⯑pable of be⯑ing mana⯑ged as Geo⯑metrical Figures.

All that is properly perceiv'd by the Viſive Faculty, amounts to no more than Colours with their Va⯑riations, and different Proportions of Light and Shade. But, the per⯑petual Mutability, and Fleetingneſs of thoſe immediate Objects of Sight, render them incapable of being managed after the manner [183] of Geometrical Figures; nor is it in any Degree uſeful that they ſhould. It's true, there be divers of 'em perceiv'd at once; and more of ſome, and leſs of others. But accurately to compute their Magnitude, and aſſign preciſe de⯑terminate Proportions, between Things ſo Variable and Inconſtant, if we ſuppoſe it poſſible to be done, muſt yet be a very trifling and in⯑ſignificant Labour.

CLVII. The Opini⯑on of thoſe who hold plain Fi⯑gures to be the imme⯑diate Ob⯑jects of Sight, con⯑ſider'd.

I muſt confeſs, it ſeems to be the Opinion of ſome very Ingenious Men, that flat or plain Figures are immediate Objects of Sight, tho' they acknowledge Solids are not. And this Opinion of their's is grounded on what is obſerv'd in Painting, wherein (ſay they) the I⯑deas immediately imprinted in the Mind, are only of Plains variouſly colour'd, which by a ſudden Act of the Judgment are changed into Solids. But, with a little Attention [184] we ſhall find the Plains here men⯑tion'd, as the immediate Objects of Sight, are not Viſible, but Tangi⯑ble Plains. For when we ſay that Pictures are Plains, we mean there⯑by, that they appear to the Touch Smooth and Uniform. But then this Smoothneſs and Uniformity, or, in other Words, this Plainneſs of the Picture, is not perceiv'd im⯑mediately by Viſion: For it appear⯑eth to the Eye Various and Multi⯑form.

CLVIII. Plains, no more the immediate Objects of Sight, than Solids.

From all which we may con⯑clude, that Plains are no more the immediate Object of Sight than So⯑lids. What we ſtrictly ſee are not Solids, nor yet Plains variouſly co⯑lour'd; they are only Diverſity of Colours. And ſome of theſe ſug⯑geſt to the Mind Solids, and others Plain Figures; juſt as they have been experienced to be connected with the one, or the other. So that we ſee Plains, in the ſame way that we [185] ſee Solids: Both being equally ſuggeſted by the immediate Ob⯑jects of Sight, which according⯑ly are themſelves Denominated Plains and Solids. But tho' they are called by the ſame Names, with the Things mark'd by them, they are nevertheleſs of a Nature intirely different, as hath been De⯑monſtrated.

CLIX. Difficult to enter pre⯑ciſely in⯑to the Thoughts of the a⯑bove men⯑tion'd In⯑telligence.

What has been ſaid is, if I miſtake not, ſufficient to Decide the Queſtion we propos'd to Exa⯑mine, concerning the Ability of a pure Spirit, ſuch as we have deſcrib'd, 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 Diſintangle in our Thoughts, the proper Ob⯑jects of Sight, from thoſe of Touch, which are Connected with them. This, indeed, in a compleat De⯑gree, [186] ſeems ſcarce poſſible to be perform'd. Which will not ſeem ſtrange to us, if we conſider how hard it is, for any one to hear the Words of his Native Lan⯑guage, which is familiar to him, pronounced in his Ears without underſtanding them. Tho' he en⯑deavour to diſunite the meaning from the Sound, it will neverthe⯑leſs intrude into his Thoughts, and he ſhall find it extream Difficult, if not impoſſible, to put him⯑ſelf exactly in the Poſture of a Foreigner, that never learnt the Language, ſo as to be affected barely with the Sounds themſelves, and not perceive the Significati⯑on annexed to them.

CXL. The Object of Geome⯑try, its not being ſuffi⯑ciently un⯑derſtood, cauſe of Difficulty and uſeleſs Labour in that Sci⯑ence.

By this time, I ſuppoſe, 'tis clear that neither Abſtract, nor Viſible Extenſion makes rhe Object of Geo⯑metry. The not diſcerning of which might, perhaps, have created ſome Difficulty, and uſeleſs Labour in [187] Mathematics. Sure I am, that ſome⯑what relating thereto has occur'd to my Thoughts, which, tho' af⯑ter the moſt anxious and repeat⯑ed Examination I am forced to think it true, doth, nevertheleſs, ſeem ſo far out of the common road of Geometry, that I know not, whether it may not be thought Preſumption, if I ſhou'd make it publick in an Age, where⯑in that Science hath receiv'd ſuch mighty Improvements by new Me⯑thods; great Part whereof, as well as of the Ancient Diſcoveries, may perhaps loſe their Reputation, and much of that Ardor, with which Men ſtudy the Abſtruſe and Fine Geometry be abated, if what to me, and thoſe few to whom I have imparted it, ſeems evidently True, ſhou'd really prove to be ſo.