I. Design.

MY Design is to shew the man­ner, wherein we perceive by Sight the Distance, Magm­tude, and Situation of Objects. Also to consider the Difference there is be­twixt the Ideas of Sight and Touch, and whether there be any Idea com­mon to both Senses. In treating of all which, it seems to me, the Writers of Optics have proceeded on wrong Principles.

II. Distance of it self In­visible.

It is, I think, agreed by all that Di­stance of it self, and immediately can­not 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 invaria­bly the same, whether the Distance be longer or shorter.

III. Remote Di­stance per­ceiv'd ra­ther by Ex­perience, than by Sense.

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

IV. Near Di­stance thought to be percei­ved 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 per­ceiv'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, ne­cessary Connexion between small Di­stance and a large and strong Ap­pearance, or between great Distance, and a little and faint Appearance. Yet there appears a very necessary Con­nexion [Page 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 Di­verging Rays.

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

VII. This de­pends not on Experi­ence.

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

VIII. These the common Accounts, but not sa­tisfactory.

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 me­diation of others.

First, It is evident that when the Mind perceives any Idea, not imme­diately and of it self, it must be by [Page 6] the means of some other Idea. Thus, for Instance, the Passions which are in the Mind of another, are of them­selves, to me invisible. I may never­theless perceive them by Sight, tho' not immediately yet, by means of the Colours they produce in the Counte­nance. We do often see Shame or Fear in the Looks of a Man, by per­ceiving the Changes of his Counte­nance to Red or Pale.

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

Moreover it is evident, that no I­dea 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 Di­stance is in it's own nature impercei­vable, 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 per­ceiv'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 up­on Sight of an Object, he compute it's Distance by the bigness of the An­gle, 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 per­ceive 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 Ma­thematicians in the World tell me, that I perceive certain Lines and An­gles 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 be­cause they have no re­al Exi­stence.

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

XV. And be­cause they are insuffi­cient to ex­plain the Phaenome­na.

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 Princi­ples wou'd not be found sufficient to explain the Phaenomena of Distance. As shall be shewn hereafter.

XVI. The Ideas that sug­gest Di­stance are 1 st. the Sen­sation ari­sing 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 Dispo­sition of our Eyes, by lessening or widening the Interval between the Pupils. This Disposition or Turn of the Eyes is attended with a Sen­sation, 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 [Page 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 dif­ferent Sensations corresponding to the different Dispositions of the Eyes, to be attended each, with a Different Degree of Distance in the Object: There has grown an Habitual or Cu­stomary Connexion, between those two sorts of Ideas. So that the Mind no sooner perceives the Sensation a­rising from the different Turn it gives the Eyes, in order to bring the Pu­pils nearer, or farther asunder; but it withal perceives the different Idea of Distance which was wont to be connected with that Sensation. Just as upon hearing a certain Sound, the Idea is immediately suggested to the Understanding, which Custom had united with it.

XVIII. Scarce room for Mistake in this mat­ter.

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

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 accord­ingly by a kind of Natural Geometry, it judges the Point of their Intersecti­on to be nearer, or farther off. But that this is not true, I am convinc'd [Page 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 incomprehen­sible.

XX. Judgment of Distance made with both Eyes, the Result of Experi­ence.

From all which it plainly fol­lows, that the Judgment we make of the Distance of an Object, view'd with both Eyes, is entirely the Re­sult of Experience. If we had not constantly found certain Sensations arising from the various Dispositi­on of the Eyes, attended with cer­tain degrees of Distance. We 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, Con­fusedness of Appear­ance.

Secondly, An Object placed at a certain Distance from the Eye, to which the breadth of the Pupil bears a considerable Proportion, being made to approach, is seen more con­fusedly. And the nearer it is brought, the more confused Appearance it makes. And this being found con­stantly to be so, there arises in the Mind an Habitual Connexion be­tween the several Degrees of Confu­sion and Distance. The greater Con­fusion still implying the lesser Di­stance, and the lesser Confusion, the greater Distance of the Object.

XXII. This the occasion of those Judg­ments at­tributed 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 Radia­ting Point fall on the Pupil. No [Page 14] Man, I believe, will pretend to see or feel those imaginary Angles, that the Rays are supposed to form accor­ding to their various Inclinations on his Eye. But he cannot choose see­ing whether the Object appear more, or less confused. It is therefore a manifest Consequence from what has been Demonstrated, that instead of the greater, or lesser Divergency of the Rays, the Mind makes use of the greater or lesser Confusedness of the Appearance, thereby to de­termine the apparent Place of an Object.

XXIII. Objection answer'd.

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

XXIV. What de­ceives the Writers of Optics in this mat­ter.

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

XXV. The Cause, why one I­dea may suggest ano­ther.

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

XXVI. This apply­ed to Con­fusion and Distance.

Thus greater Confusion having been constantly attended with near­er Distance, no sooner is the for­mer 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 Con­fused 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 ima­gine it went farther off. That Per­ception, abstracting from Custom and Experience, being equally fit­ted to produce the Idea of great Di­stance, or small Distance, or no Di­stance at all.

XXVII. 3 dly, The straining of the Eye.

Thirdly, an Object being placed at the Distance above specified, and [Page 17] brought nearer to the Eye, we may nevertheless prevent, at least for some time, the Appearance's grow­ing 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 Di­stance of the Object. It being esteem­ed so much the nearer, by how much the effort, or straining of the Eye in order to distinct Vision, is greater.

XXVIII. The Occa­sions which suggest Di­stance, have in their own Nature no Relation to it.

I have here set down those Sen­sations or Ideas, that seem to me to be the constant and general Oc­casions 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 Num­ber, Size, Kind, &c. of the things seen. Concerning which as well as all other the forementioned Oc­casions which suggest Distance, I [Page 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 sig­nifie the various Degrees thereof, otherwise than as by Experience they have been found to be connected with them.

XXIX. A difficult Case propo­sed by Dr. Barrow as repugnant to all the known Theories.

I shall proceed upon these Prin­ciples to account for a Phaenome­non, which has hitherto strangely puzzled the Writers of Optics, and is so far from being accounted for by any of their Theories of Vi­sion, that it is, by their own Con­fession, plainly repugnant to them. And of Consequence, if nothing else 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 Le­ctures.

[Page 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 plausi­ble Conjectures, instead of certain Principles) there has in them scarce any thing occur'd to my Observa­tion, 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 of­ten said by others. I think it there­fore high time to take my leave of this Subject. But before I quit it for good and all, the fair and ingenuous Dealing that I owe both to You and to Truth, obliges me to acquaint you with a certain un­toward Difficulty, which seems di­rectly opposite to the Doctrine I [Page 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 Re­fraction or Reflecti­on, 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 al­ready 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 Questi­on now is, Where the Point A ought to appear. Experience shews that it doth not appear behind at the Point Z, and it were contrary [Page 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 be­fore the Eye at a vast Distance off, so great as shou'd in some Sort, sur­pass all sensible Distance. For since if we exclude all Anticipations and Prejudices, every Object appears by so much the farther off, by how much the Rays it sends to the Eye are less Diverging. And that Object is thought to be most remote, from which Parallel Rays proceed unto the Eye. Reason wou'd make one think, that Object shou'd appear, at yet a greater Distance, which is seen by converging Rays. More­over it may in general be asked con­cerning this Case, what it is that determines the apparent Place of the Point A, and maketh it to ap­pear after a constant manner, some­times nearer, at other times farther off? To which doubt, I see no­thing [Page 27] that can be answer'd agree­able 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 na­ked Eye, but on the contrary, it doth sometimes appear much near­er. Nay, it is even certain, that by how much the Rays falling on the Eye do more converge, by so much the nearer does the Object seem to approach. For the Eye being placed close to the Point B, the Object A appears nearly in 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 [Page 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 Confu­sion. All which doth seem Repug­nant 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 Know­ledge are, every whit as much, en­danger'd by it. The ancient one especially (which is most common­ly 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 pul­led down the Superstructure he had raised on it. Which nevertheless, [Page 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 bot­tom. But as for me, neither this, nor any other Difficulty shall have so great an Influence on me, as to make me renounce that which I know to be manifestly agreeable to Reason. Especially when, as it here falls out, the Difficulty is founded in the peculiar Nature of a certain odd and particular Case. For in the present Case something peculiar lies hid, which being involv'd in the Subtilty of Nature will, perhaps, hardly be discover'd till such Time, as the manner of Vision is more per­fectly made known. Concerning which, I must own, I have hitherto been able to find out nothing that has the least shew of Probability, not to mention Certainty. I shall there­fore, leave this Knot to be united by you, wishing you may have bet­ter Success in it than I have had.’

XXX. This Case contradicts a receiv'd Principle in Catop­trics.

The ancient and receiv'd Principle which Dr. Barrow here mentions, as the main Foundation of Tacquet's Catop­trics, 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 Authori­ty 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 Phae­nomenon agrees with our Tenents. The Eye the nearer it is placed to the Point B in the above Fi­gures, the more distinct is the Ap­pearance of the Object; but as it recedes to O, the Appearance grows more Confused; and at P it sees [Page 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. Where­fore by Sect. XXI. the Object shou'd seem to approach the Eye gradu­ally, as it recedes from the Point B, viz. at O it shou'd (in conse­quence of the Principle I have laid down in the aforesaid Section) seem nearer than it did at B, and at P nearer than at O, and at Q nearer than at P; and so on, till it quite vanishes at Z. Which is the very matter of Fact, as any one that pleases may easily satisfie him­self by Experiment.

XXXII. This Phae­nomenon Illustrated.

This Case is much the same, as if we shou'd suppose an En­glish-man to meet a Foreigner, who used the same Words with the English, but in a direct contrary Sig­nification. The English-man wou'd not fail to make a wrong Judg­ment, of the Ideas annexed to [Page 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 great­er Confusions were always wont to signifie nearer Distances, they have in this Case a direct, con­trary Signification, being connect­ed 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 explain­ed.

This Phaenomenon as it entirely subverts the Opinion of those, who will have us judge of Distance by Lines and Angles, on which Sup­position it is altogether inexplica­ble, so it seems to me no small Confirmation, of the Truth of that Principle whereby it is explain'd. [Page 33] But in order to a more full Ex­plication 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 ne­cessary to premise some few Things, which are already well known to those who have any Skill in Diop­trics.

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

First, Any radiating Point is then distinctly seen, when the Rays pro­ceeding from it are, by the refra­ctive Power of the Crystalline, ac­curately 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 Vi­sion.

XXXV. The diffe­rent Effects of Parallel, Diverging and Con­verging Rays.

Secondly, Suppose in the adja­cent Figures NP represent an Eye duly framed, and retaining its na­tural [Page 34] Figure. In Fig. 1. the Rays fal­ling 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 be­fore the Retina. In which two last [Page 35] Cases, 'tis evident from the forego­ing Section, that the Appearance of the Point Z is confused. And by how much the greater is the Con­vergency, or Divergency of the Rays falling on the Pupil, by so much the farther will the Point of their reuni­on be from the Retina, either be­fore or behind it, and consequent­ly 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 diffe­rent Points become mix'd, and con­fused together. This is opposed to distinct Vision, and attends near Objects. Faint Vision is, when by reason of the Distance of the Ob­ject, or grossness of the interjacent [Page 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 re­turn.

XXXVI. How Con­verging, and Diver­ging Rays come to suggest the same Di­stance.

The Eye, or (to speak truly) the Mind perceiving only the Confu­sion it self, without ever consider­ing the Cause from which it pro­ceeds, doth constantly annex the same Degree of Distance, to the same Degree of Confusion. Whe­ther 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 di­verging to that Degree, as wou'd produce the same Confusion, which is now produced by Converging [Page 37] Rays, i. e. wou'd cover a Portion of the Retina equal to DC. vid. Fig. 3. Sup. But then this must be under­stood (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 ordina­rily concur to form our Idea of Di­stance; 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 a­right in the fore­mention'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 o­thers do, in the foremention'd Case. For, to him, greater Confusions con­stantly suggesting greater Distances, he must, as he recedes from the Glass, and the Object grows more Confus'd, [Page 38] judge it to be at a farther Distance, contrary to what they do, who have had the Perception of the Ob­ject's growing more Confused, con­nected 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 im­mediately by them, but because it judges by somewhat which is con­nected with them, and to the deter­mination whereof, they may be sub­servient. 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, accord­ing as the Object is seen by Rays more, or less Diverging; it follows, that a Man may make use of the Diver­gency 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 connect­ed. [Page 39] But, so it is, the Confusion it self is entirely neglected by Mathema­ticians, as having no necessary rela­tion with Distance, such as the great­er or lesser Angles of Divergency are conceiv'd to have. And these (espe­cially for that they fall under Ma­thematical 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 Di­stance. Whereas, in Truth, they shou'd not at all be regarded in them­selves, or any otherwise, than as they are supposed to be the Cause of Con­fused Vision.

XXXIX. The not un­derstand­ing 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 obser­ved, that the most Diverging Rays brought into the Mind the Idea of nearest Distance, and that still, as [Page 40] the Divergency decreas'd, the Dist­ance 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 ground­ed 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 learn­ed Doctor observ'd, that Diverging and Converging Rays, how oppo­site soever they may seem, do ne­vertheless agree in producing the same effect, viz. Confusedness of Vi­sion, 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 Con­vergency [Page 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 con­cluded, that those Rays which fall on the Eye with greater degrees of Convergency shou'd make the Ob­ject 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. Moly­neux in his Diop­trics, con­sider'd.

Before we dismiss this this Sub­ject, 'tis fit we take Notice of a Query, relating thereto, propo­sed by the Ingenious Mr. Moly­neux, in his Treatise of Dioptrics, Par. 1. Prop. 31. Sect. 9. where speak­ing of the Difficulty we have been explaining, he has these Words, ‘ [Page 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 in­explicable till a more intimate Knowledge of the Visive Facul­ty be obtain'd by Mortals. In the mean time, I propose it to the Consideration of the Ingeni­ous, Whether the Locus Apparens of an Object placed as in this 9th Section, be not as much be­fore the Eye, as the distinct Base is behind the Eye?’ To which Query we may venture to answer in the Negative. For in the pre­sent Case, the Rule for determin­ing the Distance of the distinct Base, or respective Focus from the [Page 43] Glass, is this. As the difference be­tween the Distance of the Object and Focus ∶ is to the Focus or Fo­cal Length ∷ So the Distance of the Object from the Glass ∶ to the Di­stance of the respective Focus or Di­stinct Base from the Glass. Vid. Moly­neux Dioptr. Par. 1. Prop. 5. Let us now suppose the Object to be pla­ced at the Distance of the Focal Length, and one half of the Fo­cal 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 Con­jecture 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 far­thest, beyond its due Distance. What­ever [Page 44] therefore is built on this Sup­position ( 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 Di­stance 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 I­dea of Distance by Sight. The Sun and Stars, the remotest Ob­jects 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 Ex­perience, which one in those Cir­cumstances [Page 45] cou'd not yet have at­tained to.

XLII. This not a­greeable to the com­mon Prin­ciples.

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 Inqui­ry we shall not find, that even those, who from their Birth have grown up in a continu'd Habit of See­ing, are irrecoverably prejudiced on the other side, viz. in thinking what they See to be at a Di­stance from them. For at this [Page 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 Ob­ject of Sight, are not without the Mind. But then say you, by Sight we have also the Ideas of Exten­sion, 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 Ob­ject do not appear as near to him, as the Colour of that Ob­ject; 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 per­ceiv'd by Sight.

XLIV. This more fully ex­plain'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 Resem­blances of things placed at a Di­stance, 'tis requisite we look near­er into the Matter, and carefully observe what is meant in com­mon 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 Semi­diameters of the Earth distant from me. Let us see what Moon this is spoken of. 'Tis plain it can­not be the visible Moon, or a­ny thing like the visible Moon, or that which I see, which is on­ly a round, luminous Plain, of a­bout Thirty visible Points in Dia­meter. For in case I am carry'd, from the place where I stand di­rectly towards the Moon; 'tis ma­nifest the Object varies, still as I [Page 48] go on; and by the time that I am advanced Fifty or Sixty Se­midiameters 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 some­thing, which I doubt whether it be a Man, or a Tree, or a Tow­er; but judge it to be at the Di­stance 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 be­ing Obscure, Small, and Faint grows, Clear, Large, and Vigo­rous. And when I come to the Mile's end, that which I saw [Page 49] first is quite lost, neither do I find any thing in the likeness of it.

XLV. In what Sense we must be un­derstood to see Distance and exter­nal Things.

In these, and the like Instances, the truth of the Matter, I find, stands thus. Having of a long time, expe­rienced certain Ideas, perceivable by Touch, as Distance, Tangible Figure, and Solidity to have been con­nected with certain Ideas of Sight, I do upon perceiving these Ideas of Sight, forthwith conclude what Tangible Ideas are, by the won­ted, ordinary course of Nature like to follow. Looking at an Object I perceive a certain Visible Figure, and Colour with some degree of Faint­ness and other Circumstances; which, from what I have formerly observ'd, determin me to think, that if I ad­vance 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 [Page 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 Under­standing, 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 sug­gestions 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 Pi­cture, [Page 51] to be convinced. Note, that when I speak of Tangible Ideas, I take the Word Idea for any the im­mediate Object of Sense, or Under­standing, in which large Significati­on it is commonly used by the Mo­derns.

XLVI. Distance and Things placed at a Distance, not other­wise per­ceived by the Eye than by the Ear.

From what we have shewn it is a manifest Consequence, that the I­deas 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 Case­ment 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 ha­ving been observed constantly to go [Page 52] together, they are spoken of as one and the same thing. By the varia­tion 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 per­ceive Distance, just after the same manner, as I do by the Eye.

XLVII. The Ideas of Sight more apt to be confoun­ded 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 Hear­ing not being so apt to be confound­ed 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 [Page 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 Ab­surdity 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 fol­low that we see the same Extensi­on, 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 ac­curate 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 Tangi­ble Figure and Extension, we are not to infer, that one and the same [Page 54] thing has divers Extensions. The true Consequence is, that the Ob­jects of Sight and Touch are two distinct things. It may perhaps, re­quire some Thought, rightly to con­ceive this Distinction. And the dif­ficulty seems not a little increas'd, because the Combination of Visi­ble Ideas hath constantly the same Name, as the Combination of Tan­gible Ideas wherewith it is con­nected. Which does of necessity arise from the use, and end of Language.

L. Objects of Sight twofold Mediate and Imme­diate.

In order therefore to treat ac­curately, and unconfusedly of Vi­sion, we must bear in Mind, that there are two sorts of Objects ap­prehended by the Eye: The one, pri­marily and immediately, the other, secondarily and by intervention of the former. Those of the first sort neither are, nor appear to be with­out the Mind, or at any distance off. They may, indeed, grow Great­er, [Page 55] or Smaller, more Confused, or more Clear, or more Faint. But, they do not, cannot Approach, or even seem to Approach, or Re­cede from us. Whenever we say an Object is at a Distance, when­ever we say, it draws near, or goes farther off; we must always mean it of the latter sort, which proper­ly belong to the Touch, and are not so truly perceived, as suggest­ed, 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 pronoun­ced in our Ears, but the Ideas corresponding thereto present them­selves 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 o­ther also. We even act in all re­spects, as tho' we heard the very [Page 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 pro­per Objects of that Sense; along with which they enter into the Mind, and with which they have a far more strict and near Con­nexion, than Ideas have with Words. Hence it is, we find it so difficult to discriminate, between the im­mediate and mediate Objects of Sight, and are so prone to at­tribute to the former, what be­longs 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 Reflexi­on. However, I doubt not, but any one that shall attentively con­sider what we have already said, and shall say upon this Subject be­fore [Page 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 Vi­sion.

LII. The recei­ved Ac­counts of our percei­ving Mag­nitude by Sight false

I have now done with Distance, and proceed to shew, how it is, that we perceive by Sight, the Magni­tude 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 demonstra­ted Lines and Angles not to be the Medium, the Mind makes use of in apprehending the Apparent Place, so neither are they, the Medium where­by it apprehends the Apparent Mag­nitude of Objects.

LIII. Magnitude perceiv'd as imme­diately, 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 ma­king one see by Geometry) is, that the same Perceptions or Ideas which sug­gest Distance, do also suggest Mag­nitude. 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 Con­nexion with the Magnitude, as with the Distance; and suggest Magni­tude as independently of Distance, [Page 59] as they do Distance independently of Magnitude. All which will be evident, to whoever considers what­has been already said, and what fol­lows.

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 Mag­nitude, or Extension. The one, pro­perly 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 in­finitely Divisible. There is a Mini­mum Tangibile, and a Minimum Visi­bile, beyond which Sense cannot per­ceive. [Page 60] This, every ones Experience will inform him.

LV. The Tangi­ble Magni­tude 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 Visi­ble Object still changing as you approach to, or recede from the Tangible Object, it hath no fixed and determinate Greatness. When­ever therefore, we speak of the Mag­nitude 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 Visi­ble Magnitude do, in truth, belong to two distinct Objects: I shall ne­vertheless (especially since those Ob­jects are called by the same Name, and are observ'd to coexist) to a­void tediousness and singularity of Speech, sometimes speak of them, as belonging to one and the same thing.

LVI. By what means, Tan­gible Mag­nitude is perceiv'd by Sight.

Now in order to discover by what means, the Magnitude of Tan­gible Objects is perceived by Sight; I need only reflect on what Passes in my own Mind. And observe what those things be, which in­troduce the Ideas of greater or les­ser into my Thoughts, when I look on any Object. And these I find to be, First, the Magnitude or Ex­tension 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 Confu­sion or Distinctness. And, Thirdly, The Vigorousness or Faintness of the aforesaid Visible Appearance. Caeteris paribus, by how much the greater or les­ser, do I conclude the Tangible Object to be. But, be the Idea im­mediately perceived by Sight never so large, yet if it be withal Con­fused, [Page 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 ap­prehend it to be yet greater. What is here meant, by Confusion and Faintness, has been Explain'd in Sect. XXXV.

LVII. This far­ther en­larged on.

Moreover, the Judgments we make of Greatness do, in like man­ner as those of Distance, depend on the Disposition of the Eyes, al­so on the Figure, Number of in­termediate Objects, and other Cir­cumstances that have been observ'd to attend great, or small Tangi­ble Magnitudes. Thus, for Instance, The very same Quantity of Visi­ble 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 [Page 63] a Tower and a Man, no one, I sup­pose, need be told.

LVIII. No necessa­ry Connexi­on between, Confusion or Faintness of Appear­ance, and small or great Mag­nitude.

It is also evident, that Confusion, Faintness, &c. have no more a neces­sary 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 Appear­ance to be connected, with great or little Magnitude, than we shou'd that it was connected with great or little Distance.

LIX. The Tangi­ble Magni­tude of an Object, more heed­ed 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 dif­ference [Page 64] there is, betwixt the Ex­tension 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 Ob­jects that environ us, in propor­tion as they are adapted to be­nefit, or injure our own Bodies, and thereby, produce in our Minds the Sensations of Pleasure, or Pain. Now Bodies operating on our Or­gans, by an immediate Applicati­on: And the Hurt and Advantage arising there-from, depending alto­gether on the Tangible, ang not at all on the Visible, Qualities of any Object. This is a plain Rea­son, why those shou'd be regard­ed by us much more than these. And for this End, chiefly, the Vi­sive Sense seems to have been be­stowed [Page 65] on Animals, viz. that by the Perception of Visible Ideas (which in themselves are not ca­pable of affecting, or any wise alter­ing the Frame of their Bodies) they may be able to foresee (from the Experience they have had, what Tan­gible 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 preser­vation 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 sen­sibly 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 great­ness of the Object. The Visible Magnitude being far greater, at one Station, than it is at the o­ther.

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

Inches, Feet, &c. are settled, sta­ted Lengths, whereby we measure Objects, and estimate their Mag­nitude, we say, for Example, an Object appears to be Six Inches, or Six Foot long. Now, that this cannot be meant of Visible Inch­ches, &c. is evident, because a Vi­sible Inch is it self no constant, de­terminate Magnitude, and cannot, therefore, serve to mark out, and determin the Magnitude of any o­ther [Page 67] thing. Take an Inch mark'd upon a Ruler; view it, successive­ly, 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 Vi­sible 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 as­sign'd, why we shou'd pitch on one, more than another. And ex­cept there be some invariable, de­terminate Extension fixed on, to be mark'd by the Word Inch, 'tis plain, it can be used to little Pur­pose; and to say, a Thing con­tains this or that Number of Inch­es, shall imply no more than that it is extended, without bringing any particular Idea of that Exten­sion into the Mind. Farther, an [Page 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 great­er than the other. From all which it is manifest, that the Judgments we make of the Magnitude of Ob­jects by Sight, are altogether in re­ference to their Tangible Extensi­on. 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 neverthe­less little taken Notice of.

LXII. No necessa­ry Conexi­on between Visible and Tangible Extension.

Now, that there is no necessa­ry Connexion, between these two Distinct Extensions is evident from hence. Because our Eyes might have been framed in such a man­ner, as to be able to see nothing but what were less than the Mini­mum Tangibile. In which Case, it's not [Page 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 Judg­ments 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 be­twixt them.

LXIII. Greater Vi­sible Mag­nitude might sig­nifie 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 ob­serve to accompany it: But also, that the greater Visible Magnitudes might have been Connected with, and In­troduced into our Minds, lesser Tangible Magnitudes, and Vice Ver­sa. Nay, that it often is so, we [Page 70] have daily Experience; that Object which makes a strong and large Appearance, not seeming near so great, as another the Visible Mag­nitude whereof is much less, but more faint.

LXIV. The Judg­ments we make of Magnitude depend al­together on Experience

From which, and from Sect. LVII, and LVIII. it is manifest, that as we do not perceive the Magnitude of Objects immediate­ly by Sight, so neither do we per­ceive them, by the Mediation of any thing which has a necessary Connexion with them. Those Ideas that now suggest unto us, the va­rious Magnitudes of External Ob­jects, 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 [Page 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 Mag­nitude 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 In­visible, 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 o­therwise, and why.

We are nevertheless exceeding Prone to imagine, those things which are perceived only by the Mediation of others, to be them­selves the immediate Objects of Sight: Or, at least, to have in their own Nature a Fitness to be suggest­ed by them, before ever they had been experienced to Coexist with them. From which prejudice eve­ry one, perhaps, will not find it easy to emanicipate himself, by a­ny the clearest Convictions of Rea­son. And there are some Grounds to think, that if there was one only invariable, and universal Lan­guage in the World, and that Men were born with the Faculty of speaking it; it wou'd be the O­pinion 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 affix­ed to them. All which seems to [Page 73] arise, from want of a due Appli­cation of our Discerning Faculty, thereby to Discriminate between the Ideas that are in our Under­standings, 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 Hori­zon than in the Me­ridian.

There is a Celebrated Phaeno­menon, the Solution whereof I shall attempt to give, by the Principles that have been laid down, in re­ference 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 un­der which the Diameter of the Moon is seen, be not observ'd greater in the former Case, than [Page 74] in the latter. Moreover, the Ho­rizontal Moon doth not constant­ly appear of the same Bigness, but at some times seemeth far great­er than at others.

LXVIII. The cause of this Phaenome­non, assign­ed.

Now in order to explicate the reason, of the Moon's appearing greater than ordinary in the Ho­rizon; it must be observ'd, that the Particles which compose our Atmosphaere, do intercept the Rays of Light, proceeding from any Ob­ject 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 intercept­ed; and by consequence, the Ap­pearance 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, be­tween the Eye, and the Moon, when situated in the Horizon, there lies [Page 75] a far greater Quantity of Atmo­sphaere, than there does when the Moon is in the Meridian. Whence it comes pass, that the Appearance of the Horizontal Moon is fain­ter, 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 Hori­zontal Moon, why greater at one time than ano­ther.

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 Conse­quence, that Luminary, tho' in the very same Situation, is at one time judged greater than at another.

LXX. The Ac­count we have gi­ven, prov'd to be true.

That we have here given the true Account of the Phaenomena of the Horizontal Moon, will, I sup­pose, [Page 76] be farther Evident to any one from the following Conside­rations. First, 'Tis plain, that which in this Case suggests the Idea of greater Magnitude, must be some­thing which is it self perceiv'd; for, that which is unperceiv'd can­not suggest to our Perception a­ny other thing. Secondly, It must be something that does not con­stantly remain the same, but is subject to some Change or Va­riation, since the Appearance of the Horizontal Moon varies, be­ing 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 Appear­ance is as great as ever. And yet, Fourthly, It cannot be the Vi­sible Figure or Magnitude, since that remains the same, or is ra­ther [Page 77] lesser, by how much the Moon is nearer to the Horizon. It re­mains therefore, that the true Cause is that Affection or Alteration of the Visible Appearance, which pro­ceeds 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 con­firmed, by the Moon's appearing greater in a Mist.

Add to this, that in misty Wea­ther it is a common Observation, that the Appearance of the Hori­zontal Moon is far larger than u­sual, which greatly conspires with, and strengthens our Opinion. Nei­ther wou'd it prove, in the least, Ir­reconcilable 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 [Page 78] the place where we stand; we ought also to take into our Thoughts, the whole Sum of Vapours and Ex­halations, which lie betwixt the Eye and the Moon: All which cooperating to render the Appear­ance of the Moon more Faint, and thereby increase it's Magni­tude, it may chance to appear greater than it usually does, even in the Horizontal Position, at a time when, tho' there be no ex­traordinary 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 Exhalati­ons, 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 Inter­cept a great Part of the Rays of Light, shou'd render the Appear­ance [Page 79] of the Moon in the Meridi­an as large, as when it is viewed in the Horizon. To which I an­swer, 'tis not Faintness any how apply'd, that suggests greater Mag­nitude. There being no necessary, but only an experimental Connexi­on 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 ob­served to attend the Vision of great Magnitudes. When from a Distance (I speak with the Vulgar) we be­hold great Objects, the Particles of the intermediate Air and Va­pours, which are themselves unper­ceivable, do interrupt the Rays of Light, and thereby render the Ap­pearance less Strong and Vivid; now, Faintness of Appearance cau­sed in this Sort, hath been ex­perienced to coexist with great Magnitude. But, when it is cau­sed by the Interposition of an Opa­que, [Page 80] sensible Body, this Circum­stance alters the Case; so that a Faint Appearance this way caused, does not suggest greater Magni­tude, because it hath not been ex­perienced to coexist with it.

LXXIII. The way wherein Faintness suggests greater Magnitude Illustrated.

Faintness, as well as all other Ideas or Perceptions, which sug­gest Magnitude or Distance, does it in the same way, that Words sug­gest the Notions to which they are annexed. Now, it is known, a Word pronounced with certain Circum­stances, 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 dif­ferent Context of Words. This well consider'd may, perhaps, pre­vent some Objections that might otherwise be made, against what we have offer'd as the true Ex­plication of the Appearance of the Horizontal Moon.

LXXIV. Appear­ance of the Horizontal Moon, why thought difficult to explain.

If we attentively consider the Phae­nomenon 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 Ob­ject 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 great­er in one Situation than the o­ther? 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 Ho­rizontal, than when in the Meri­dional Position: And yet it is E­steemed [Page 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 Ho­rizon, than in the Meridian, so nei­ther is it thought to be so. It hath been already shewn, that in any act of Vision, the Visible Ob­ject absolutely, or in it self, is lit­tle 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 Ob­ject. This duly consider'd, it will be no hard matter to reconcile, the seeming Contradiction there is, that the Moon shou'd appear of [Page 83] a different Bigness, the visible Mag­nitude thereof remaining still the same. For by Sect. LVI. the very same visible Extension, with a dif­ferent Faintness, shall suggest a dif­ferent Tangible Extension. When, therefore, the Horizontal Moon is said to appear greater than the Me­ridional Moon; this must be un­derstood, not of a greater Visi­ble Extension, but of a greater Tangible Extension; which, by reason of the more than ordinary Faintness of the Visible Appear­ance, is suggested to the Mind a­long with it.

LXXV. Attempts towards the Soluti­on of it made by several, but in vain.

Many Attempts have been made by Learned Men, to account for this Appearance. Gassendus, Des­cartes, 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. [Page 84] Numb. 187, p. 314. where you may see their several Opinions at large set forth and confuted, not with­out some Surprize at the gross Blunders, that Ingenious Men have been forced into, by endeavour­ing 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 rela­ting to the same Affair, by the Celebrated Dr. Wallis, wherein he pretends to account for that Phae­nomenon; which, tho' it seems not to contain any thing new, or different from what had been said before by others, I shall ne­vertheless consider in this place.

LXXVI. The Opini­on of Dr. Wallis.

His Opinion in short is this. We judge not of the Magni­tude of an Object by the Optic Angle alone, but by the Optic Angle in Conjunction with the [Page 85] Distance, Hence, tho' the An­gle remain the same, or even becomes less; yet if withal the Distance seem to have been in­creas'd, the Object shall appear greater. Now, one way whereby we estimate the Distance of any thing, is by the Number and Ex­tent 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 Di­stance, and consequently magnify the Appearance. And this, accord­ing to Dr. Wallis, is the true Ac­count of the extraordinary Large­ness 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 unsa­tisfactory.

With reference to this Opinion, not to repeat what has been al­ready said concerning Distance, I shall only observe, First, That if the Prospect of interjacent Ob­jects 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 or­dinary. 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 there­by 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 Hori­zon; which Suggestion occasions [Page 87] a sudden Judgment of Sense, that the Moon is farther off, and lar­ger than usual. For ask any Man, who from such a Station behold­ing the Horizontal Moon, shall think her greater than usual, whe­ther he have at that time in his Mind any Idea of the intermedi­ate 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 Judg­ment? He will, without doubt, reply in the Negative, and de­clare the Horizontal Moon shall appear greater than the Meridio­nal, 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 intro­ducing into the Mind another, whilst it self is not perceiv'd, this has already fallen under our Ob­servation, and is too evident to [Page 88] need any farther Enlargement on it. Secondly, It seems impossible by this Hypothesis, to account for the Moon's appearing in the ve­ry 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 Explica­tion from them.

LXXVIII. How Lines and Angles may be of use in com­puting ap­parent Magni­tudes.

This Phaenomenon of the Hori­zontal 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 out­ward Objects. There is, never­theless, 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 immedi­ate [Page 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 Op­tics: That it can hardly be very Precise and Exact, since the Judgments we make of the Mag­nitude of External Things, do often depend on several Circum­stances, which are not Proportio­nal to, or capable of being defin'd by Lines and Angles.

LXXIX. One born Blind, be­ing made to See, what Judgment he'd make of Magni­tude.

From what has been said we may safely deduce this Conse­quence, 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 in­tromitted by them, from what others do. He wou'd not con­sider the Ideas of Sight with re­ference to, or as having any Connexion with the Ideas of [Page 90] Touch. His View of them be­ing intirely terminated within them­selves, he can no otherwise judge them Great or Small, than as they contain a greater or lesser Num­ber 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 e­vident, one in those Circumstan­ces would judge his Thumb, with which he might hide a Tower, or hinder its being seen, e­qual to that Tower, or his Hand, the Interposition whereof might con­ceal the Firmament from his View, equal to the Firmament. How great an Inequality soever there may, in our Apprehensions, seem [Page 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 Pre­judice, we cannot totally extricate our selves, without some Labour and Striving of Thought.

LXXX. The Mini­mum Vi­sibile the same to all Creatures.

For the better clearing up the Nature of Vision, and setting the manner wherein we perceive Mag­nitudes in a due Light, I shall proceed to make some Observa­tions concerning Matters relating thereto, whereof the want of Re­flexion, and duly separating be­tween Tangible and Visible Ideas, is apt to create in us mistaken and confused Notions. And, First, I shall observe that the Minimum [Page 92] Visibile is exactly equal in all Be­ings whatsoever, that are endow'd with the Visive Faculty. No ex­quisite Formation of the Eye, no peculiar Sharpness of Sight, can make it less in one Creature, than in another. For it not be­ing 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 Detracti­on of some part be made equal to the former: It doth, therefore, con­sist of Parts: Which is inconsistent with the Notion of a Minimum Visi­bile, 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 [Page 93] perceivable by the Man. To which I answer, the Minimum Vi­sibile having (in like manner as all other the Proper and Imme­diate Objects of Sight) been shewn not to have any Existence with­out the Mind of him who sees it, it follows, there cannot be any part of it that is not actu­ally perceiv'd, and therefore Visi­ble. Now, for any Object to con­tain 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 bound­ed 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 [Page 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 Pros­pect of the circumjacent Fields, Mountains, Sea, and open Firma­ment. 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 o­ther corresponding Point: It fol­lows, 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 Pro­spect is intercepted by them. Whenever, therefore, we are said to have a greater Prospect at one [Page 95] time than another; this must be understood with relation, not to the proper and immediate, but the secondary and mediate Ob­jects of Vision, which, as hath been shewn, do properly belong to the Touch.

LXXXIII Two Im­perfections in the Vi­sive Fa­culty.

The Visive Faculty consider'd, with reference to it's immediate Objects, may be found to La­bour of two Defects. First, In respect of the Extent or Number of visible Points that are at once perceivable by it, which is nar­row and limited to a certain De­gree. It can take in at one View but a certain, determinate Num­ber of Minima Visibilia, beyond which it cannot extend it's Pro­spect. Secondly, Our Sight is de­fective 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 [Page 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 Per­fections.

Corresponding to these two De­fects of Sight, we may imagine as many Perfections, viz. 1 st. That of comprehending in one View, a greater number of Visible Points. 2 dly, Of being able to View them all equally, and at once, with the utmost Clearness and Distinction. That these Perfections are not actu­ally 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 nei­ther see more Visible Points, nor are the Collateral Points more Di­stinct, [Page 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 dif­ferent from what we behold with the naked Eye. But herein con­sists the most remarkable Difference, viz. That whereas the Objects per­ceived 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 di­stant Objects to the Parts of our own Body, which much condu­ceth 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 Microscopi­cal Eyes, consider'd.

Hence it's evident, that were our Eyes turned into the Nature of Mi­croscopes, we shou'd not be much [Page 98] benefited by the Change. We shou'd be depriv'd of the fore­mention'd Advantage we at pre­sent 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 Pene­tration than it now hath. But I wou'd fain know wherein con­sists that Sharpness, which is e­steem'd so great an Excellency of Sight. It is certain from what we have already shewn, that the Mi­nimum Visibile is never Greater, or Lesser, but in all Cases constant­ly 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 Per­ceptions of Sight and Touch, which before enabled us to regulate our Actions by the Eye: It wou'd [Page 99] now be render'd utterly unservi­ceable to that Purpose. Which whether it be a desirable Perfecti­on, 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 Con­veniency of Life.

LXXXVIII Difficulty concerning Erect Vi­sion.

Having finish'd what I intend­ed to say, concerning the Distance and Magnitude of Objects, I come now to treat of the Manner, where­in the Mind perceives by Sight their Situation. Among the Discoveries of the last Age, it is reputed none of the [Page 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 Ob­jects are Painted on the Retina, or Fund of the Eye. That we can see no thing which is not so Paint­ed. And that, according as the Picture is more Distinct or Con­fused, 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 be­ing 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 in­verted, it is demanded how it comes to pass, that we see the Ob­jects erect and in their natural Posture?

LXXXIX The com­mon 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, con­siders this Ray as coming in a direct Line, from the lower part of the Object; and in like man­ner 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 Fi­gure, C the lower Point of the Object ABC is projected on c the upper part of the Eye. So like­wise,

the highest Point A is pro­jected on a the lowest part of the Eye; which makes the Repre­sentation cba inverted. But the Mind considering the Stroak that is made on c as coming in the [Page 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 Situa­tion of the Object ABC, notwith­standing the Picture of it be in­verted. Moreover, this is illustra­ted 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 perpen­dicular 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 Ob­ject, 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, [Page 103] Dioptr. par. 2. c. 7. p. 289.) allow­ed by all Men as Satisfactory.

XC. The same shewn to be false.

But how reasonable and satis­factory soever, this account may be thought by others, to me cer­tainly it does not seem, in any degree, True. Did I perceive those Impulses, Decussations, and Directi­ons 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 Pro­bability. 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 Esti­mate of the Situation of Objects. Moreover I appeal to any one's Experience, whether he be consci­ous to himself, that he thinks on the Intersection made by the Ra­dious Pencils, or pursue the Im­pulses [Page 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 ne­ver thought on by Children, Idi­ots, or in Truth by any other, save only those who have apply­ed themselves to the Study of Op­tics. And for the Mind to judge of the Situation of Objects, by those things, without perceiving them, or to perceive them with­out knowing it, take which you please, 'tis Perfectly beyond my Comprehension. Add to this, that the explaining the manner of Vi­sion 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 Di­stance from us, contrary to what hath been Demonstrated. We may therefore, venture to pronounce this Opinion concerning the way where­in [Page 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 distin­guishing between I­deas of Sight and Touch, Cause of Mistake, in this Mat­ter.

It remains, therefore, that we look for some other Explication of this Difficulty. And I believe it not impossible to find one, pro­vided we Examine it to the Bot­tom, and carefully distinguish be­tween the Ideas of Sight and Touch; which cannot be too oft incul­cated in treating of Vision. But more especially throughout the con­sideration 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, pro­per 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 ta­king 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 famili­ar to us, to divest our selves in­tirely 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, en­deavour to frame true Concepti­ons, of what might reasonably be supposed to pass in his Mind.

XCIII. Such a one might by Touch, at­tain to have Ideas of Upper and Low­er.

It is certain, that a Man actu­ally Blind, and who had conti­nued so from his Birth, wou'd by the Sense of Feeling attain to have Ideas of Upper and Lower. By [Page 107] the Motion of his Hand he might discern the Situation of any Tangi­ble Object placed within his Reach. That part on which he felt him­self supported, or towards which he perceiv'd his Body to gravitate, he wou'd term Lower, and the con­trary to this Upper. And accor­dingly denominate whatsoever Ob­jects he touch'd.

XCIV. Which Modes of Situation he'd attri­bute only to things Tangible.

But then, whatever Judgments he makes concerning the Situati­on of Objects, are confin'd to those only that are perceivable by Touch. All those things that are intangi­ble, and of a spiritual Nature, his Thoughts and Desires, his Passi­ons, and in general all the Mo­difications 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 Sig­nification, [Page 108] wou'd never be apply­ed to any thing, that was not conceiv'd to exist without the Mind. For a Man Born Blind, and re­maining in the same State, cou'd mean nothing else by the Words Higher and Lower, than a great­er or lesser Distance from the Earth: Which Distance he wou'd measure by the Motion or Appli­cation of his Hand, or some o­ther Part of his Body. It is, there­fore, 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, E­rect or In­verted.

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 In­verted; for it hath been already Demonstrated in Sect. XLI, that [Page 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 ap­ply the Terms Up and Down, High and Low, were such only as affect­ed, or were some way perceiv'd by his Touch. But the proper Objects of Vision make a new Set of Ideas, perfectly distinct and dif­ferent from the former, and which can in no sort make themselves perceiv'd by Touch. There is, there­fore, nothing at all that cou'd in­duce 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 Illus­trated by an Exam­ple.

To set this Matter in a clearer Light, I shall make use of an Ex­ample. Suppose the above-men­tioned Blind Person do, by his Touch, perceive a Man to stand Erect. Let us enquire into the manner of this. By the applica­tion 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 Com­bination of a certain Tangible Fi­gure, Bulk, and Consistency of Parts is called the Head, another the Hand, a Third the Foot, and so of the rest. All which Com­plex Ideas cou'd, in his Understand­ing, be made up only of Ideas perceivable by Touch. He had al­so by his Touch obtain'd an Idea of Earth or Ground, towards which he perceives the Parts of his Bo­dy to have a natural Tendency. [Page 111] Now, by Erect nothing more be­ing meant, than that perpendicu­lar 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 de­nominate that Man Erect. But if we suppose him on a sudden to re­ceive 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 per­ceived as existing without, he cou'd [Page 112] not know that in propriety of Lan­guage, they were applicable to it.

XCVII. By what means he'd come to de­nominate Visible Ob­jects high or low, &c.

Afterwards, when upon turning his Head or Eyes, up and down, to the right and left, he shall ob­serve the Visible Objects to change, and shall also attain to know, that they are call'd by the same Names, and Connected with the Ob­jects 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 ver­sa.

And this seems to me the true Reason, why he shou'd think those Objects uppermost that are Pain­ted on the lower part of his Eye. For, by turning the Eye up they shall be distinctly seen; as likewise, [Page 113] they that are Painted on the high­est part of the Eye shall be di­stinctly seen, by turning the Eye down, and are for that Reason e­steemed 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 ac­count 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 Rea­son, why the Mind shou'd deno­minate the Objects of Sight ac­cordingly High or Low. And with­out this Motion of the Eye, this turning it up and down in or­der 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 [Page 114] act of Seeing including nothing in it to that Purpose, whereas the different Situations of the Eye, na­turally direct the Mind to make a suitable Judgement, of the Si­tuation of Objects intromitted by it.

XCIX. How he wou'd per­ceive by Sight the Situation of Exter­nal Objects.

Farther, when he has by Experi­ence 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 Si­tuation of Visible Things in re­spect 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 propen­sion to think the contrary, no Argu­ment a­gainst 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. [Page 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 suffici­ently of the Matter, might have of their being able to determine by the Eye, at first view, whe­ther Objects were Erect or Inverse.

CI. Objection.

It will, perhaps, be objected to our Opinion, that a Man, for in­stance, 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 alter­ing the Situation of the Eye, we shou'd have determined whether he were Erect or Inverted. For [Page 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 pos­sible, by virtue of the Visive Fa­culty alone, without super-adding any Experience of Touch, or al­tering the Position of the Eye, e­ver 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, whe­ther [Page 117] the Head or Feet were near­est 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 be­tween the Ideas of both Senses.

CIII. An Object cou'd not be known at first Sight by the Co­lour.

That which I see is only varie­ty 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 combina­tions 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. [Page 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 Con­nexion, between any given Visi­ble Magnitude, and any one par­ticular Tangible Magnitude. But that it is intirely the result of Custom and Experience, and de­pends on foreign and accidental Circumstances, that we can by the Perception of Visible Extensi­on inform our selves, what may be the Extension of any Tangible Object connected therewith. Hence, [Page 119] 'tis certain that neither the Visi­ble Magnitude of Head or Foot, wou'd bring along with them in­to 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 Con­nexion with the Tangible Figure thereof, so as at first Sight to sug­gest it to the Mind. For Figure is the Termination of Magnitude. Whence it follows, that no Vi­sible 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 [Page 120] to the Touch, may to Sight, if view'd thro' a Microscope, seem quite otherwise.

CVI. In the first act of Visi­on, no Tan­gible Thing wou'd be suggested by Sight.

From all which laid together, and duly consider'd, we may clear­ly deduce this Inference, viz. In the first act of Vision, no Idea entering by the Eye, wou'd have a perceivable Connexion with the I­deas to which the Names Earth, Man, Head, Foot, &c. were annex­ed, in the Understanding of a Per­son Blind from his Birth: So as in any sort to introduce them in­to 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 per­haps, 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, [Page 121] Size, nor Figure of the Visible Feet, have any necessary Connexion with the Ideas that compose the Tangi­ble 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 Con­nexion. Yet thus much seems un­deniable. Namely, that the Num­ber of the Visible Feet, being the same with that of the Tangible Feet: I may from hence, without any Ex­perience of Sight, reasonably con­clude that they represent, or are connected with the Feet rather than the Head. I say, it seems the I­dea of Two Visible Feet will soon­er suggest to the Mind, the Idea of Two Tangible Feet than of one Head. So that the Blind Man up­on first reception of the Visive Fa­culty might know, which were the Feet or Two, and which, the Head or One.

CVIII. Number of things Vi­sible, wou'd not, at first Sight, sug­gest the like number of things Tan­gible.

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, cor­responding to them. A Picture Painted with great variety of Co­lours, 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 num­ber of things Tangible, from the number of things Visible. I shou'd not therefore at first open­ing my Eyes conclude, that be­cause I see Two, I shall feel Two. How therefore can I, before Ex­perience 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 he­terogeneous [Page 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 Crea­ture of the Mind.

But for a fuller Illustration of this Matter, it ought to be con­sider'd, that Number (however some may reckon it amongst the Prima­ry Qualities) is nothing fix'd, and settled, really existing in things them­selves. It is intirely the Creature of the Mind, considering, either a Simple Idea by it self, or any Com­bination 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 [Page 124] in which there are many Win­dows, and many Chimneys, has an equal right to be called one. And many Houses go to the ma­king of one City. In these and the like Instances, it's evident the Unite constantly relates to the particu­lar 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 there­of, is mark'd by one Name. Now, this Naming and Combining to­gether of Ideas is perfectly Arbi­trary, 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, num­ber 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, par­cel 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 toge­ther 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 [Page 126] Combinations: till such time, as by observing the Motion of the Parts of the Man, and other Ex­periences he comes to know, which are to be separated, and which to be collected together.

CXI. The Situa­tion of any Object, de­termin'd with re­spect 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 Ob­jects of either Kind, we indiffe­rently attribute the Terms High and Low, Right and Left, and such like, denoting the Position or Si­tuation of things. But then we must well observe, that the Po­sition 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, accor­ding as it is more or less di­stant from the Tangible Earth. And in like manner, we denomi­nate any Object of Sight High or [Page 127] Low, in proportion as it is more or less Distant, from the Visible Earth. But to define the Situa­tion of Visible Things, with rela­tion to the Distance they bear from any Tangible Thing, or vi­ce versa: This were absurd and perfectly unintelligible. For all Vi­sible Things are equally in the Mind, and take up no part of the Exter­nal Space: And, consequently, are Equidistant from any Tangi­ble Thing which exists without the Mind.

CXII. No Di­stance great or small, between a Visible and Tangible Thing.

Or rather, to speak truly, the pro­per Objects of Sight are at no Di­stance, 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 re­spect of Distance, which exist af­ter the same manner, or apper­tain unto the same Sense. For by the Distance between any Two [Page 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 per­ceivable by Sight, nor by Touch, i. e. it is utterly inconceivable. This, perhaps, will not find an easy Admission into all Men's Un­derstandings: However, I shou'd gladly be informed whether it be not True, by any one who will be at the pains to Reflect a lit­tle, and apply it home to his Thoughts.

CXII. The not ob­serving this, cause of difficul­ty in Erect Vision,

The not observing what has been deliver'd in the two last Sections, seems to have occasion'd no small [Page 129] part of the Difficulty that occurs in the Business of Erect Appear­ances. The Head, which is Paint­ed nearest the Earth, seems to be farthest from it; and on the o­ther Hand, the Feet, which are Painted farthest from the Earth, are thought nearest to it. Here­in lies the Difficulty, which va­nishes if we express the thing more clearly, and free from Ambigui­ty, 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 Sup­position, that the Eye or Visive Fa­culty, or rather the Soul by means thereof, shou'd judge of the Situ­ation of Visible Objects, with Re­ference to their Distance from the Tangible Earth? Whereas it's e­vident, [Page 130] the Tangible Earth is not perceiv'd by Sight: And it hath been shewn in the two last pre­ceding 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 o­therwise includes nothing un­accounta­ble.

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 Pic­tures 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 [Page 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 in­verted.

But, say you, the Picture of the Man is inverted, and yet the Ap­pearance 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 un­dermost, you mean that it is near­est to the Earth; and by the Heels being uppermost, that they are farthest from the Earth. I ask a­gain, what Earth you mean? You cannot mean the Earth that is Painted on the Eye, or the Vi­sible Earth. For the Picture of the Head is farthest from the Pic­ture of the Earth; and the Pic­ture of the Feet nearest to the Pic­ture [Page 132] of the Earth; and accordingly, the Visible Head is farthest from the Visible Earth, and the Visible Feet, nearest to it. It remains, there­fore, that you mean the Tangible Earth: And so determine the Si­tuation of Visible Things, with re­spect to Tangible Things; contra­ry to what hath been demonstra­ted 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 Rela­tion to one another, in point of Distance or Position.

CXVI. Cause of Mistake in this Mat­ter.

Farther, What greatly contributes to make us mistake in this Mat­ter 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 a­nother looking on the Fund of our own Eye, and beholding the Pictures Painted thereon. Suppose [Page 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 in­verted in B. But this is wrong. There are projected in little on the Bot­tom 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 lar­ger Images are deemed the true Objects, and the lesser only Pict­ures in miniature. And it is with respect to those greater Images, that it determines the Situation of the smaller Images. So that com­paring the little Man with the great Earth, A judges him inver­ted, or that the Feet are farthest from, and the Head nearest to the great Earth. Whereas, if A compare the little Man with the [Page 134] little Earth, then he will appear Erect, i. e. his Head shall seem far­thest 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 Re­presentation 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 them­selves, 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 be­tween the Ideas of Sight, and things Tangible. It hath likewise been de­monstrated, 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 Disposi­tion of Colours, which constitute the Visible Man, or Picture of a Man, and that other Combinati­on of far different Ideas, sensible by Touch, which compose the Tan­gible Man. But if this be the Case, how come they to be ac­counted Pictures or Images, since [Page 136] that supposes them to copy or represent some Originals or o­ther?

CXVIII. In what Sense they are Pictures

To which I answer. In the foremention'd Instance, the Eye A takes the little Images, inclu­ded within the Representation of the other Eye B, to be Pictures or Copies, whereof the Archetypes are not things existing with­out but, the larger Pictures pro­jected on it's own Fund: And which by A are not thought Pic­tures, 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 project­ed thereon shall, to C, seem Pic­tures or Images, in the same Sense that those projected on B do to A.

CXIX. In this Af­fair we must care­fully di­stinguish between Ideas of Sight and Touch.

Rightly to conceive the Busi­ness in hand, we must carefully distinguish between the Ideas of [Page 137] Sight and Touch, between the Vi­sible and Tangible Eye, for cer­tainly on the Tangible Eye, no­thing either is or seems to be Painted. Again, the Visible Eye, as well as all other Visible Ob­jects, hath been shewn to exist only in the Mind, which perceiv­ing its own Ideas, and compa­ring them together, doth call some Pictures in respect of others. What hath been said being rightly com­prehended and laid together, does, I think, afford a full and genu­ine Explication of the Erect Ap­pearance of Objects, which Phaeno­menon, 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 The­ory of Vi­sion.

In treating of these things, the use of Language is apt to occa­sion some Obscurity and Confu­sion, and create in us wrong Ideas. For Language being accomodated [Page 138] to the common Notions and Prejudices of Men, it is scarce possible to deliver the naked and precise Truth, without great Cir­cumlocution, Impropriety, and (to an unwary Reader) seeming Con­tradictions. 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 Ex­pression; 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 Que­stion, whe­ther there is any Idea common to Sight and Touch, stated.

We have shewn the way where­in the Mind by Mediation of Visible Ideas, doth perceive or apprehend the Distance, Magnitude [Page 139] and Situation of Tangible Ob­jects. 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 com­mon 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 numeri­cal 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 ne­vertheless different, and have an Existence very distinct and Sepa­rate from them. So that the Que­stion is not now concerning the same numerical Ideas, but whether there be any one and the same sort or Species of Ideas equally [Page 140] perceivable to both Senses? Or, in other Words, whether Exten­sion, Figure, and Motion perceiv'd by Sight, are not specifically di­stinct from Extension, Figure and Motion perceived by Touch.

CXXII. Abstract Extension enquir'd into.

But, before I come more par­ticularly 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 Extensi­on from all other Tangible and Visible Qualities, and frame there­of an Abstract Idea, which Idea they will have common both to Sight and Touch. We are there­fore to understand by Extension in Abstract, an Idea of Extensi­on, v. g. a Line or Surface, in­tirely stript of all other sensible [Page 141] Qualities and Circumstances that might determine it to any particular Existence. It is neither Black, nor White, nor Red, nor hath it a­ny Colour at all, or any Tan­gible 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 incom­prehensible.

Now I do not find that I can perceive, imagine, or any wise frame in my Mind such an ab­stract Idea, as is here spoken of. A Line, or Surface which is nei­ther 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 Ob­ject of Geo­metry.

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 conse­quently is not the Object of Geo­metry. I know it is a Tenent as well of the Modern as the An­cient Philosophers, that all gene­ral Truths are concerning Uni­versal, Abstract Ideas, without which, we are told, there cou'd be no Science, no Demonstrati­on 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 Demonstra­tions in Geometry might be Uni­versal, tho' they who make 'em, [Page 143] never think of Abstract general I­deas of Triangles or Circles.

CXV. The gene­ral Idea of a Triangle, consider'd.

After reiterated Efforts and pangs of Thought, in order to appre­hend the general Idea of v. g. a Triangle, I have found it alto­gether incomprehensible. And sure­ly 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 Un­derstanding: He, who has so far distinguish'd himself from the ge­nerality of Writers, by the Clear­ness and Significancy of what he Says. Let us therefore see how that great Man describes the ge­neral, or, which is the same thing, the Abstract Idea of a Triangle. ‘It must be, ( says he) neither Ob­lique, nor Rectangle, neither E­quilateral, Equicrural, nor Sca­lenon; but all and none of these at once. In effect it is some­what imperfect that cannot exist; [Page 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 ne­ver 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 ‘re­quire some Pains and Skill to Form this general Idea of a Tri­angle,’ 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 con­ceiv'd, [Page 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 ma­nifest, 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 never­theless talk at this rate, seems very surprising. But my Wonder is les­sen'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 Scien­ces. But this Matter, taken in its full Extent, were a Subject too vast and comprehensive to be in­sisted on in this place. I shall on­ly observe that your Metaphysici­ans, [Page 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 perempto­rily declare them to be the Subject, of all the Eternal, Immutable, Uni­versal Truths, in Geometry. And so much for Extension in Abstract.

CXXVI. Vacuum or pure Space, not com­mon to Sight and Touch.

Some, perhaps, may think pure Space, Vacuum, or Trine Dimen­sion 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 Demonstra­ted to be a meer Delusion, ari­sing from the quick and sudden Suggestion of Fancy, which so closely Connects the Idea of Di­stance with those of Sight, that we are apt to think it is it self [Page 147] a proper and immediate Object of that Sense, till Reason corrects the Mistake.

CXXVII. There is no Idea or kind of I­dea, com­mon 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 se­parate 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 ven­ture to lay down the following Proposition, viz. The Extension, Fi­gures, 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 [Page 148] both Senses. This Proposition may, without much Difficulty, be col­lected from what hath been said in several Places of this Essay. But, because it seems so remote from, and contrary to, the receiv'd No­tions and settled Opinion of Man­kind; I shall attempt to demon­strate it more particularly, and at large, by the following Arguments.

CXXVIII. First Ar­gument in Proof here­of.

First, When upon Perception of an Idea, I range it under this or that sort; it is because it's per­ceiv'd after the same manner, or because it has a Likeness or Con­formity 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 com­mon with the Ideas I have before known and nam'd, as to make me give it the same Name with them. [Page 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 Re­flexion.

CXXIX. Second Ar­gument.

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 there­fore a direct Consequence, that there is no Idea common to both Senses.

CXXX. Visible Fi­gure and Extension, not distinct Ideas from Colour.

It is, I know, a prevailing O­pinion, even amongst those who have Thought and Writ most Ac­curately concerning our Ideas, and the Ways whereby they enter in­to the Understanding, that some­thing 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 I­deas [Page 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 I­dea 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, ex­clusive of all Colour; and on the other hand, whether he can conceive Colour without Visible Extension. For my own part, I must con­fess, I am not able to attain so great a nicety of Abstraction. I know very well that, in a strict [Page 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 de­gree more perfect and compre­hensive than I can pretend to. I own indeed, that by the media­tion 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 Com­prehensive than the Hearing: Which beside Sounds, which are pecu­liar 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 Ar­gument.

Thirdly, It is, I think, an Axi­om universally receiv'd, that Quan­tities of the same Kind may be ad­ded together, and make one intire [Page 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 Sur­face. These three Kinds of Quan­tity being thought incapable of any such mutual Addition, and consequently of being compa­red together, in the several ways of Proportion, are by them, for that reason, esteem'd intirely Dis­parate 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 Heterogene­ous. I acknowledge my self to be of the latter Sort. A Blue, and and a Red Line I can conceive ad­ded together into one Sum, and making one continu'd Line; but [Page 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 particu­lar Person, to determine for him­self.

CXXXII. Confirma­tion drawn from Mr. Moly­neux'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 Pro­blem, 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. ‘ Sup­pose a Man Born Blind, and now Adult, and taught by his Touch to di­stinguish between a Cube, and a Sphere of the same Metal, and nighly of the same Bigness, so as to tell, when he felt one and t'other, which is the Cube, and which the Sphere. Sup­pose then the Cube and Sphere pla­ced on a Table, and the Blind Man [Page 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 attain­ed the Experience, that what af­fects his Touch so or so, must affect his Sight so or so: Or that a pro­tuberant Angle in the Cube, that pressed his Hand unequally, shall appear to his Eye, as it doth in the Cube. I agree with this think­ing Gentleman, whom I am proud to call my Friend, in his Answer to this his Problem; and am of opinion, that the Blind Man, at first Sight, would not be able with certainty to say, which was the Globe, which the Cube, whilst he only saw them.’ Essay on Hu­man Understand. b. ii. c. 9. s. 8.

CXXXIII. Which is falsly sol­ved, if the common Supposition be true.

Now, if a Square Surface per­ceiv'd by Touch be of the same Sort, with a Square Surface percei­ved 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 Surfa­ces: Upon the Supposition that a Visible and Tangible Square dif­fer 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 Tangi­ble [Page 157] Extension and Figures, or else, that the Solution of this Problem, given by those two very thought­ful and ingenious Men, is wrong.

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

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

CXXXV. Farther Reflexion, on the fore­going Pro­blem.

I cannot let go the above-men­tion'd Problem, without some Re­flexion 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. [Page 158] vid. Sect. CVI. Cube, Sphere, Table, are Words he has known applied to Things perceivable by Touch, but to Things perfectly Intangi­ble he never knew them apply'd. Those Words, in their wonted ap­plication, always mark'd out to his Mind Bodies, or Solid Things which were perceiv'd by the Re­sistance they gave. But there is no Solidity, no Resistance or Pro­trusion 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 sug­gest 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 be­ing, beside this Manner or Circum­stance, 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 Mo­tion not common to Sight and Touch.

Visible Figure and Extension ha­ving been demonstrated, to be of a Nature intirely Different and He­terogeneous, from Tangible Fi­gure 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, [Page 150] it being an evident Corollary from what we have shewn, concerning the Difference there is betwixt Vi­sible and Tangible Extension. But for a more full and express Proof hereof, we need only observe, that one who had not yet experien­ced Vision, wou'd not, at first Sight, know Motion. Whence it clear­ly follows, that Motion perceiva­ble by Sight is of a Sort distinct from Motion perceivable by Touch. The Antecedent I prove thus. By Touch he cou'd not perceive a­ny Motion, but what was up or down, to the right or left, near­er or farther from him; besides these, and their several Varieties or Complications, it's impossible he shou'd have any Idea of Motion. He wou'd not therefore think a­ny 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 [Page 161] plain that by the meer act of Visi­on, he cou'd not know Motion upwards or downwards, to the right or left, or in any other pos­sible Direction. From which I con­clude, he'd not know Motion at all at first Sight. As for the I­dea of Motion in Abstract, I shall not waste Paper about it, but leave it to my Reader, to make the best he can on't. To me 'tis perfect­ly Unintelligible.

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

The Consideration of Motion, may furnish a new Field for In­quiry. But since the manner where­in the Mind apprehends by Sight, the Motion of Tangible Objects, with the various Degrees thereof, may be easily collected, from what has been said concerning the man­ner, wherein that Sense doth sug­gest their various Distances, Mag­nitudes, and Situations; I shall not enlarge any farther on this Sub­ject: But proceed to enquire what [Page 150] [...] [Page 161] [...] [Page 162] may be alleg'd, with greatest ap­pearance of Reason, against the Proposition we have Demonstra­ted to be true. For where there is so much Prejudice to be en­counter'd, a bare and naked De­monstration of the Truth will scarce suffice. We must also, satisfie the Scruples that Men may Start, in favour of their preconceiv'd No­tions, shew whence the Mistake arises, how it came to spread, and carefully disclose and root out those false Perswasions, that an early Pre­judice 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 de­manded, how Visible Extension and Figures come to be call'd by the same Name, with Tangible Ex­tension and Figures, if they are not of the same Kind with them? It must be something more than Humour or Accident, that cou'd occasion a Custom so constant and uni­versal [Page 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 ac­counted 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 Let­ters, 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 be­ing regarded in their own Nature, or otherwise than as they are marks of Things, it had been superflu­ous, and beside the design of Lan­guage, to have given them Names distinct from those of the Things marked by them. The same Rea­son [Page 164] holds here also. Visible Fi­gures are the marks of Tangible Figures, and from Sect. LIX, it is plain, that in themselves they are lit­tle regarded, or upon any other Score than for their Connexion with Tan­gible Figures, which by Nature they are 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 re­spective Tangible Figures suggest­ed 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 Cir­cle.

But say you, surely a Tangible Square is liker to a Visible Square than to a Visible Circle: It has four Angles, and as many Sides; so also has the Visible Square, but the Visible Circle has no such thing, being bounded by one uniform Curve, without right Lines or An­gles; [Page 165] which makes it unfit to represent the Tangible Square, but very fit to represent the Tan­gible Circle. Whence it clearly follows, that Visible Figures are Patterns of, or of the same Spe­cies with, the respective Tangible Figures represented by them; that they are like unto them, and of their own Nature fitted to re­present them as being of the same sort; and that they are in no respect arbitrary Signs, as Words.

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

I Answer it must be acknow­ledg'd, the Visible Square is fit­ter than the Visible Circle to re­present 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 [Page 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 ne­cessary, that the Visible Figure which shall be most proper to mark it, contain four distinct, equal Parts corresponding to the four Sides of the Tangible Square; as like­wise four other distinct and equal Parts, whereby to denote the four equal Angles of the Tangible Square. And accordingly we see the Vi­sible Figures contain in them di­stinct Visible Parts answering to the distinct Tangible Parts of the Figures signify'd, or suggested by them.

CXLIII. But it doth not hence follow, that a Visible Square is like a Tan­gible Square.

But it will not hence follow, that any Visible Figure is like un­to, or of the same Species with, its corresponding Tangible Figure, unless it be also shewn, that not only the Number, but also the Kind of the Parts be the same in both. [Page 167] To Illustrate this, I observe that Visible Figures represent Tangible Figures, much after the same man­ner that written Words do Sounds. Now, in this respect, Words are not Arbitrary, it not being indif­ferent, what written Word stands for any Sound. But it is requi­site, that each Word contain in it 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 di­stinct Characters, thereby to mark each particular Difference or Part of the whole Sound. And yet [Page 168] no Body, I presume, will say, the single Letter a or the Word A­dultery are like unto, or of the same Species with, the respective Sounds by them Represented. It is indeed Arbitrary that, in ge­neral, Letters of any Language represent Sounds at all; but when that is once agreed, it is not Ar­bitrary what Combination of Let­ters shall represent this or that par­ticular Sound. I leave this with the Reader to pursue, and ap­ply it in his own Thoughts.

CXLIV. Why we are more apt to confound Visible with Tan­gible I­deas, than other Signs with the Things sig­nify'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 Con­nexion with Tangible Ideas has been [Page 169] learnt, at our first Entrance into the World, and ever since, almost eve­ry Moment of our Lives, it has been occurring to our Thoughts, and fastening and striking deeper on our Minds. When we observe that Signs are variable and of Hu­man Institution, when we re­member, there was a time they were not connected in our Minds, with those things they now so readily suggest; but, that their Signification was learned by the slow Steps of Experience. This preserves us from confounding them. But, when we find the same Signs suggest the same Things all over the World; when we know they are not of Human Institution, and cannot remember that we ever learn'd their Signifi­cation; 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 [Page 170] Things respectively represented by them, and that is by a natural Re­semblance they suggest them to our Minds.

CXLV. Several o­ther Rea­sons hereof, assign'd.

Add to this, that whenever we make a nice Survey of any Ob­ject, successively directing the Op­tic Axis to each Point thereof; there are certain Lines and Fi­gures 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 be­side the Touch. Sounds, for Ex­ample, 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 [Page 171] time great variety of Visible Ob­jects, very separate and distinct from each other. Now Tangible Extension being made up, of se­veral distinct coexistent parts, we may hence gather another Reason, that may dispose us to imagine a Likeness, or 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 Tan­gible Figures are suggested by them. So swift, and sudden, and unper­ceiv'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 reject­ing any O­pinion, no Argument of its Truth.

The Prejudice which is ground­ed on these, and whatever other Causes may be assign'd thereof, [Page 172] sticks so fast on our Understand­ings, 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, Magni­tude, 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 Ob­jects of Vi­sion, the Language of Nature.

Upon the whole, I think we may fairly conclude, that the pro­per Objects of Vision constitute the Universal Language of Nature, whereby we are instructed how to regulate our Actions, in or­der to attain those things, that are necessary to the Preservation and Well-being of our Bodies, as [Page 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 sig­nify, and mark out unto us the Objects which are at a distance, is the same with that of Lan­guages and Signs of Human Ap­pointment; which do not sug­gest the things signify'd, by any Likeness or Identity of Nature, but only by an Habitual Con­nexion, that Experience has made us to observe between 'em.

CXLVIII In it there is much ad­mirable, and deser­ving our attention.

Suppose one who had always continu'd Blind, be told by his Guide, that after he has advan­ced so many Steps, he shall come to the Brink of a Precipice, or be stopt by a Wall; must not this to him seem very admirable and surprizing? He can't con­ceive how 'tis possible for Mor­tals, [Page 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' Fami­liarity make it less observ'd) find therein sufficient Cause of Admi­ration. The wonderful Art and Contrivance wherewith it is ad­justed, to those Ends and Purpo­ses for which it was apparently design'd, the vast Extent, Num­ber, and Variety of Objects that are, at once, with so much Ease, and Quickness, and Pleasure, sug­gested by it: All these afford Subject for much and pleasing Speculation; and may, if any thing, give us some Glimmer­ing, Analogous, Praenotion of Things, that are placed beyond the certain Discovery, and Com­prehension of our present State.

CXLIX. Question propos'd, concerning the Object of Geome­try.

I do not design to trouble my self much with drawing Corollaries, from the Doctrine I have hither­to laid down. If it bears the Test, others may, so far as they shall think convenient, employ their Thoughts in extending it farther, and applying it to whate­ver Purposes it may be subser­vient to. Only, I cannot forbear making some Inquiry concerning the Object of Geometry, which the Subject we have been upon 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 Heteroge­neous 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 Visi­ble Exten­sion the Ob­ject of Geo­metry.

Some things there are which, at first sight, incline one to think [Page 176] Geometry conversant about Visi­ble Extension. The constant use of the Eyes, both in the Practi­cal and Speculative Parts of that Science, doth very much induce us thereto. It would, without doubt, seem odd to a Mathema­tician, to go about to convince him, the Diagrams he saw upon Paper were not the Figures, or even the Likeness of the Figures, which make the Subject of the Demonstration. The contrary be­ing held an unquestionable Truth, not only by Mathematicians, but also by those who apply them­selves more particularly to the Study of Logick; I mean, who consider the Nature of Science, Certainty, and Demonstration: It being by them assign'd as one Reason, of the extraordinary Clear­ness and Evidence of Geometry, that in that Science the Reason­ings are free from those Incon­veniences, which attend the use of [Page 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 Demon­stration, I leave to be consi­der'd.

CLI. Visible Ex­tension shewn not to be the Ob­ject of Geo­metry.

To come to a Resolution in this Point, we need only ob­serve 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 Great­ness; and that Men measure al­together, by the Application of Tangible Extension to Tangible Extension. All which makes it evident, that Visible Extension and Figures are not the Object of Geo­metry.

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

It is, therefore, plain that Vi­sible Figures are of the same Use in Geometry, that Words are. And the one may as well be ac­counted the Object of that Science, as the other; neither of them being any otherwise concern'd therein, than as they represent or suggest to the Mind the particu­lar Tangible Figures connected with them. There is, indeed, this Difference betwixt the Significa­tion of Tangible Figures by Vi­sible Figures, and of Ideas by Words. That whereas the Latter is variable and uncertain, depend­ing altogether on the Arbitrary Appointment of Men; the For­mer is 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 [Page 179] speaks to our Eyes, is not liable to that Misinterpretation and Am­biguity, that Languages of Hu­man Contrivance are unavoidably subjected to. From which may, in some measure, be derived that peculiar Evidence and Clearness of Geometrical Demonstrations.

CLIII. It is pro­pos'd to en­quire, 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 ne­vertheless, for the fuller Illustra­tion thereof, take into my Thoughts the Case of an Intelligence, or Unbody'd Spirit, which is sup­pos'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 con­tains no Contradiction in it. Let [Page 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 Sci­ence.

CLIV. He cannot understand those parts which re­late to So­lids, and their Sur­faces and Lines ge­nerated by their Secti­on.

First, then 'tis certain, the a­foresaid 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 demon­strated to be the Effect of the Experience we have had, what I­deas of Touch are connected with such and such Ideas attending Vi­sion. But the Intelligence here [Page 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 con­sequently of Space or Body, ei­ther immediately or by Suggestion. Whence it is plain, he can have no Notion of those parts of Geo­metry, which relate to the Men­suration of Solids, and their Con­vex or Concave Surfaces, and contemplate the Properties of Lines generated by the Section of a Solid. The conceiving of any part where­of, is beyond the Reach of his Fa­culties.

CLV. Nor even the Ele­ments of plain Geo­metry.

Farther, he cannot comprehend the manner wherein Geometers de­scribe a right Line or Circle: The Rule and Compass with their Use, being things of which it's impos­sible he should have any Notion. Nor is it an easier matter for him, to conceive the placing of [Page 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 inca­pable of be­ing mana­ged as Geo­metrical Figures.

All that is properly perceiv'd by the Visive Faculty, amounts to no more than Colours with their Va­riations, and different Proportions of Light and Shade. But, the per­petual Mutability, and Fleetingness of those immediate Objects of Sight, render them incapable of being managed after the manner [Page 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 de­terminate Proportions, between Things so Variable and Inconstant, if we suppose it possible to be done, must yet be a very trifling and in­significant Labour.

CLVII. The Opini­on of those who hold plain Fi­gures to be the imme­diate Ob­jects of Sight, con­sider'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 I­deas 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 [Page 184] we shall find the Plains here men­tion'd, as the immediate Objects of Sight, are not Visible, but Tangi­ble Plains. For when we say that Pictures are Plains, we mean there­by, 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 im­mediately by Vision: For it appear­eth to the Eye Various and Multi­form.

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

From all which we may con­clude, that Plains are no more the immediate Object of Sight than So­lids. What we strictly see are not Solids, nor yet Plains variously co­lour'd; they are only Diversity of Colours. And some of these sug­gest 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 [Page 185] see Solids: Both being equally suggested by the immediate Ob­jects of Sight, which according­ly 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 De­monstrated.

CLIX. Difficult to enter pre­cisely in­to the Thoughts of the a­bove men­tion'd In­telligence.

What has been said is, if I mistake not, sufficient to Decide the Question we propos'd to Exa­mine, 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 Ob­jects of Sight, from those of Touch, which are Connected with them. This, indeed, in a compleat De­gree, [Page 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 Lan­guage, which is familiar to him, pronounced in his Ears without understanding them. Tho' he en­deavour to disunite the meaning from the Sound, it will neverthe­less intrude into his Thoughts, and he shall find it extream Difficult, if not impossible, to put him­self 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 Significati­on annexed to them.

CXL. The Object of Geome­try, its not being suffi­ciently un­derstood, cause of Difficulty and useless Labour in that Sci­ence.

By this time, I suppose, 'tis clear that neither Abstract, nor Visible Extension makes rhe Object of Geo­metry. The not discerning of which might, perhaps, have created some Difficulty, and useless Labour in [Page 187] Mathematics. Sure I am, that some­what relating thereto has occur'd to my Thoughts, which, tho' af­ter the most anxious and repeat­ed 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, where­in that Science hath receiv'd such mighty Improvements by new Me­thods; great Part whereof, as well as of the Ancient Discoveries, may perhaps lose their Reputation, and much of that 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.