The Works of George Berkeley Part 33

142. I answer, it must be acknowledged the visible square is fitter than the visible circle to represent the tangible square, but then it is not because it is liker, or more of a species with it; but, because the visible square contains in it several distinct parts, whereby to mark the several distinct corresponding parts of a tangible square, whereas the visible circle doth not. The square perceived by touch hath four distinct equal sides, so also hath it four distinct equal angles. It is therefore necessary that the visible figure which shall be most proper to mark it contain four distinct equal parts, corresponding to the four sides of the tangible square; as likewise four other distinct and equal parts, whereby to denote the four equal angles of the tangible square. And accordingly we see the visible figures contain in them distinct visible parts, answering to the distinct tangible parts of the figures signified or suggested by them.

143. But, it will not hence follow that any visible figure is like unto or of the same species with its corresponding tangible figure-unless it be also shewn that not only the number, but also the kind of the parts be the same in both. To ill.u.s.trate 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 annexed to it-in the formation whereof there being eight different collisions or modifications of the air by the organs of speech, each of which produces a difference of sound, it was fit the word representing it should consist of as many distinct characters, thereby to mark each particular difference or part of the whole sound. And yet n.o.body, I presume, will say the single letter _a_, or the word _adultery_, are alike unto or of the same species with the respective sounds by them represented. It is indeed arbitrary that, in general, letters of any language represent sounds at all; but, when that is once agreed, it is not arbitrary what combination of letters shall represent this or that particular sound. I leave this with the reader to pursue, and apply it in his own thoughts.

144. It must be confessed that we are not so apt to confound other signs with the things signified, or to think them of the same species, as we are visible and tangible ideas. But, a little consideration will shew us how this may well be, without our supposing them of a like nature. These signs are constant and universal; their connexion with tangible ideas has been learnt at our first entrance into the world; and ever since, almost every moment of our lives, it has been occurring to our thoughts, and fastening and striking deeper on our minds. When we observe that signs are variable, and of human inst.i.tution; 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 inst.i.tution, and cannot remember that we ever learned their signification, but think that at first sight they would have suggested to us the same things they do now: all this persuades us they are of the same species as the things respectively represented by them, and that it is by a natural resemblance they suggest them to our minds.

145. Add to this that whenever we make a nice survey of any object, successively directing the optic axis to each point thereof, there are certain lines and figures, described by the motion of the head or eye, which, being in truth perceived by feeling(446), do nevertheless so mix themselves, as it were, with the ideas of sight that we can scarce think but they appertain to that sense. Again, the ideas of sight enter into the mind several at once, more distinct and unmingled than is usual in the other senses beside the touch. Sounds, for example, perceived at the same instant, are apt to coalesce, if I may so say, into one sound: but we can perceive, at the same time, great variety of visible objects, very separate and distinct from each other. Now, tangible(447) extension being made up of several distinct coexistent parts, we may hence gather another reason that may dispose us to imagine a likeness or a.n.a.logy 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(448) they have with each other. We cannot open our eyes but the ideas of distance, bodies, and tangible figures are suggested by them. So swift, and sudden, and unperceived is the transit from visible to tangible ideas that we can scarce forbear thinking them equally the immediate object of vision.

146. The prejudice(449) which is grounded on these, and whatever other causes may be a.s.signed thereof, sticks so fast on our understandings, that it is impossible, without obstinate striving and labour of the mind, to get entirely clear of it. But then the reluctancy we find in rejecting any opinion can be no argument of its truth, to whoever considers what has been already shewn with regard to the prejudices we entertain concerning the distance, magnitude, and situation of objects; prejudices so familiar to our minds, so confirmed and inveterate, as they will hardly give way to the clearest demonstration.

147. Upon the whole, I think we may fairly conclude(450) that the proper objects of Vision const.i.tute 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 also to avoid whatever may be hurtful and destructive of them.

It is by their information that we are princ.i.p.ally 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 signified by any likeness or ident.i.ty of nature, but only by an habitual connexion that experience has made us to observe between them(451).

148. Suppose one who had always continued blind be told by his guide that after he has advanced so many steps he shall come to the brink of a precipice, or be stopped by a wall; must not this to him seem very admirable and surprising? He cannot conceive how it is possible for mortals to frame such predictions as these, which to him would seem as strange and unaccountable as prophecy does to others. Even they who are blessed with the visive faculty may (though familiarity make it less observed) find therein sufficient cause of admiration. The wonderful art and contrivance wherewith it is adjusted to those ends and purposes for which it was apparently designed; the vast extent, number, and variety of objects that are at once, with so much ease, and quickness, and pleasure, suggested by it-all these afford subject for much and pleasing speculation, and may, if anything, give us some glimmering a.n.a.logous praenotion of things, that are placed beyond the certain discovery and comprehension of our present state(452).

149. I do not design to trouble myself 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 is no such idea as that of extension in abstract(453); and that there are two kinds of sensible extension and figures, which are entirely distinct and heterogeneous from each other(454). Now, it is natural to inquire which of these is the object of geometry(455).

150. Some things there are which, at first sight, incline one to think geometry conversant about visible extension. The constant use of the eyes, both in the practical and speculative parts of that science, doth very much induce us thereto. It would, without doubt, seem odd to a mathematician to go about to convince him the diagrams he saw upon paper were not the figures, or even the likeness of the figures, which make the subject of the demonstration-the contrary being held an unquestionable truth, not only by mathematicians, but also by those who apply themselves more particularly to the study of logic; I mean who consider the nature of science, certainty, and demonstration; it being by them a.s.signed 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 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 a.s.sert of abstract ideas being the object of geometrical demonstration I leave to be considered.

151. To come to a resolution in this point, we need only observe what has been said in sect. 59, 60, 61, 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.

152. 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 concerned 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 fixed, and immutably the same in all times and places. A visible square, for instance, suggests to the mind the same tangible figure in Europe that it doth in America. Hence it is, that the voice of nature, which speaks to our eyes, is not liable to that misinterpretation and ambiguity that languages of human contrivance are unavoidably subject to(456). From which may, in some measure, be derived that peculiar evidence and clearness of geometrical demonstrations.

153. Though what has been said may suffice to shew what ought to be determined with relation to the object of geometry, I shall, nevertheless, for the fuller ill.u.s.tration thereof, take into my thoughts the case of an intelligence or unbodied spirit, which is supposed to see perfectly well, i.e. to have a clear perception of the proper and immediate objects of sight, but to have no sense of touch(457). Whether there be any such being in nature or no, is beside my purpose to inquire; it suffices, that the supposition contains no contradiction in it. Let us now examine what proficiency such a one may be able to make in geometry. Which speculation will lead us more clearly to see whether the ideas of sight can possibly be the object of that science.

154. _First_, then, it is certain the aforesaid intelligence could have no idea of a solid or quant.i.ty of three dimensions, which follows from its not having any idea of distance. We, indeed, are p.r.o.ne to think that we have by sight the ideas of s.p.a.ce 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 spoken of is supposed to have no experience of touch. He would not, therefore, judge as we do, nor have any idea of distance, outness, or profundity, nor consequently of s.p.a.ce or body, either immediately or by suggestion. Whence it is plain he can have no notion of those parts of geometry which relate to the mensuration of solids, and their convex or concave surfaces, and contemplate the properties of lines generated by the section of a solid. The conceiving of any part whereof is beyond the reach of his faculties.

155. _Farther_, he cannot comprehend the manner wherein geometers describe a right line or circle; the rule and compa.s.s, with their use, being things of which it is impossible he should have any notion. Nor is it an easier matter for him to conceive the placing of one plane or angle on another, in order to prove their equality; since that supposes some idea of distance, or external s.p.a.ce. 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 inquiry, 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 plane, as will appear to whoever shall reflect a little on it.

156. All that is properly perceived by the visive faculty amounts to no more than colours with their variations, and different proportions of light and shade-but the perpetual mutability and fleetingness of those immediate objects of sight render them incapable of being managed after the manner of geometrical figures; nor is it in any degree useful that they should. It is true there be divers of them perceived at once; and more of some, and less of others: but accurately to compute their magnitude, and a.s.sign precise determinate proportions between things so variable and inconstant, if we suppose it possible to be done, must yet be a very trifling and insignificant labour.

157. I must confess, it seems to be the opinion of some very ingenious men that flat or plane figures are immediate objects of sight, though they acknowledge solids are not. And this opinion of theirs is grounded on what is observed in painting, wherein (say they) the ideas immediately imprinted in the mind are only of planes variously coloured, which, by a sudden act of the judgment, are changed into solids: but, with a little attention, we shall find the planes here mentioned as the immediate objects of sight are not visible but tangible planes. For, when we say that pictures are planes, we mean thereby that they appear to the touch smooth and uniform. But then this smoothness and uniformity, or, in other words, this planeness of the picture is not perceived immediately by vision; for it appeareth to the eye various and multiform.

158. From all which we may conclude that planes are no more the immediate object of sight than solids. What we strictly see are not solids, nor yet planes variously coloured-they are only diversity of colours. And some of these suggest to the mind solids, and others plane figures; just as they have been experienced to be connected with the one or the other: so that we see planes in the same way that we see solids-both being equally suggested by the immediate objects of sight, which accordingly are themselves denominated planes and solids. But, though they are called by the same names with the things marked by them, they are, nevertheless, of a nature entirely different, as hath been demonstrated(458).

159. What has been said is, if I mistake not, sufficient to decide the question we proposed to examine, concerning the ability of a pure spirit, such as we have described, to know geometry. It is, indeed, no easy matter for us to enter precisely into the thoughts of such an intelligence; because we cannot, without great pains, cleverly separate and disentangle in our thoughts the proper objects of sight from those of touch which are connected with them. This, indeed, in a complete degree seems scarce possible to be performed; which will not seem strange to us, if we consider how hard it is for any one to hear the words of his native language, which is familiar to him, p.r.o.nounced in his ears without understanding them. Though he endeavour to disunite the meaning from the sound, it will nevertheless intrude into his thoughts, and he shall find it extreme difficult, if not impossible, to put himself exactly in the posture of a foreigner that never learnt the language, so as to be affected barely with the sounds themselves, and not perceive the signification annexed to them.

160. By this time, I suppose, it is clear that neither abstract nor visible extension makes the object of geometry; the not discerning of which may, perhaps, have created some difficulty and useless labour in mathematics. [(459)Sure I am that somewhat relating thereto has occurred to my thoughts; which, though 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 should make it public, in an age wherein that science hath received such mighty improvements by new methods; great part whereof, as well as of the ancient discoveries, may perhaps lose their reputation, and much of that ardour with which men study the abstruse and fine geometry be abated, if what to me, and those few to whom I have imparted it, seems evidently true, should really prove to be so.]

An Appendix To The Essay On Vision

[_This Appendix is contained only in the second edition._]

The censures which, I am informed, have been made on the foregoing _Essay_ inclined me to think I had not been clear and express enough in some points; and, to prevent being misunderstood for the future, I was willing to make any necessary alterations or additions in what I had written. But that was impracticable, the present edition having been almost finished before I received this information. Wherefore, I think it proper to consider in this place the princ.i.p.al objections that are come to my notice.

In the _first_ place, it is objected, that in the beginning of the Essay I argue either against all use of lines and angles in optics, and then what I say is false; or against those writers only who will have it that we can perceive by sense the optic axes, angles, &c., and then it is insignificant, this being an absurdity which no one ever held. To which I answer that I argue only against those who are of opinion that we perceive the distance of objects by lines and angles, or, as they term it, by a kind of innate geometry. And, to shew that this is not fighting with my own shadow, I shall here set down a pa.s.sage from the celebrated Des Cartes(460):-

[Ill.u.s.tration]

"Distantiam praeterea discimus, per mutuam quandam conspirationem oculorum.

Ut enim caecus noster duo bacilla tenens, _A E_ et _C E_, de quorum longitudine incertus, solumque intervallum manuum _A_ et _C_, c.u.m magnitudine angulorum _A C E_, et _C A E_ exploratum habens, inde, ut ex Geometria quadam omnibus innata, scire potest ubi sit punctum _E_. Sic quum nostri oculi _R S T_ et _r s t_ ambo, vertuntur ad _X_, magnitudo lineae _S s_, et angulorum _X S s_ et _X s S_, certos nos reddunt ubi sit punctum _X_. Et idem opera alterutrius possumus indagare, loco illum movendo, ut si versus _X_ illum semper dirigentes, prime sistamus in puncto _S_, et statim post in puncto _s_, hoc sufficiet ut magnitudo lineae _S s_, et duorum angulorum _X S s_ et _X s S_ nostrae imaginationi simul occurrant, et distantiam puncti _X_ nos edoceant: idque per actionem mentis, quae licet simplex judicium esse videatur, ratiocinationem tamen quandam involutam habet, similem illi, qua Geometrae per duas stationes diversas, loca inaccessa dimetiuntur."

[Ill.u.s.tration]

I might ama.s.s together citations from several authors to the same purpose, but, this being so clear in the point, and from an author of so great note, I shall not trouble the reader with any more. What I have said on this head was not for the sake of rinding fault with other men; but, because I judged it necessary to demonstrate in the first place that we neither see distance _immediately_, nor yet perceive it by the mediation of anything that hath (as lines and angles) a _necessary_ connexion with it. For on the demonstration of this point the whole theory depends(461).

_Secondly_, it is objected, that the explication I give of the appearance of the horizontal moon (which may also be applied to the sun) is the same that Ga.s.sendus had given before. I answer, there is indeed mention made of the grossness of the atmosphere in both; but then the methods wherein it is applied to solve the phenomenon are widely different, as will be evident to whoever shall compare what I have said on this subject with the following words of Ga.s.sendus:-

"Heinc dici posse videtur: solem humilem oculo spectatum ideo apparere majorem, quam dum altius egreditur, quia dum vicinus est horizonti prolixa est series vaporum, atque adeo corpusculorum quae solis radios ita retundunt, ut oculus minus conniveat, et pupilla quasi umbrefacta longe magis amplificetur, quam dum sole multum elato rari vapores intercipiuntur, solque ipse ita splendescit, ut pupilla in ipsum spectans contractissima efficiatur. Nempe ex hoc esse videtur, cur visibilis species ex sole procedens, et per pupillam amplificatam intromissa in retinam, ampliorem in illa sedem occupet, majoremque proinde creet solis apparentiam, quam dum per contractam pupillam eodem intromissa contendit."

Vid. _Epist. 1. De Apparente Magnitudine Solis Humilis et Sublimis_, p. 6.

This solution of Ga.s.sendus proceeds on a false principle, to wit, that the pupil's being enlarged augments the species or image on the fund of the eye.

_Thirdly_, against what is said in Sect. 80, it is objected, that the same thing which is so small as scarce to be discerned by a man, may appear like a mountain to some small insect; from which it follows that the _minimum visibile_ is not equal in respect of all creatures(462). I answer, if this objection be sounded to the bottom, it will be found to mean no more than that the same particle of matter which is marked to a man by one _minimum visibile_, exhibits to an insect a great number of _minima visibilia_. But this does not prove that one _minimum visibile_ of the insect is not equal to one _minimum visibile_ of the man. The not distinguishing between the mediate and immediate objects of sight is, I suspect, a cause of misapprehension in this matter.

Some other misinterpretations and difficulties have been made, but, in the points they refer to, I have endeavoured to be so very plain that I know not how to express myself more clearly. All I shall add is, that if they who are pleased to criticise on my _Essay_ would but read the whole over with some attention, they might be the better able to comprehend my meaning, and consequently to judge of my mistakes.

I am informed that, soon after the first edition of this treatise, a man somewhere near London was made to see, who had been born blind, and continued so for about twenty years(463). Such a one may be supposed a proper judge to decide how far some tenets laid down in several places of the foregoing Essay are agreeable to truth; and if any curious person hath the opportunity of making proper interrogatories to him thereon, I should gladly see my notions either amended or confirmed by experience(464).

A TREATISE CONCERNING THE PRINCIPLES OF HUMAN KNOWLEDGE

[(465)PART I]

WHEREIN THE CHIEF CAUSES OF ERROR AND DIFFICULTY IN THE SCIENCES, WITH THE GROUNDS OF SCEPTICISM, ATHEISM, AND IRRELIGION, ARE INQUIRED INTO

_First Published in 1710_