George Berkeley | 3. Geometry and Vision

George Berkeley
 (1685 –1753)

Geometry and Vision | Part 3

1. The New Theory of Vision

Although Berkeley did not mention his immaterialism in An Essay towards a New Theory of Vision, this work throws important light upon his quarrel with the mathematicians and his rejection of the rationalist point of view.

It contains, too, an interesting statement of what Berkeley then thought about geometry.

Furthermore, the Essay helps us to see, from what Berkeley said about the objects of vision, how he came to the view that sensible qualities cannot exist “without the mind.”

Among the main contentions of the book is the claim that distance is not immediately perceived by sight; it is “suggested” in part by the sensations we get in moving our eyes but mainly by association with the ideas of touch.

According to Berkeley, we see the distance (and size) of things only in the sense in which we see a man’s shame and anger: We see his face, and the expression on it suggests to us how he is feeling.

In themselves, shame and anger are invisible.

Similarly, we see shapes and colours, which are signs of what we would touch if we were to stretch out our hands, but distance itself is no more seen than anger is.

In expounding this view, Berkeley developed the thesis that the objects of sight and touch are utterly disparate, so that no feature of the one can have more than a contingent connection with any feature of the other.

2. Descartes’s Theory of the Perception of Distance

Consideration should first be given to Berkeley’s criticisms of an important geometrical account of how distance is perceived and assessed, the account given by René Descartes in his Dioptrics (1637):

In this work Descartes referred to 6 “qualities we perceive in the objects of sight,” namely, light, colour, shape, distance, magnitude, and situation.

Descartes argued that one of the ways in which men ascertain the distance of objects is by means of the angles formed by straight lines running from each of their eyes and converging at the object seen.

He illustrated this by reference to a blind man with a stick (the length of which he does not know) held in each hand:

When he brings the points of the sticks together at the object, he forms a triangle with one hand at each end of the base,

and if he knows how far apart his hands are, and what angles the sticks make with his body, he can, “by a kind of geometry innate in all men” know how far away the object is.

The same geometry would apply, Descartes argued, if the observer’s eyes are regarded as ends of the base of a triangle, and straight lines from them are regarded as converging at the object.

The more obtuse the base angles formed by the lines running from this base and converging at the object, the farther away the object must be; the more acute these angles, the nearer the object must be.

Berkeley put the matter somewhat differently from Descartes,

pointing out that according to the latter’s view the more acute the angle formed at the object by the lines converging from the eyes, the farther away it must be; the more obtuse this angle, the nearer the object must be.

It is important to notice that this “must” is the “must” of mathematical necessity:

From what Descartes said, it is necessarily the case that the more acute this angle is, the farther away the object is; the more obtuse the angle, the nearer the object.

“Nearer” and “farther” logically depend upon the obtuseness or acuteness of the angle.

In criticizing this view, therefore, Berkeley was criticizing the view that distance is known a priori by the principles of an innate geometry

according to which we know that the distance of the object must vary in accordance with the angle made at the object by straight lines converging there from the eyes of the observer.

3. Berkeley’s Criticism of Descartes

Against Descartes’s view Berkeley brought a complex argument that for purposes of exposition, is here broken up into 3 parts:

1) The first is that people who know nothing of the geometry of the matter can nevertheless notice the relative distance of things from them.

This is not very convincing, for Descartes obviously thought that the geometry he regarded as “innate in all men” might be employed by them without their having reflected on it.

2) The second argument used by Berkeley is that the lines and angles referred to by Descartes “have no real existence in nature, being only a hypothesis framed by the mathematicians.”

This argument is of interest in showing how Berkeley thought that mathematicians were inclined to deal in fictitious entities, but it is unlikely that Descartes was deceived by them in this way.

3) Berkeley’s third and main argument was based upon a theory that he expressed in the words, “distance, of itself and immediately, cannot be seen.”

William Molyneux, from whose Dioptrics (1692) Berkeley borrowed this theory, had supported it by the argument that

since distance is a line or length directed endwise from the object seen to the eye, it can reach the eye at only one point, which must necessarily remain the same however near or far away the object is.

If this argument is accepted, then distance could not possibly be seen, and could only be judged or, as Berkeley believed, “suggested.”

4. Distance Is Suggested By What Is Seen

What, then, according to Berkeley, is seen?

The answer is not altogether clear, but it would seem that he thought that the immediate object of vision is 2-dimensional, containing relations of above and below and of one side and the other, with no necessary connection with a third dimension.

Hence the relation between what is immediately seen on the one hand and the distance of objects on the other must be contingent and cannot be necessary.

Distance, then, must be ascertained by means of something that has only a contingent relationship with what is seen.

Berkeley mentioned the sensations we have when we adjust our eyes, the greater confusedness of objects as they come very close to the eyes, and the sensations of strain as we try to see what is very near.

But he mainly relied on the associations between what a man has touched and what he now sees:

For example, when a man now sees something faint and dim, he may, from past experience, expect that if he approaches and touches it he will find it bright and hard.

When he sees something at a distance, he is really seeing certain shapes and colours, which suggest to him what tangible ideas he would have if he were near enough to touch it.

Just as one does not hear a man’s thoughts, which are suggested by the sounds he makes, so one does not directly see distance, which is suggested by what is seen.

5. Sight and Touch

Berkeley’s view that distance is not immediately perceived by sight is rejected by some writers on the ground that it is plainly contradicted by experience:

We just do see visual depth, it is held, so that it is idle to deny this fact on the basis of an argument purporting to prove that we cannot.

Again, some critics have argued not only that we do get our idea of distance from sight, but also that touch is vague and uninformative by comparison with sight, and hence less effective in giving knowledge of the material world.

This discussion need not be developed, however,

since, although he said in the Essay that by touch we get knowledge of objects that exist “without the mind” (§55), Berkeley’s real view was that no sensible thing could so exist.

It cannot be denied that on occasion Berkeley’s language was imprecise:

A crucial example of this occurs in his discussion of the question of whether a man born blind would, on receiving his sight, see things at a distance from him:

According to Berkeley, of course, he would not;

but to such a man, the most distant objects “would all seem to be in his eye, or rather in his mind”

and would appear

It will be noticed how readily Berkeley passed from “in his eye” to “in his mind,” and how he assimilated such very different things as sensations and thoughts.

Indeed it is hard not to conclude that he thought that whatever was not seen at a distance must appear to be in the mind.

If this is true, then one of the objects of the Essay was to show that the immediate objects of vision must be in the mind because they are not seen at a distance.

6. Geometries of Sight and of Touch

As already seen, an extremely important thesis of the Essay is that the objects of sight and the objects of touch are radically different from one another.

We see visible objects and we touch tangible objects, and it is absurd to suppose that we can touch what we see or see what we touch.

According to Berkeley, it follows from this that tangible shape and visible shape have no necessary connection with one another.

Geometers certainly supposed themselves to be concerned with shapes in abstraction from their being seen or touched, but Berkeley did not allow that this is possible.

A purely visual geometry would necessarily be confined to 2 dimensions, so that the 3-dimensional geometry that we have must be fundamentally a geometry of touch.

He reinforced this strangely pragmatic view with the observation

that a sighted but disembodied being that could not touch or manipulate things would be unable to understand even plane geometry,

since without a body it would not understand the handling of rulers and compasses and the drawing of lines and the placing of shapes against one another.