An Enquiry Concerning the Principles of Natural Knowledge/Chapter 17

CHAPTER XVII

FIGURES

62. Sense-Figures. 62.1 There are two types of objects which can be included under the general name of ‘figures’; objects of one type will be termed ‘sense-figures,’ and of the other type ‘geometrical figures.’

Figures of either type arise from the perception of the relation of sense-objects to the properties which their situations have in respect to their relations of extension with other events. The primary type of figure is the sense-figure and the geometrical figure is derivative from it.

62.2 Every sort of sense-object will have its own peculiar sort of sense-figure. The sense-figures associated with some sorts of sense-objects (e.g. smells and tastes) are barely perceptible, whereas the sense-figures associated with other sorts of sense-objects (e.g. sights and touches) are of insistent obviousness. The condition that a sense-object should have a figure within a given duration can be precisely stated: A sense-object O, as perceived in a situation σ which extends throughout a duration d of a time-system α, possesses a figure in d, if every volume of σ, lying in a moment of α inherent in d, is congruent with every other such volume.

Owing to the inexactitude of perception small quantitative defects from the rigorous fulfilment of this condition do not in practice hinder the perception of figure. Namely, the possession of sense-figure follows from the sufficiently approximate fulfilment of this condition. The durations which are important from the point of view of sense-figures are those which form present durations of perceptions — in general, those durations which are cogredient with a percipient event and are each short enough to form one immediate present. Thus in the numerous instances in which there is no large change within such an immediate present, there is a perceived figure. Accordingly we can define a sense-figure precisely as follows:

The figure, for a time-system α, of sense-object O in situation σ is the relation holding, and only holding, between O and any α-volume congruent to a member of the set of α-volumes of σ.

This definition is only important when the α-volumes of σ are all nearly congruent to each other; because only in that case is this relation recognisable in perception.

62.3 Thus, each sense-object is primarily capable of its own sort of sense-figure and of that sort only. There are the sense-figures of blue of one shade, and the sense-figures of blue of another shade, and the separate sets of figures belonging to all the shades of reds and greens and yellows. There is the set of figures of the touch of velvet, and the set of figures of the touch of marble at particular temperatures of hand and surface and with a particular polish of surface.

62.4 But there is an analogy of sense-objects and this begets an analogy of figures. For example, there is an analogy between blues of all shades, and a corresponding analogy between their sets of figures. Each such analogy amid sense-objects issues in an object of a type not hitherto named. Call it the type of ‘generalised sense-objects.’ For example, we can recognise blue and ignore its particular shade. Correspondingly we can recognise a blue sense-figure, and ignore the differences between a light-blue sense-figure and a dark-blue sense-figure. We can go further, and recognise colour and ignore the particular colour; and correspondingly there are recognisable sight-figures underlying figures of particular shades of particular colours.

62.5 But it would be a mistake to insist on the derivation of the generalised sense-figures from the recognition of generalised sense-objects. In general the converse process would seem to be nearer the truth. Namely, the analogy amid sense-figures is more insistently perceptible than the analogy amid sense-objects; and the derivation is as much from the generalised sense-figure to the generalised sense-object as in the converse order.

We must go further than this. Perceptive insistency is not ranged in the order of simplicity as determined by a reflective analysis of the elements of our awareness of nature. Sense-figures possess a higher perceptive insistency than the corresponding sense-objects. We first notice a dark-blue figure and pass to the dark-blueness.

62.6 Indeed the high perceptive power of figures is at once the foundation of our natural knowledge and the origin of our philosophical errors. It has led the theory of space to be annexed to objects and not to events, and thus created the fatal divorce between space and time. A figure, being an object, is not in space or time, except in a derivative sense.

This perceptive power of figures carries us to the direct recognition of sorts of objects which otherwise would remain in the region of abstract logical concepts. For example, our perception of sight-figures leads to the recognition of colour as being what is common to all particular colours.

63. Geometrical Figures. 63.1 The generalisation which introduces geometrical figures is an extreme instance of the sort of generalisation already considered. Namely, instead of generalising from a dark-blue figure to a sight-figure, we pass to the concept of the relation of any sense-object to the volumes of its situation. This concept of a figure, in which any particular sense has been lost sight of, would be entirely without any counterpart in perception, if it were not for the fact of perceptual objects. A perceptual object is the association in one situation of a set of sense-objects, in general ‘conveyed’ by the normal perception of one of them. The high perceptive capacity of sense-figures leads to their association in a generalised figure, which is the geometrical figure of the object. Indeed, the insistent obviousness of the geometrical figure is one reason for the perception of perceptual objects. The object is not the figure, but our awareness of it is derived from our awareness of the figure. The reason for discriminating the perceptual object from its figure in that situation is that the physical object persists while its figure changes. For example, a sock can be twisted into all sorts of figures.

63.2 The current doctrine of different kinds of space — tactual space, visual space, and so on — arises entirely from the error of deducing space from the relations between figures. With such a procedure, since there are different types of figures for different types of sense, evidently there must be different types of space for different types of sense. And the demand created the supply.

63.3 If however the modern assimilation of space and time is to hold, we must then go further and admit different kinds of time for different kinds of sense, namely a tactual time, a visual time, and so on. If this be allowed, it is difficult to understand how the disjecta membra of our perceptual experience manage to collect themselves into a common world.

For example, it would require a pre-established harmony to secure that the visual newspaper was delivered at the visual time of the visual breakfast in the visual room and also the tactual newspaper was delivered at the tactual time of the tactual breakfast in the tactual room. It is difficult enough for the plain man — such as the present author — to accept the miracle of getting the two newspapers into the two rooms daily with such admirable exactitude at the same time. But the additional miracle introduced by the two times is really incredible.

The procedure of this enquiry admits the different types of figures, but rejects the different types of space.