For example, the hairs and nails are utterly devoid of sensibility, as everyone knows.  Nevertheless, if the ends of the nails or hairs are touched, ever so lightly, we feel that they are touched, and the sensation seems to be situated in the nails or hairs.  Nay more, if a walking-stick a yard long is held firmly by the handle and the other end is touched, the tactile sensation, which is a state of our own consciousness, is unhesitatingly referred to the end of the stick; and yet no one will say that it is there.

Let us now suppose that, instead of one pin’s point resting against the end of my finger, there are two.  Each of these can be known to me, as we have seen, only as a state of a thinking mind, referred outwards, or localized.  But the existence of these two states, somehow or other, generates in my mind a host of new ideas, which did not make their appearance when only one state was present.

For example, I get the ideas of co-existence, of number, of distance, and of relative place or direction.  But all these ideas are ideas of relations, and imply the existence of something which perceives those relations.  If a tactile sensation is a state of the mind, and if the localization of that sensation is an act of the mind, how is it conceivable that a relation between two localized sensations should exist apart from the mind?  It is, I confess, quite as easy for me to imagine that redness may exist apart from a visual sense, as it is to suppose that co-existence, number, and distance can have any existence apart from the mind of which they are ideas.

Thus it seems clear that the existence of some, at any rate, of Locke’s primary qualities of matter, such as number and extension, apart from mind, is as utterly unthinkable as the existence of colour and sound under like circumstances.

Will the others—­namely, figure, motion and rest, and solidity—­withstand a similar criticism?  I think not.  For all these, like the foregoing, are perceptions by the mind of the relations of two or more sensations to one another.  If distance and place are inconceivable, in the absence of the mind, of which they are ideas, the independent existence of figure, which is the limitation of distance, and of motion, which is change of place, must be equally inconceivable.  Solidity requires more particular consideration, as it is a term applied to two very different things, the one of which is solidity of form, or geometrical solidity; while the other is solidity of substance, or mechanical solidity.

If those motor nerves of a man by which volitions are converted into motion were all paralysed, and if sensation remained only in the palm of his hand (which is a conceivable case), he would still be able to attain to clear notions of extension, figure, number, and motion, by attending to the states of consciousness which might be aroused by the contact of bodies with the sensory surface of the palm.  But it does not appear that such a person could arrive at any conception of geometrical solidity.  For that which does not come in contact with the sensory surface is non-existent for the sense of touch; and a solid body, impressed upon the palm of the hand, gives rise only to the notion of the extension of that particular part of the solid which is in contact with the skin.