suppose, to take for example the visual sensations, that A produces two simultaneous sensations, a sensation purely luminous a and a colored sensation a´ , that B produces in the same way simultaneously a luminous sensation b and a colored sensation b´ , that if these different sensations are transmitted to me by the same retinal fiber, a is identical with b , but that in general the colored sensations a´ and b´ produced by different bodies are different? In that case it would be the identity of the sensation a which accompanies a´ with the sensation b which accompanies b´ , which would tell that all these sensations are transmitted to me by the same fiber.
However it may be with this hypothesis and although I am led to prefer to it others considerably more complicated, it is certain that we are told in some way that there is something in common between these sensations a + a´ and b +b´, without which we should have no means of recognizing that the object B has taken the place of the object A.
Therefore I do not further insist and I recall the hypothesis I have just made: I suppose that I have ascertained that the impressions which I attribute to B are transmitted to me at the instant β by the same fibers, optic as well as tactile, which, at the instant α, had transmitted to me the impressions that I attributed to A. If it is so, we shall not hesitate to declare that the point occupied by B at the instant β is identical with the point occupied by A at the instant α.
I have just enunciated two conditions for these points being identical; one is relative to sight, the other to touch. Let us consider them separately. The first is necessary, but is not sufficient. The second is at once necessary and sufficient. A person knowing geometry could easily explain this in the following manner: Let O be the point of the retina where is formed at the instant α the image of the body A; let M be the point of space occupied at the instant α by this body A; let M´ be the point of space occupied at the instant β by the body B. For this body B to form its image in O, it is not necessary that the points M and M´ coincide; since vision acts at a distance, it suffices for the three points O M M´ to be in a straight line. This condition that the two objects form their image on O is therefore necessary, but not sufficient for the points M and M´ to coincide. Let now P be the point occupied by my finger and where it remains, since it does not budge. As touch does not act at a distance, if the body A touches my finger at the instant α, it is because M and P coincide; if B touches my finger at the instant β, it is because M´ and P coincide. Therefore M and M´ coincide. Thus this condition that if A touches my finger at the instant α, B touches it at the instant β, is at once necessary and sufficient for M and M´ to coincide.
But we who, as yet, do not know geometry can not reason thus; all that we can do is to ascertain experimentally that the first condition relative to sight may be fulfilled without the second, which is relative to touch, but that the second can not be fulfilled without the first.
Suppose experience had taught us the contrary, as might well be; this hypothesis contains nothing absurd. Suppose, therefore, that we had ascertained experimentally that the condition relative to touch may be fulfilled without that