bearing, not on space, but on bodies.*
Supplement
- To complete the matter, I ought to speak of a very delicate question, which would require long development; I shall confine myself to summarizing here what I have expounded in the Revue de Métaphysique et de Morale and in The Monist. When we say space has three dimensions, what do we mean?
We have seen the importance of those 'internal changes' revealed to us by our muscular sensations. They may serve to characterize the various attitudes of our body. Take arbitrarily as origin one of these attitudes A. When we pass from this initial attitude to any other attitude B, we feel a series of muscular sensations, and this series S will define B. Observe, however, that we shall often regard two series S and S´ as defining the same attitude B (since the initial and final attitudes A and B remaining the same, the intermediary attitudes and the corresponding sensations may differ). How then shall we recognize the equivalence of these two series? Because they may serve to compensate the same external change, or more generally because, when it is a question of compensating an external change, one of the series can be replaced by the other. Among these series, we have distinguished those which of themselves alone can compensate an external change, and which we have called 'displacements.' As we can not discriminate between two displacements which are too close together, the totality of these displacements presents the characteristics of a physical continuum; experience teaches us that they are those of a physical continuum of six dimensions; but we do not yet know how many dimensions space itself has, we must first solve another question.
What is a point of space? Everybody thinks he knows, but that is an illusion. What we see when we try to represent to ourselves a point of space is a black speck on white paper, a speck of chalk on a blackboard, always an object. The question should therefore be understood as follows:
What do I mean when I say the object B is at the same point that the object A occupied just now? Or further, what criterion will enable me to apprehend this?
I mean that, although I have not budged (which my muscular sense tells me), my first finger which just now touched the object A touches at present the object B. I could have used other criteria; for instance another finger or the sense of sight. But the first criterion is sufficient; I know that if it answers yes, all the other criteria will give the same response. I know it by experience, I can not know it a priori. For the same reason I say that touch can not be exercised at a distance; this is another way of enunciating the same experimental fact. And if, on the contrary, I say that sight acts at a distance, it means that the criterion furnished by sight may respond yes while the others reply no.
And in fact, the object, although