Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/20

 the persistent ultimate points in successive configurations at successive ultimate instants of time. Here ‘ultimate’ means ‘not analysable into a complex of simpler entities.’ The introduction of the principle of relativity adds to the complexity — or rather, to the perplexity — of this conception of nature. The statement of general character of ultimate fact must now be amended into ‘persistent ultimate material with successive mutual ultimate relations at successive ultimate instants of time.’

Space issues from these mutual relations of matter at an instant. The first criticism to be made on such an assertion is that it is shown to be a metaphysical fairy tale by any comparison with our actual perceptual knowledge of nature. Our knowledge of space is based on observations which take time and have to be successive, but the relations which constitute space are instantaneous. The theory demands that there should be an instantaneous space corresponding to each instant, and provides for no correlation between these spaces; while nature has provided us with no apparatus for observing them.

2.3 It is an obvious suggestion that we should amend our statement of ultimate fact, as modified by the acceptance of relativity. The spatial relations must now stretch across time. Thus if P, P′, P″, etc. be material particles, there are definite spatial relations connecting P, P′, P″, etc. at time t1 with P, P′, P″, etc. at time t2, as well as such relations between P and P′ and P″, etc. at time t1 and such relations between P and P′ and P″, etc. at time t2. This should mean that P at time t2 has a definite position in the spatial configuration constituted by the relations between P, P′, P″, etc. at time t1.