Page:Our knowledge of the external world.djvu/165

 different shades in the spectrum, and so on, are all in the nature of unverifiable hypotheses—perfectly possible logically, perfectly consistent with the known facts, and simpler technically than any other tenable hypotheses, but not the sole hypotheses which are logically and empirically adequate.

If a relational theory of instants is constructed, in which an “instant” is defined as a group of events simultaneous with each other and not all simultaneous with any event outside the group, then if our resulting series of instants is to be compact, it must be possible, if x wholly precedes y, to find an event z, simultaneous with part of x, which wholly precedes some event which wholly precedes y. Now this requires that the number of events concerned should be infinite in any finite period of time. If this is to be the case in the world of one man’s sense-data, and if each sense-datum is to have not less than a certain finite temporal extension, it will be necessary to assume that we always have an infinite number of sense-data simultaneous with any given sense-datum. Applying similar considerations to space, and assuming that sense-data are to have not less than a certain spatial extension, it will be necessary to suppose that an infinite number of sense-data overlap spatially with any given sense-datum. This hypothesis is possible, if we suppose a single sense-datum, e.g. in sight, to be a finite surface, enclosing other surfaces which are also single sense-data. But there are difficulties in such a hypothesis, and I do not know whether these difficulties could be successfully met. If they cannot, we must do one of two things: either declare that the world of one man’s sense-data is not continuous, or else refuse to admit that there is any lower limit to the duration and extension of a single sense-datum. I do not know what