Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/45



7. Consentient Sets. 7.1 A traveller in a railway carriage sees a fixed point of the carriage. The wayside stationmaster knows that the traveller has been in fact observing a track of points reaching from London to Manchester. The stationmaster notes his station as fixed in the earth. A being in the sun conceives the station as exhibiting a track in space round the sun, and the railway carriage as marking out yet another track. Thus if space be nothing but relations between material bodies, points as simple entities disappear. For a point according to one type of observation is a track of points according to another type. Galileo and the Inquisition are only in error in the single affirmation in which they both agreed, namely that absolute position is a physical fact — the sun for Galileo and the earth for the Inquisition.

7.2 Thus each rigid body defines its own space, with its own points, its own lines, and its own surfaces. Two bodies may agree in their spaces; namely, what is a point for either may be a point for both. Also if a third body agrees with either, it will agree with both. The complete set of bodies, actual or hypothetical, which agree in their space-formation will be called a ‘consentient’ set.

The relation of a ‘dissentient’ body to the space of a consentient set is that of motion through it. The dissentient body will itself belong to another consentient set. Every body of this second set will have a