had moved, unless, indeed, all the other points were so connected that the movement of one would involve the movement of all.
We have just pointed out an extreme case, viz., that in which all except one had kept their relative positions; but, without entering into details, it is easy to see that among all the possible ways of explaining the change in the state of the system there may be some much simpler than others, and which without hesitation we regard as much more probable.
If, without being limited to two distinct times, observation should follow the system through its successive states, there would be hypotheses as to the absolute movements of the different points of the system, which would be considered preferable for the explanation of their relative movements. Thus, without reference to the relative size of the heavenly bodies and to knowledge of the laws of gravitation, the hypothesis of Copernicus would explain the apparent motions of the planetary system more simply and plausibly than those of Ptolemy or Tycho.
In the preceding paragraph we have only looked on motion as a geometric relation, a change of position, without reference to any idea of cause or motive power or any knowledge of the laws which govern the movements of matter. From this new point of view other considerations of probability will arise. If, for instance, the mass of the body A is considerably greater than that of the body B we judge that the change in the relative situation of the bodies A and B is more probably due to the displacement of B than of A.