When we discussed Laplace's hypothesis, we saw that from the present state of the world the whole future can be predicted unambiguously, or, in other words, from the known initial positions and velocities of the masses a definite set of final positions follows. However, initial as well as final positions are only mathematical concepts, that is, in the last resort, numerical values of coordinates. If we want to regard Laplace's hypothesis as a statement about the real world, it must be possible to deduce unambiguously, from the observed initial state, the final state that is to be observed; that is, through refinement of the means of observation we must be able to determine the initial state so exactly numerically that from the same initial state a definite final state follows. If many experiments are made, it must be possible to reduce the scattering of the observed final state to any degree. Laplace's conception of the world thus tacitly incorporates the deterministic hypothesis in the sense of chapter VI, section 5. It has to do this tacitly because it does not give any indication as to how the numbers coordinated to the initial state of the masses can actually be found.