Although the sense of "determined" in which the future is determined by the mere fact that it will be what it will be is sufficient (at least so it seems to me) to refute some opponents of determinism, notably M. Bergson and the pragmatists, yet it is not what most people have in mind when they speak of the future as determined. What they have in mind is a formula by means of which the future can be exhibited, and at least theoretically calculated, as a function of the past. But at this point we meet with a great difficulty, which besets what has been said above about deterministic systems, as well as what is said by others. If formulæ of any degree of complexity, however great, are admitted, it would seem that any system, whose state at a given moment is a function of certain measurable quantities, must be a deterministic system. Let us consider, in illustration, a single material particle, whose co-ordinates at time _t_ are [Math: x_{t}, y_{t}, z_{t}]. Then, however, the particle moves, there must be, theoretically, functions [Math: f_{1}, f_{2}, f_{3}], such that [Math: x_{t} = f_{t}(t), y_{t} = f_{2}(t), z_{t} = f_{3}(t).] It follows that, theoretically, the whole state of the material universe at time _t_ must be capable of being exhibited as a function of _t_. Hence our universe will be deterministic in the sense defined above. But if this be true, no information is conveyed about the universe in stating that it is deterministic. It is true that the formulæ involved may be of strictly infinite complexity, and therefore not practically capable of being written down or apprehended. But except from the point of view of our knowledge, this might seem to be a detail: in itself, if the above considerations are sound, the material universe _must_ be deterministic, _must_ be subject to laws.