Unfortunately, however, the definition in Baldwin's _Dictionary_ says that what is necessary is not only "true under all circumstances" but is also "true." Now these two are incompatible. Only propositions can be "true," and only propositional functions can be "true under all circumstances." Hence the definition as it stands is nonsense. What is meant seems to be this: "A proposition is necessary when it is a value of a propositional function which is true under all circumstances, i.e. for all values of its argument or arguments." But if we adopt this definition, the same proposition will be necessary or contingent according as we choose one or other of its terms as the argument to our propositional function. For example, "if Socrates is a man, Socrates is mortal," is necessary if Socrates is chosen as argument, but not if _man_ or _mortal_ is chosen. Again, "if Socrates is a man, Plato is mortal," will be necessary if either Socrates or _man_ is chosen as argument, but not if Plato or _mortal_ is chosen. However, this difficulty can be overcome by specifying the constituent which is to be regarded as argument, and we thus arrive at the following definition: "A proposition is _necessary_ with respect to a given constituent if it remains true when that constituent is altered in any way compatible with the proposition remaining significant." We may now apply this definition to the definition of causality quoted above. It is obvious that the argument must be the time at which the earlier event occurs. Thus an instance of causality will be such as: "If the event [Math: e_{1}] occurs at the time [Math: t_{1}], it will be followed by the event [Math: e_{2}]." This proposition is intended to be necessary with respect to [Math: t_{1}], i.e. to remain true however [Math: t_{1}] may be varied. Causality, as a universal law, will then be the following: "Given any event [Math: t_{1}], there is an event [Math: e_{2}] such that, whenever [Math: t_{1}] occurs, [Math: e_{2}] occurs later." But before this can be considered precise, we must specify how much later [Math: e_{2}] is to occur. Thus the principle becomes:-- "Given any event [Math: e_{1}], there is an event [Math: e_{2}] and a time-interval τ such that, whenever [Math: e_{1}] occurs, [Math: e_{2}] follows after an interval τ." I am not concerned as yet to consider whether this law is true or false. For the present, I am merely concerned to discover what the law of causality is supposed to be. I pass, therefore, to the other definitions quoted above. The second definition need not detain us long, for two reasons. First, because it is psychological: not the "thought or perception" of a process, but the process itself, must be what concerns us in considering causality. Secondly, because it is circular: in speaking of a process as "taking place in consequence of" another process, it introduces the very notion of cause which was to be defined.