Page:Mysticism and Logic and Other Essays.djvu/195

Rh 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 e 1 occurs at the time t 1 it will be followed by the event e 2 ." This proposition is intended to be necessary with respect to t 1, i.e. to remain true however t 1 may be varied. Causality, as a universal law, will then be the following: "Given any event e 1 there is an event e 2 such that, whenever e 1 occurs, e 2 occurs later." But before this can be considered precise, we must specify how much later e 2 is to occur. Thus the principle becomes:—

"Given any event e 1, there is an event e 2 and a time-interval τ such that, whenever e 1 occurs, 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.