When we say that something is "always true" or "true in all cases," it is clear that the "something" involved cannot be a proposition. A proposition is just true or false, and there is an end of the matter. There are no instances or cases of "Socrates is a man" or "Napoleon died at St Helena." These are propositions, and it would be meaningless to speak of their being true "in all cases." This phrase is only applicable to propositional functions. Take, for example, the sort of thing that is often said when causation is being discussed. (We are net concerned with the truth or falsehood of what is said, but only with its logical analysis.) We are told that is, in every instance, followed by . Now if there are "instances" of , must be some general concept of which it is significant to say " is ," " is ," " is ," and so on, where , , are particulars which are not identical one with another. This applies, e.g., to our previous case of lightning. We say that lightning () is followed by thunder (). But the separate flashes are particulars, not identical, but sharing the common property of being lightning. The only way of expressing a [Pg 157] common property generally is to say that a common property of a number of objects is a propositional function which becomes true when any one of these objects is taken as the value of the variable. In this case all the objects are "instances" of the truth of the propositional function—for a propositional function, though it cannot itself be true or false, is true in certain instances and false in certain others, unless it is "always true" or "always false." When, to return to our example, we say that is in every instance followed by , we mean that, whatever may be, if is an , it is followed by a ; that is, we are asserting that a certain propositional function is "always true." Sentences involving such words as "all," "every," "a," "the," "some" require propositional functions for their interpretation. The way in which propositional functions occur can be explained by means of two of the above words, namely, "all" and "some."