Introduction to Mathematical Philosophy

by Bertrand Russell

and

have to be determined as definite classes before such expressions become true or false.

The notion of "cases" or "instances" depends upon propositional functions. Consider, for example, the kind of process suggested by what is called "generalisation," and let us take some very primitive example, say, "lightning is followed by thunder." We have a number of "instances" of this, i.e. a number of propositions such as: "this is a flash of lightning and is followed by thunder." What are these occurrences "instances" of? They are instances of the propositional function: "If

is a flash of lightning,

is followed by thunder." The process of generalisation (with whose validity we are fortunately not concerned) consists in passing from a number of such instances to the universal truth of the propositional function: "If

is a flash of lightning,