Given a proposition, such as "Socrates is before Aristotle," we have certain constituents and also a certain form. But the form is not itself a new constituent; if it were, we should need a new form to embrace both it and the other constituents. We can, in fact, turn all the constituents of a proposition into variables, while keeping the form unchanged. This is what we do when we use such a schema as "," which stands for any [Pg 198] one of a certain class of propositions, namely, those asserting relations between two terms. We can proceed to general assertions, such as " is sometimes true"—i.e. there are cases where dual relations hold. This assertion will belong to logic (or mathematics) in the sense in which we are using the word. But in this assertion we do not mention any particular things or particular relations; no particular things or relations can ever enter into a proposition of pure logic. We are left with pure forms as the only possible constituents of logical propositions. I do not wish to assert positively that pure forms—e.g. the form ""—do actually enter into propositions of the kind we are considering. The question of the analysis of such propositions is a difficult one, with conflicting considerations on the one side and on the other. We cannot embark upon this question now, but we may accept, as a first approximation, the view that forms are what enter into logical propositions as their constituents. And we may explain (though not formally define) what we mean by the "form" of a proposition as follows:— The "form" of a proposition is that, in it, that remains unchanged when every constituent of the proposition is replaced by another. Thus "Socrates is earlier than Aristotle" has the same form as "Napoleon is greater than Wellington," though every constituent of the two propositions is different. We may thus lay down, as a necessary (though not sufficient) characteristic of logical or mathematical propositions, that they are to be such as can be obtained from a proposition containing no variables (i.e. no such words as all, some, a, the, etc.) by turning every constituent into a variable and asserting that the result is always true or sometimes true, or that it is always true in respect of some of the variables that the result is sometimes true in respect of the others, or any variant of these forms. And another way of stating the same thing is to say that logic (or mathematics) is concerned only with forms, and is concerned with them only in the way of stating that they are always or [Pg 199] sometimes true—with all the permutations of "always" and "sometimes" that may occur.