Note 149 — Chapter IV

Mrs Ladd Franklin, in an article on The Proposition in Baldwin’s Dictionary of Philosophy and Psychology, reaches the result arrived at in this section from a different point of view. Mrs Franklin shews that, if we express everything that can be said in the form of existential propositions (that is, propositions affirming or denying existence), it is at once evident that the actual number of different statements possible in terms of X and Y and their contradictories x and y is eight. For the combinations of X and Y and their contradictories are XY, Xy, xY, xy, and we can affirm each of these combinations to exist or to be non-existent. Hence it is clear that eight different statements of fact are possible, and that these eight must remain different, no matter what the form in which they may be expressed.

It may be worth adding that the conditional and disjunctive forms as well as the categorical may here be included on the understanding that all the propositions are interpreted assertorically. Thus, the four following propositions are, on the above understanding, equivalent to one another: All X is Y (categorical); If anything is X, it is Y (conditional); Nothing is Xy (existential); Everything is x or Y (disjunctive).