People who are cynical as to the morality of the English are often unpleasantly surprised to learn that “All trespassers will be prosecuted” does not necessarily imply that “some trespassers will be prosecuted.” The view that universal propositions are non-existential is now generally held: Bradley and Venn seem to have been the first to hold this, while older logicians, such as De Morgan,[45] considered universal propositions to be existential, like particular ones.

If the Gnat[46] had been content to affirm his proposition about the means of subsistence of Bread-and-Butter flies, in consequence of their lack of which such flies always die, without pointing out such an insect and thereby proving that the class of them is not null, Alice’s doubt as to the existence of the class in question, even if it were proved to be well founded, would not have affected the validity of the proposition.

This brings us to a great convenience in treating universal propositions as non-existential: we can maintain that all x’s are y’s at the same time as that no x’s are y’s, if only x is the null-class. Thus, when Mr. MacColl[47] objected to other symbolic logicians that their premisses imply that all Centaurs are flower-pots, they could reply that their premisses also imply the more usual view that Centaurs are not flower-pots.

CHAPTER XVIII