UNIVERSAL AND PARTICULAR PROPOSITIONS
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.
FOOTNOTES:
[45] Cf., e.g., _F. L._, p. 4.
[46] See Appendix L.
[47] Cf., e.g., _Md._, N. S., vol. xiv., July, 1905, pp. 399-400.