# Page:Carroll - Game of Logic.djvu/46

Secondly, take "no ${\displaystyle x}$ are ${\displaystyle y}$". Here we only understand "are" to mean "are, as an actual fact"——which does not at all imply that no ${\displaystyle x}$ can be ${\displaystyle y}$. But they understand the Proposition to mean, not only that none are ${\displaystyle y}$, but that none can possibly be ${\displaystyle y}$. So they mean more than we do: their meaning includes ours (for of course "no ${\displaystyle x}$ can be ${\displaystyle y}$" includes "no ${\displaystyle x}$ are ${\displaystyle y}$"), but ours does not include theirs. For example, "no Policemen are eight feet high" would be true in our Game (since, as an actual fact, no such splendid specimens are ever found), but it would be false, according to these writers (since the Attributes "belonging to the Police Force" and "eight feet high" are quite compatible: there is nothing to prevent a Policeman from growing to that height, if sufficiently rubbed with Rowland's Macassar Oil——which is said to make hair grow, when rubbed on hair, and so of course will make a Policeman grow, when rubbed on a Policeman).
Thirdly, take "all ${\displaystyle x}$ are ${\displaystyle y}$", which consists of the two partial Propositions "some ${\displaystyle x}$ are ${\displaystyle y}$" and "no ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$". Here, of course, the treatises mean less than we do in the first part, and more than we do in the second. But the two operations don't balance each other——