Page:Carroll - Game of Logic.djvu/45

§ 2.]

Let me mention, in conclusion, that you may perhaps meet with logical treatises in which it is not assumed that any Thing exists at all, but "some $$x$$ are $$y$$" is understood to mean "the Attributes $$x$$, $$y$$ are compatible, so that a Thing can have both at once", and "no $$x$$ are $$y$$" to mean "the Attributes $$x$$, $$y$$ are incompatible, so that nothing can have both at once".

In such treatises, Propositions have quite different meanings from what they have in our 'Game of Logic', and it will be well to understand exactly what the difference is.

First take "some $$x$$ are $$y$$". Here we understand "are" to mean "are, as an actual fact"which of course implies that some $$x$$-Things exist. But they (the writers of these other treatises) only understand "are" to mean "can be", which does not at all imply that any exist. So they mean less than we do: our meaning includes theirs (for of course "some $$x$$ are $$y$$" includes "some $$x$$ can be $$y$$"), but theirs does not include ours. For example, "some Welsh hippopotami are heavy" would be true, according to these writers (since the