# Page:Carroll - Game of Logic.djvu/35

§ 1.]
19
PROPOSITIONS.

we should transfer it to the smaller Diagram thus,

 1 0

and read it "all ${\displaystyle x^{\prime }}$ are ${\displaystyle y}$."

Two more remarks about Propositions need to be made.

One is that, in every Proposition beginning with "some" or "all", the actual existence of the 'Subject' is asserted. If, for instance, I say "all misers are selfish," I mean that misers actually exist. If I wished to avoid making this assertion, and merely to state the law that miserliness necessarily involves selfishness, I should say "no misers are unselfish" which does not assert that any misers exist at all, but merely that, if any did exist, they would be selfish.

The other is that, when a Proposition begins with "some" or "no", and contains more than two Attributes, these Attributes may be re-arranged, and shifted from one Term to the other, ad libitum. For example, "some ${\displaystyle abc}$ are ${\displaystyle def}$" may be re-arranged as "some ${\displaystyle bf}$ are ${\displaystyle acde}$," each being equivalent to "some Things are ${\displaystyle abcdef}$". Again "No wise old men are rash and reckless gamblers" may be re-arranged as "No rash old gamblers are wise and reckless," each being equivalent to "No men are wise old rash reckless gamblers."