Page:Carroll - Game of Logic.djvu/47

§ 2.] any more than you can console a man, for having knocked down one of his chimneys, by giving him an extra door-step.

If you meet with Syllogisms of this kind, you may work them, quite easily, by the system I have given you: you have only to make 'are' mean 'are capable of being', and all will go smoothly. For "some $$x$$ are $y$" will become "some $$x$$ are capable of being $y$", that is, "the Attributes $x$, $$y$$ are compatible". And "no $$x$$ are $y$" will become "no $$x$$ are capable of being $y$", that is, "the Attributes $x$, $$y$$ are incompatible". And, of course, "all $$x$$ are $y$" will become "some $$x$$ are capable of being $y$, and none are capable of being $y^\prime$", that is, "the Attributes $x$, $$y$$ are compatible, and the Attributes $x$, $$y^\prime$$ are incompatible." In using the Diagrams for this system, you must understand a red counter to mean "there may possibly be something in this compartment," and a grey one to mean "there cannot possibly be anything in this compartment."