# Page:Carroll - Game of Logic.djvu/47

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 ${\displaystyle x}$ are ${\displaystyle y}$" will become "some ${\displaystyle x}$ are capable of being ${\displaystyle y}$", that is, "the Attributes ${\displaystyle x}$, ${\displaystyle y}$ are compatible". And "no ${\displaystyle x}$ are ${\displaystyle y}$" will become "no ${\displaystyle x}$ are capable of being ${\displaystyle y}$", that is, "the Attributes ${\displaystyle x}$, ${\displaystyle y}$ are incompatible". And, of course, "all ${\displaystyle x}$ are ${\displaystyle y}$" will become "some ${\displaystyle x}$ are capable of being ${\displaystyle y}$, and none are capable of being ${\displaystyle y^{\prime }}$", that is, "the Attributes ${\displaystyle x}$, ${\displaystyle y}$ are compatible, and the Attributes ${\displaystyle x}$, ${\displaystyle y^{\prime }}$ 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."