Page:Carroll - Game of Logic.djvu/37

In the first case (when, for example, the Premisses are "some $m$ are $x$" and "no $m$ are $y^{\prime }$") the Term, which occurs twice, is called 'the Middle Term', because it serves as a sort of link between the other two Terms.

In the second case (when, for example, the Premisses are "no $m$ are $x^{\prime }$" and "all $m^{\prime }$ are $y$") the two Terms, which contain these contradictory Attributes, may be called 'the Middle Terms'.

Thus, in the first case, the class of "$m$-Things" is the Middle Term; and, in the second case, the two classes of "$m$-Things" and "$m^{\prime }$-Things" are the Middle Terms.

The Attribute, which occurs in the Middle Term or Terms, disappears in the Conclusion, and is said to be "eliminated", which literally means "turned out of doors".

Now let us try to draw a Conclusion from the two Premisses—

"Some new Cakes are unwholesome;	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$
No nice Cakes are unwholesome."

In order to express them with counters, we need to divide Cakes in three different ways, with regard to newness, to niceness, and to wholesomeness. For this we must use the larger Diagram, making $x$ mean "new", $y$ "nice", and $m$ "wholesome". (Everything