Page:Carroll - Game of Logic.djvu/42

tribute belonging to the 'Middle Terms', we will let $m$ stand for "canny",$x$ for "Dragons", and $y$ for "Scotchmen". So that our two Premisses are, in full,

"All Dragon-Animals are uncanny (Animals);	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$
All Scotchman-Animals are canny (Animals)."

And these may be expressed, using letters for words, thus:

"All $x$ are $m^{\prime }$;	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$
All $y$ are $m$."

The first Premiss consists, as you already know, of two parts:

"Some $x$ are $m^{\prime }$,"

and "No $x$ are $m$."

And the second also consists of two parts:

Some $y$ are $m$,"

and "No $y$ are $m^{\prime }$."

Let us take the negative portions first.

We have, then, to mark, on the larger Diagram, first, "no $x$ are $m$", and secondly, "no $y$ are $m^{\prime }$". I think you will see, without further explanation, that the two results, separately, are

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