Page:Carroll - Game of Logic.djvu/42

26
[Ch. I.
NEW LAMPS FOR OLD.

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

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

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