# Page:Carroll - Game of Logic.djvu/93

§ 7.]
77
BOTH DIAGRAMS EMPLOYED.
1.  1 0
 1

Let "periods" be Universe; ${\displaystyle m}$ = "days"; ${\displaystyle x}$ = "rainy"; ${\displaystyle y}$ = "tiresome".

 Some ${\displaystyle m}$ are ${\displaystyle x}$; All ${\displaystyle xm}$ are ${\displaystyle y}$. ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ ∴ Some ${\displaystyle x}$ are ${\displaystyle y}$.

i.e. Some rainy periods are tiresome.

N.B. These are not legitimate Premisses, since the Conclusion is really part of the second Premiss, so that the first Premiss is superfluous. This may be shown, in letters, thus:—

"All ${\displaystyle xm}$ are ${\displaystyle y}$" contains "Some ${\displaystyle xm}$ are ${\displaystyle y}$", which contains "Some ${\displaystyle x}$ are ${\displaystyle y}$". Or, in words, "All rainy days are tiresome" contains "Some rainy days are tiresome", which contains "Some rainy periods are tiresome".

Moreover, the first Premiss, besides being superfluous, is actually contained in the second; since it is equivalent to "Some rainy days exist", which, as we know, is implied in the Proposition "All rainy days are tiresome".

Altogether, a most unsatisfactory Pair of Premisses!

[See p. 53]