Page:Carroll - Game of Logic.djvu/74

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[Ch. III.
found written at three of the corners of the compartment (except in the case of ${\displaystyle m^{\prime }}$, which is not actually inserted in the Diagram, but is supposed to stand at each of its four outer corners).
22. If the Universe of Things be divided with regard to three different Attributes; and if two Propositions be given, containing two different couples of these Attributes; and if from these we can prove a third Proposition, containing the two Attributes that have not yet occurred together; the given Propositions are called 'the Premisses', the third one 'the Conclusion', and the whole set 'a Syllogism'. For example, the Premisses might be "no ${\displaystyle m}$ are ${\displaystyle x^{\prime }}$" and "all ${\displaystyle m^{\prime }}$ are ${\displaystyle y}$"; and it might be possible to prove from them a Conclusion containing ${\displaystyle x}$ and ${\displaystyle y}$.
23. If an Attribute occurs in both Premisses, the Term containing it is called 'the Middle Term'. For example, if the Premisses are "some ${\displaystyle m}$ are ${\displaystyle x}$" and "no ${\displaystyle m}$ are ${\displaystyle y^{\prime }}$", the class of "${\displaystyle m}$-Things" is 'the Middle Term.'
If an Attribute occurs in one Premiss, and its contradictory in the other, the Terms containing them may be called 'the Middle Terms'. For example, if the Premisses are "no ${\displaystyle m}$ are ${\displaystyle x^{\prime }}$" and "all ${\displaystyle m^{\prime }}$ are ${\displaystyle y}$", the two classes of "${\displaystyle m}$-Things" and "${\displaystyle m^{\prime }}$-Things" may be called 'the Middle Terms'.