Page:Carroll - Game of Logic.djvu/36

 Now suppose we divide our Universe of Things in three ways, with regard to three different Attributes. Out of these three Attributes, we may make up three different couples (for instance, if they were $$a$$, $$b$$, $$c$$, we might make up the three couples $$ab$$, $$ac$$, $$bc$$). Also suppose we have two Propositions given us, containing two of these three couples, and that from them we can prove a third Proposition containing the third couple. (For example, if we divide our Universe for $$m$$, $$x$$, and $$y$$ ; and if we have the two Propositions given us, "no $$m$$ are $$x^\prime$$" and "all $$m^\prime$$ are $$y$$", containing the two couples $$mx$$ and $$my$$, it might be possible to prove from them a third Proposition, containing $$x$$ and $$y$$.)

In such a case we call the given Propositions &apos;the Premisses&apos;, the third one &apos;the Conclusion&apos; and the whole set &apos;a Syllogism&apos;.

Evidently, one of the Attributes must occur in both Premisses; or else one must occur in one Premiss, and its contradictory in the other.