Page:Carroll - Game of Logic.djvu/21

§1.] of the left-hand half; so that they must be nice. Hence if there are any Cakes in this compartment, they must have the double &apos;Attribute&apos; "new and nice": or, if we use letters, they must be "$x y$."

Observe that the letters $$x$$, $$y$$ are written on two of the edges of this compartment. This you will find a very convenient rule for knowing what Attributes belong to the Things in any compartment. Take No. 7, for instance. If there are any Cakes there, they must be "$x^\prime y$", that is, they must be "not-new and nice."

Now let us make another agreementthat a red counter in a compartment shall mean that it is &apos;occupied&apos;, that is, that there are some Cakes in it. (The word 'some,' in Logic, means 'one or more': so that a single Cake in a compartment would be quite enough reason for saying "there are some Cakes here"). Also let us agree that a grey counter in a compartment shall mean that it is &apos;empty&apos;, that is, that there are no Cakes in it. In the following Diagrams, I shall put '1' (meaning 'one or more') where you are to put a red counter, and '0' (meaning 'none') where you are to put a grey one.

As the Subject of our Proposition is to be "new Cakes", we are only concerned, at present, with the upper half of the cupboard, where all the Cakes have the attribute $$x$$, that is, "new."