# Page:Carroll - Game of Logic.djvu/44

28
[Ch. I.
NEW LAMPS FOR OLD.

And now how much of this information can usefully be transferred to the smaller Diagram?

Let us take its four compartments, one by one.

As to No. 5? This, we see, is wholly 'empty'. (So mark it with a grey counter.)

As to No. 6? This, we see, is 'occupied'. (So mark it with a red counter.)

As to No. 7? Ditto, ditto.

As to No. 8? No information.

The smaller Diagram is now pretty liberally marked:—

 0 1 1

And now what Conclusion can we read off from this? Well, it is impossible to pack such abundant information into one Proposition: we shall have to indulge in two, this time.

First, by taking ${\displaystyle x}$ as Subject, we get "all ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$", that is,

"All Dragons are not-Scotchmen":

secondly, by taking ${\displaystyle y}$ as Subject, we get "all ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$", that is,

"All Scotchmen are not-Dragons".

Let us now write out, all together, our two Premisses and our brace of Conclusions.