The Game of Logic | Page 5

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would mean "no x are y'," or, "no new Cakes are not-nice."
What would you make of this, I wonder?

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I hope you will not have much trouble in making out that this
represents a DOUBLE Proposition: namely, "some x are y, AND some
are y'," i.e. "some new are nice, and some are not-nice."
The following is a little harder, perhaps:
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This means "no x are y, AND none are y'," i.e. "no new are nice, AND
none are not-nice": which leads to the rather curious result that "no new
exist," i.e. "no Cakes are new." This is because "nice" and "not-nice"
make what we call an 'EXHAUSTIVE' division of the class "new
Cakes": i.e. between them, they EXAUST the whole class, so that all
the new Cakes, that exist, must be found in one or the other of them.
And now suppose you had to represent, with counters the contradictory
to "no Cakes are new", which would be "some Cakes are new", or,
putting letters for words, "some Cakes are x", how would you do it?
This will puzzle you a little, I expect. Evidently you must put a red
counter SOMEWHERE in the x-half of the cupboard, since you know
there are SOME new Cakes. But you must not put it into the
LEFT-HAND compartment, since you do not know them to be NICE:
nor may you put it into the RIGHT-HAND one, since you do not know
them to be NOT-NICE.
What, then, are you to do? I think the best way out of the difficulty is to
place the red counter ON THE DIVISION-LINE between the
xy-compartment and the xy'-compartment. This I shall represent (as I

always put '1' where you are to put a red counter) by the diagram
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Our ingenious American cousins have invented a phrase to express the
position of a man who wants to join one or the other of two
parties--such