*Project Gutenberg*. Public domain.

This kind of Universal Proposition (where the Subject
is a single Thing) is called an ‘*individual*’
Proposition.

Now let us take “*Nice* Cakes” as the
Subject of Proposition: that is, let us fix our
thoughts on the *left*-*hand* half of the cupboard,
where all the Cakes have attribute y, that is, “nice.”

----- Suppose we find it marked like this:-- | | | 1 | What would that tell us? | | ----- | | | | | | -----

I hope that it is not necessary, after explaining
the *horizontal* oblong so fully, to spend much
time over the *upright* one. I hope you will
see, for yourself, that this means “some y are
x”, that is,

“Some nice Cakes are new.”

“But,” you will say, “we have had
this case before. You put a red counter into
No. 5, and you told us it meant ’some new Cakes
are nice’; and *now* you tell us that it
means ‘some *nice* Cakes are *new*’!
Can it mean *both*?”

The question is a very thoughtful one, and does you
*great* credit, dear Reader! It *does*
mean both. If you choose to take x (that is,
“new Cakes”) as your Subject, and to regard
No. 5 as part of a *horizontal* oblong, you may
read it “some x are y”, that is, “some
new Cakes are nice”: but, if you choose
to take y (that is, “nice Cake”) as your
Subject, and to regard No. 5 as part of an *upright*
oblong, *then* you may read it “some y are
x”, that is, “some nice Cakes are new”.
They are merely two different ways of expressing
the very same truth.

Without more words, I will simply set down the other ways in which this upright oblong might be marked, adding the meaning in each case. By comparing them with the various cases of the horizontal oblong, you will, I hope, be able to understand them clearly.

You will find it a good plan to examine yourself on this table, by covering up first one column and then the other, and ’dodging about’, as the children say.

Also you will do well to write out for yourself two
other tables—one for the *lower* half
of the cupboard, and the other for its *right*-*hand*
half.

And now I think we have said all we need to say about the smaller Diagram, and may go on to the larger one.

_________________________________________________ | Symbols. | Meanings. _______________|_________________________________ ----- | | | | | | | Some y are x’; | | |i.e. Some nice are not-new. ----- | | | | | 1 | | | | | ----- | | ----- | | | | No y are x; | 0 | |i.e. No nice are new. | | | ----- | [Observe that this is merely another way of | | | expressing “No new are nice.”] | | | | | | ----- | | ----- | | | | | | | No y are x’;