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’;