Logic -- Juvenile literature; Logic, Symbolic and mathematical
No, my dear impulsive Reader, it is 'Universal'. Remember that,
few as they are (and I grant you they couldn't well be fewer),
they are (or rather 'it is') ALL that you have given me! Thus, if
(leaving 'red' out of the question) I divide my Universe of Cakes
into two classes--the Cakes you have given me (to which I assign
the upper half of the cupboard), and those you HAVEN'T given me
(which are to go below)--I find the lower half fairly full, and the
upper one as nearly as possible empty. And then, when I am told
to put an upright division into each half, keeping the NICE Cakes
to the left, and the NOT-NICE ones to the right, I begin by carefully
collecting ALL the Cakes you have given me (saying to myself, from
time to time, "Generous creature! How shall I ever repay such
kindness?"), and piling them up in the left-hand compartment. AND
IT DOESN'T TAKE LONG TO DO IT!
Here is another Universal Proposition for you. "Barzillai Beckalegg
is an honest man." That means "ALL the Barzillai Beckaleggs, that
I am now considering, are honest men." (You think I invented that
name, now don't you? But I didn't. It's on a carrier's cart,
somewhere down in Cornwall.)
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."
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Suppose we find it marked like this:-- | |
| 1 |
What would that tell us? | |
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| |
| |
| |
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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.
Public-domain text, read in full here on John Shaqi.
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