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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 as
their two parties ‘Democrats’ and ’Republicans’—but
can’t make up his mind which. Such
a man is said to be “sitting on the fence.”
Now that is exactly the position of the red counter
you have just placed on the division-line. He
likes the look of No. 5, and he likes the look of
No. 6, and he doesn’t know which to jump
down into. So there he sits astride, silly fellow,
dangling his legs, one on each side of the fence!
Now I am going to give you a much harder one to make
out. What does this mean?
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This is clearly a double Proposition. It
tells us not only that “some x are y,”
but also the “no x are not y.”
Hence the result is “All x are y,”
i.e. “all new Cakes are nice”, which
is the last of the three Propositions at the head
of this Section.
We see, then, that the Universal Proposition
“All new Cakes are nice”
consists of two Propositions taken together,
namely,
“Some new Cakes
are nice,”
and “No new Cakes are not-nice.”
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would mean “all x are y’ “, that
is,
“All new Cakes are not-nice.”
Now what would you make of such a Proposition as “The
Cake you have given me is nice”? Is it
Particular or Universal?
“Particular, of course,” you readily reply.
“One single Cake is hardly worth calling ‘some,’
even.”
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.)
