The Game of Logic | Page 6

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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."
In the same way
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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.)
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:-- | |
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What would that tell us? | |
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