The Game of Logic | Page 3

WHOLE of their Subjects--the one denying niceness, and the other
asserting it, of the WHOLE class of "new Cakes". Lastly, if you would
like to have a definition of the word 'PROPOSITION' itself, you may
take this:--"a sentence stating that some, or none, or all, of the Things
belonging to a certain class, called its 'Subject', are also Things
belonging to a certain other class, called its 'Predicate'".
You will find these seven words--PROPOSITION, ATTRIBUTE,
TERM, SUBJECT, PREDICATE, PARTICULAR,
UNIVERSAL--charmingly useful, if any friend should happen to ask if
you have ever studied Logic. Mind you bring all seven words into your
answer, and you friend will go away deeply impressed--'a sadder and a
wiser man'.
Now please to look at the smaller Diagram on the Board, and suppose it
to be a cupboard, intended for all the Cakes in the world (it would have
to be a good large one, of course). And let us suppose all the new ones
to be put into the upper half (marked 'x'), and all the rest (that is, the
NOT-new ones) into the lower half (marked 'x''). Thus the lower half
would contain ELDERLY Cakes, AGED Cakes, ANTE-DILUVIAN
Cakes--if there are any: I haven't seen many, myself--and so on. Let us
also suppose all the nice Cakes to be put into the left-hand half (marked

'y'), and all the rest (that is, the not-nice ones) into the right-hand half
(marked 'y''). At present, then, we must understand x to mean "new", x'
"not-new", y "nice", and y' "not-nice."
And now what kind of Cakes would you expect to find in compartment
No. 5?
It is part of the upper half, you see; so that, if it has any Cakes in it,
they must be NEW: and it is part of the left-hand half; so that they must
be NICE. Hence if there are any Cakes in this compartment, they must
have the double 'ATTRIBUTE' "new and nice": or, if we use letters, the
must be "x y."
Observe that the letters x, y are written on two of the edges of this
compartment. This you will find a very convenient rule for knowing
what Attributes belong to the Things in any compartment. Take No. 7,
for instance. If there are any Cakes there, they must be "x' y", that is,
they must be "not-new and nice."
Now let us make another agreement--that a red counter in a
compartment shall mean that it is 'OCCUPIED', that is, that there are
SOME Cakes in it. (The word 'some,' in Logic, means 'one or more' so
that a single Cake in a compartment would be quite enough reason for
saying "there are SOME Cakes here"). Also let us agree that a grey
counter in a compartment shall mean that it is 'EMPTY', that is that
there are NO Cakes in it. In the following Diagrams, I shall put '1'
(meaning 'one or more') where you are to put a RED counter, and '0'
(meaning 'none') where you are to put a GREY one.
As the Subject of our Proposition is to be "new Cakes", we are only
concerned, at present, with the UPPER half of the cupboard, where all
the Cakes have the attribute x, that is, "new."
Now, fixing our attention on this upper half, suppose we found it
marked like this,
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| 1 | |
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that is, with a red counter in No. 5. What would this tell us, with regard
to the class of "new Cakes"?
Would it not tell us that there are SOME of them in the x
y-compartment? That is, that some of them (besides having the
Attribute x, which belongs to both compartments) have the Attribute y
(that is, "nice"). This we might express by saying "some x-Cakes are
y-(Cakes)", or, putting words instead of letters,
"Some new Cakes are nice (Cakes)",
or, in a shorter form,
"Some new Cakes are nice".
At last we have found out how to represent the first Proposition of this
Section. If you