|
.-------.

[In the "books" example, this Proposition would be "No old
English books exist".]

Similarly we may represent the three similar Propositions "No xy'
exist", "No x'y exist", and "No x'y' exist".

[The Reader should make out all these for himself. In the
"books" example, these three Propositions would be "No old
foreign books exist", &c.]
pg030
We have seen that the Proposition "No x exist" may be represented by
placing _two Grey_ Counters in the North Half, one in each Cell.

.-------.
|( )|( )|
|---|---|
| | |
.-------.

We have also seen that these two _Grey_ Counters, taken _separately_,
represent the two Propositions "No xy exist" and "No xy' exist".

Hence we see that the Proposition "No x exist" is a _Double_
Proposition, and is equivalent to the _two_ Propositions "No xy exist"
and "No xy' exist".

[In the "books" example, this Proposition would be "No old books
exist".

Hence this is a _Double_ Proposition, and is equivalent to the
_two_ Propositions "No old _English_ books exist" and "No old
_foreign_ books exist".]

Sec. 3.

_Representation of Propositions of Relation._

Let us take, first, the Proposition "Some x are y".

This tells us that at least _one_ Thing, in the _North_ Half, is also in
the _West_ Half. Hence it must be in the space _common_ to them, that
is, in the _North-West Cell_. Hence the North-West Cell is _occupied_.
And this we can represent by placing a _Red_ Counter in it.

.-------.
|(.)| |
|---|---|
| | |
.-------.

[Note that the _Subject_ of the Proposition settles which _Half_
we are to use; and that the _Predicate_ settles in which
_portion_ of it we are to place the Red Counter.

In the "books" example, this Proposition would be "Some old
books are English".]

Similarly we may represent the three similar Propositions "Some x are
y'", "Some x' are y", and "Some x' are y'".

[The Reader should make out all these for himself. In the
"books" example, these three Propositions would be "Some old
books are foreign", &c.]
pg031
Let us take, next, the Proposition "Some y are x".

This tells us that at least _one_ Thing, in the _West_ Half, is also in
the _North_ Half. Hence it must be in the