| | |(.)| |
| Some x' are y, | |---|---| | Some y' are x | |---|---| |
| and some are y' | |(.)|(.)| | and some are x' | | |(.)| |
| | .-------. | | .-------. |
.-------------------------------------------------------------.

pg036

CHAPTER IV.

_INTERPRETATION OF BILITERAL DIAGRAM WHEN MARKED WITH COUNTERS._

The Diagram is supposed to be set before us, with certain Counters
placed upon it; and the problem is to find out what Proposition, or
Propositions, the Counters represent.

As the process is simply the reverse of that discussed in the previous
Chapter, we can avail ourselves of the results there obtained, as far as
they go.

First, let us suppose that we find a _Red_ Counter placed in the
North-West Cell.

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

We know that this represents each of the Trio of equivalent Propositions

"Some xy exist" = "Some x are y" = "Some y are x".

Similarly we may interpret a _Red_ Counter, when placed in the
North-East, or South-West, or South-East Cell.

Next, let us suppose that we find a _Grey_ Counter placed in the
North-West Cell.

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

We know that this represents each of the Trio of equivalent Propositions

"No xy exist" = "No x are y" = "No y are x".

Similarly we may interpret a _Grey_ Counter, when placed in the
North-East, or South-West, or South-East Cell.
pg037
Next, let us suppose that we find a _Red_ Counter placed on the
partition which divides the North Half.

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

We know that this represents the Proposition "Some x exist."

Similarly we may interpret a _Red_ Counter, when placed on the partition
which divides the South, or West, or East Half.

* * * * *

Next, let us suppose that we find _two Red_ Counters placed in the North
Half, one in each Cell.

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

We know that this represents the _Double_ Proposition "Some x are y and
some are y'".

Similarly we may interpret _two Red_ Counters, when placed in the South,
or West, or East Half.

* * * *