Complete Works of Lewis Carroll (145 page)

Similarly we may represent the seven similar Propositions “All
x
are
y
′
”, “All
x
′
are
y
”, “All
x
′
are
y
′
”, “All
y
are
x
”, “All
y
are
x
′
”, “All
y
′
are
x
”, and “All
y
′
are
x
′
”.

Let us take, lastly, the Double Proposition “Some
x
are
y
and some are
y
′
”, each part of which we already know how to represent.

Similarly we may represent the three similar Propositions, “Some
x
′
are
y
and some are
y
′
”, “Some
y
are
x
and some are
x
′
”, “Some
y
′
are
x
and some are
x
′
”.

The Reader should now get his genial friend to question him, severely, on these two Tables.
The
Inquisitor
should have the Tables before him: but the
Victim
should have nothing but a blank Diagram, and the Counters with which he is to represent the various Propositions named by his friend, e.g.
“Some
y
exist”, “No
y
′
are
x
”, “All
x
are
y
”, &c.
&c.

TABLE III.

  Some
xy
exist

   = Some
x
are
y

   = Some
y
are
x
  

  All
x
are
y
  

  Some
xy
′
exist

   = Some
x
are
y
′

   = Some
y
′
are
x
  

  All
x
are
y
′
  

  Some
x
′y
exist

   = Some
x
′
are
y

   = Some
y
are
x
′
  

  All
x
′
are
y
  

  Some
x
′y′
exist

   = Some
x
′
are
y
′

   = Some
y
′
are
x
′
  

  All
x
′
are
y
′
  

  No
xy
exist