Complete Works of Lewis Carroll (145 page)

BOOK: Complete Works of Lewis Carroll
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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

BOOK: Complete Works of Lewis Carroll
3.21Mb size Format: txt, pdf, ePub
ads

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