Bilateral Diagrams

The meaning of the diagrams below has been explained elsewhere. Here I only collected the simplest configurations for the reference sake.

Some x exist  No x exist
Some x' exist  No x' exist
Some y exist  No y exist
Some y' exist  No y' exist
Some xy exist
   = Some x are y
   = Some y are x
  No xy exist
   = No x are y
   = No y are x
Some x'y exist
   = Some x' are y
   = Some y are x'
  No x'y exist
   = No x' are y
   = No y are x'
Some x'y' exist
   = Some x' are y'
   = Some y' are x'
  No x'y' exist
   = No x' are y'
   = No y' are x'
Some xy' exist
   = Some x are y'
   = Some y' are x
  No xy' exist
   = No x are y'
   = No y' are x
All x are y  All x are y'
All x' are y  All x' are y'
All y are x exist  All y are x'
All y' are x  All y' are x'
Some x are y,
some are y'
  Some x' are y,
some are y'
Some y are x,
some are x'
  Some y' are x,
some are x'

Lewis Carroll

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