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'

• Introduction
• Controversial Venn Diagrams
  • From K.Devlin, MATHEMATICS: The Science of Patterns
  • From W.Dunham, The Mathematical Universe
  • Venn Diagrams applet I
  • Venn Diagrams applet II
• Bilateral Diagrams
  • Interpretation of Bilateral diagrams
  • Bilateral diagrams applet
• Syllogisms
• Trilateral Diagrams
  • Interpretation of Trilateral diagrams
  • Trilateral diagrams applet
• Sample soriteses
• The Game

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