Lewis Carroll's Game of Logic

In the preface to his Game of Logic Lewis Carroll remarked:

In the applet below, the number of counters is limitless while, since you are reading this page, you have a chance to become a Player. The device is supposed to help you solve sorites problems. The applet consists of two parts: 12 trilateral diagrams and 3 diagrams. There is a check box at the bottom of the applet that pops up bilateral diagrams' window. That window is associated with a selected trilateral diagram. You may cycle through the latter by clicking "<" and ">" buttons. Trilateral diagrams have three attributes: horizontal, vertical, and inner denoted as x/x', y/y', and m/m'. In the bilateral diagram window you can give these attributes arbitrary names: type them in and press "Enter." The first bilateral diagram is used to define a statement with two attributes: x and m. The second should related y and m. For the applet to work, the two premises must be defined in such a way as to have eliminands twice as vertical attributes according to the diagram:

If you manage to do that, these two will serve as premises of a syllogism whose conclusion (if any) will by displayed in the third diagram.

The process is reflected in the trilateral diagrams. For example, this is how they look like for the sample sorites:

With the applet, it's easy to see that on the last step we might have drawn a stronger conclusion, viz., all b are c'. Please try other examples.

• 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