Lewis Carroll's Logic Game

Lewis Carroll's fame is universal. I can easily cite a couple dozen books that mention him or quote from his books. Temptation to quote from Alice's experiences with which so many people can identify, is indeed great. But the trend may be reversing. In the introduction to a book I have recently come across, the author found it necessary to mention that in the whole of the book there is not a single reference to either Alice in Wonderland or Through the Looking Glass - the two books that made the name of Lewis Carroll a household item the world over. However, his other works are either forgotten or known far less. In real life he was a mathematician C. L. Dodgson with deep interest in symbolic logic and logical reasoning. I have described elsewhere one of his probability and the doublets puzzles.

The next few pages will be devoted to his Logic Game, an invention that competes with a device for solving logical problems known by the name of Venn Diagrams - bequested to us by another otherwise very little known mathematician J. Venn. Naming of the diagrams after Venn is as universal as it is controversial. As a tool for solving logical puzzles, the diagrams become of little value with the number of conditions in access of 3-4. To Venn's credit it can be said that his research grew into a respectable branch of Combinatorial Mathematics of which you can learn from Internet references below. Lewis Carroll's Logic Game is all but forgotten.

I believe it was Serge Lang, a well known american mathematician, who once said that the best way to learn a new topic is to write a book about it. This was said long before the Web made Internet another household word. Otherwise, Lang, I believe, would agree that writing Web pages also provides a solid edifying experience. (Of course, this is only true if one takes Web page creation seriously.) So I decided that for me the best way to master Lewis Carroll's game is to write as I read. This page is the first step towards attaining mastery of Lewis Carroll's method. The plan is as follows:

• 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

References

1. L. Carroll, Symbolic Logic, Game of Logic, Dover, 1958
2. L. Carroll, Lewis Carroll's Symbolic Logic, Clarkson N. Porter, 1986
3. W. Dunham, The Mathematical Universe, John Wiley & Sons, NY, 1994.
4. M. Gardner, Mathematical Circus, Vintage Books, NY, 1981
5. M. Gardner, Logic Machines and Diagrams, The U. of Chicago Press, 1982
6. D. Pedoe, The Gentile Art of Mathematics, Dover, 1973

On Internet

1. A Survey of Venn Diagrams
   Very informative place with huge bibliography on the subject of Venn diagrams.
2. Eric W. Weisstein. "Venn Diagram." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/VennDiagram.html
3. A Proof of distributive law for sets using Venn diagrams