Symbolic Logic Part I was published in 1896. When Lewis Carroll (Charles Lutwidge Dodgson) died two years later, Part II was lost. Because they couldn’t find the manuscript, many people doubted that he ever wrote Part II. But almost eighty years after his death, portions of Part II were recovered and finally published. The following puzzles are from the combined volume, Lewis Carroll’s Symbolic Logic, edited by William Warren Bartley, III.
These puzzles are called soriteses or polysyllogisms. Carroll began with a series of “if this, then that” statements. He rewrote them to make them more confusing, and then he mixed up the order to create a challenging puzzle.
Given each set of premises, what conclusion can you reach?
The Teachable Kittens
- No kitten that loves fish is unteachable.
- No kitten without a tail will play with a gorilla.
- Kittens with whiskers always love fish.
- No teachable kitten has green eyes.
- No kittens have tails unless they have whiskers.
The Donkey and the Buffalo
- Animals that do not kick are always unexcitable.
- Donkeys have no horns.
- A buffalo can always toss one over a gate.
- No animals that kick are easy to swallow.
- No hornless animal can toss one over a gate.
- All animals are excitable, except buffalo.
The Circus Pigs
- All who neither dance on tightropes nor eat penny-buns, are old.
- Pigs that are liable to giddiness are treated with respect.
- A wise balloonist takes an umbrella with him.
- No one ought to lunch in public, who looks ridiculous and eats penny-buns.
- Young creatures who go up in balloons are liable to giddiness.
- Fat creatures who look ridiculous may lunch in public, provided they do not dance on tightropes.
- No wise creatures dance on tightropes, if liable to giddiness.
- A pig looks ridiculous carrying an umbrella.
- All who do not dance on tightropes, and who are treated with respect, are fat.
For more of Lewis Carroll’s mathematical recreations, games, puzzles, and word play, ask your librarian about The Universe in a Handkerchief by Martin Gardner.
To Be Continued…
Read all the posts from the September/October 1999 issue of my Mathematical Adventures of Alexandria Jones newsletter.
Denise Gaskins' Let's Play Math 
Here is an introduction into Lewis Carroll’s Game of Logic:
http://www.cut-the-knot.org/LewisCarroll/index.shtml
Lewis Carroll developed two kinds of diagrams – bilateral and trilateral – as the tools for solving soriteses. Find at the above url Java implementations of the diagrams and the game itself.
The textbook by Hurley reprints about a dozen of the Lewis Carrol sorites. I don’t remember if all his officers are poultry, or if none are, and if no terriers wander the heavens, of if nothing that wanders the heavens is a terrier. In any case, all good fun and mildly challenging.
Jonathan