School Information System: Lewis Carroll logic puzzles

May 5, 2012

Lewis Carroll logic puzzles

I had another long plane flight recently, so I decided to try making another game, to explore exactly what types of mathematical reasoning might be amenable to gamification. I decided to start with one of the simplest types of logical argument (and one of the few that avoids the disjunction problem mentioned in the previous post), namely the Aristotelian logic of syllogistic reasoning, most famously exemplified by the classic syllogism:

Major premise: All men are mortal.

Minor premise: Socrates is a man.

Conclusion: Socrates is a mortal.

There is a classic collection of logic puzzles of Lewis Carroll (from his book on symbolic logic), in which he presents a set of premises and asks to derive a conclusion using all of the premises. Here are four examples of such sets:

Posted by Jim Zellmer at May 5, 2012 1:01 AM
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Comments

This puzzle reminds me of the wonderful logic puzzles in Raymond Smullyan's books, such as "What is the name of this book?" and "The Lady or the Tiger?". Smullyan even wrote a Lewis Carroll themed book called "Alice in Puzzle Land"

Posted by: Sudoku Man at May 10, 2012 8:02 PM

These classic collections from Lewis Carroll are cute but logically at least incomplete if not wrong. In order for most of these logic puzzles to be solved, there has to be a number of unstated premises made explicit before these puzzles can be solved.

It is critical to make explicit the unstated premises since these unstated premises might be conditional or just plain wrong.

For example, the first puzzle is missing premises that relate and define the words "babies", "nobody" and "persons".

Lewis Carroll's logic puzzles might be acceptable, and perhaps well-formed when he devised them, but the preciseness and understanding of logic has evolved considerably since that time.

Posted by: Larry Winkler at May 11, 2012 9:50 AM