Martin Gardner was a kind of gateway drug. When I was a kid I went to the same secondary school that my dad taught at. That wasn’t a particular problem for me but it meant I had to hand around school until he was heading home.
This meant sitting in the school library by myself reading, which, being a bookish sort, was not any great hardship. I ploughed through the sci-fi books but on other occasions, I’d just look at random books. It was in this way I stumbled across old Penguin (or Pelican?) editions of Gardner’s Mathematical Puzzle’s and Diversions books. Now, I was not much of one for mathematics at the time but I liked puzzles and I liked the odd, arcane nature of these books.
As an older teen Gardner led me to other writers: Douglas Hofstadter (notably I read Metamagical Themas first then Godel, Escher, Bach) but also Raymond Smullyan.
Like Gardner, Smullyan combined a love of puzzles and magic but also the absurd. That logic and absurdity are natural companions is something that people find paradoxical. People think it odd that Lewis Carroll was both an eminent logician and author of Alice in Wonderland despite the absurdism of the Alice books often relying on wordplay and uncooperative literalism.
Smullyan, who died last Monday (Feb 6th 2017) tied absurdity more closely to logic in his complex puzzle books. The connection is overt – using weird settings and strange kinds of people (knights, vampires among others) with proscriptive approaches to communication. The New York times has a substantial sample here https://www.nytimes.com/interactive/2017/02/11/obituaries/smullyan-logic-puzzles.html
So why the close connection between the absurd and logic?
Two elements are at play. Firstly the necessary insistence on literalism. Exactly WHAT is being said? It is an insistence that when applied to normal conversation is a breach of normal social conventions. Secondly, the use of absurd or nonsensical propositions and conclusions helps highlight FORMAL aspects of an argument from informal and empirical aspects. To see how a syllogism functions (for example) it can be misleading to use a string of commonplace truths.
For example, Wikipedia uses this example for Felapton:
No flowers are animals. All flowers are plants. ∴ Some plants are not animals. (SoP)
But to see the formal connection writers like Carroll might use more odd juxtapositions
No elephants are professors. All elephants are stamp collectors. ∴ Some stamp collectors are not professors.
Formal truths need to hold even in absurd worlds.
Smullyan wrote a whole bunch of wonderfully weird books, that used puzzles and odd juxtapositions to exemplify logic and reasoning. I think his most substantial achievement was Forever Undecided: A Puzzle Guide to Godel that used his signature style to lead the reader to Godel’s incompleteness theorems in a charmingly accessible manner.
Logician, Taoist, Magician – a 97 year life of tricks, puzzles and deep thoughts.