October 26, 2009

Swallowing Elephants

Elephants always wear pink trousers.
Every creature that eats honey can play the bagpipes.
Anything that is easy to swallow eats honey.
No creature that wears pink trousers can play the bagpipes.

Therefore: Elephants are easy to swallow.

Is the deduction correct or not?


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  1. Simon

    No, elephants are not easy to swallow.

    Firstly, we can take these two statements

    Elephants always wear pink trousers.
    No creature that wears pink trousers can play the bagpipes.

    and deduce that

    Elephants can not play the bagpipes.

    If we then combine that with

    Every creature that eats honey can play the bagpipes.

    then we can deduce that

    Elephants do not eat honey

    and, seeing as

    Anything that is easy to swallow eats honey

    we can therefore deuce that

    Elephants are not easy to swallow.

    26 Oct 2009, 11:29

  2. David Buckley

    Or, more simply, the only swallowing related statment doesn’t imply anything is easy to swallow. So the combination of them can’t, either.

    That the statements actually imply the reverse isn’t something I bothered to deduce after that, though it’s perhaps interesting.

    26 Oct 2009, 11:36

  3. Simon Whitehouse

    Hi David

    But

    Anything that is easy to swallow eats honey

    So, if you could deduce that elephants eat honey then they would also be easy to swallow, surely?

    26 Oct 2009, 11:52

  4. David Buckley

    Nope. That statement says that (easy to swallow) implies (eats honey), but doesn’t say the reverse.

    To give a real-world example, people who are seeking employment can claim benefits. But some people cheat the system and can claim benefits anyway.

    (seeking employment) implies (can claim benefits), but this statement doesn’t tell you that the people who can claim benefits are seeking employment.

    26 Oct 2009, 12:17

  5. Simon Whitehouse

    slaps forehead

    Yes, of course. I shouldn’t have made that mistake and thanks for pointing it out.

    So, what I did was to deduce that elephants can’t be eaten easily when all I had to do was note that it couldn’t be deduced that any creature could be eaten easily.

    Taking the long way around as usual.

    26 Oct 2009, 13:23

  6. Eleanor Lovell

    Yes, the deduction is false.

    Suppose for the sake of argument that elephants are easy to swallow. Then the third statement in the puzzle tells us that elephants eat honey. The second then tells us that elephants can play the bagpipes. On the other hand, the first statement tells us that elephants wear pink trousers, in which case the fourth statement tells us that elephants can’t play the bagpipes. So we get a logical contradiction. The only way out is if elephants are not easy to swallow.

    There’s a systematic method for answering such questions as outlined by Prof Ian Stewart here:

    First, turn everything into symbols. Let

    E be the statement: “Is an elephant.”
    H be the statement: “Eats honey.”
    S be the statement: “Is easy to swallow.”
    P be the statement: “Wears pink trousers.”
    B be the statement: “Can play the bagpipes.”

    We use the logical symbols
    → meaning ‘implies’
    ¬ meaning ‘not’.

    Then the first four statements read:
    E → P
    H → B
    S → H
    P → ¬ B

    We need two of the mathematical laws of logic:

    X → Y is the same as ¬ Y → ¬ X
    If X → Y → Z, then X → Z

    Using these, we can rewwrite the conditions as:

    E → P → ¬ B → ¬ H → ¬ S

    So E → ¬ S. That is, elephants are not easy to swallow.

    This list of attributes suggests yet another way to get to the answer: think about an elephant (E) that (P) wears pink trousers, (¬ B) does not play the bagpipes, (¬ H) does not eat honey, and (¬ S) is not easy to swallow. Than all four statements in the puzzle are true, but ‘elephants are easy to swallow’ is false.

    27 Oct 2009, 11:16

  7. Vince Samios

    Funny – I tried to swallow an elephant once – and regardless of philosophical discussion – it didn’t work…

    http://vincesamios.com

    30 Oct 2009, 15:02


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