Sunday, November 18, 2012

The Paradox of the Swans

A wise man once observed that "All swans are white." is true if and only if "Things that are not white are not swans".

So one day, you see a green mini. That is a thing that is not white, and lo, it is not a swan.

So the green mini is evidence that things that are not white are not swans, and so it is evidence that all swans are white.

If you do not buy this argument, why do you believe that swans are white?


  1. I believe the usual form of this has black ravens rather than white swans. Since there notoriously are black swans, this may be a good thing.

    I shan't comment on the paradox itself for (I conjecture) the same reason as yours for not saying more: namely, that readers may prefer to think it through for themselves.

  2. Indeed the beloved Squeaky, sometime swan of Queen's College. Nevertheless, I will bet £1 of my own money against 1p of anyone else's that the first swan I see tomorrow will be white!

    Your conjecture is correct. People who want the answer can get it from me in person. My haunts are known.

  3. Or indeed from me; I conjecture (slightly less confidently than before) that the two of us would say extremely similar things.

  4. If I lived in a world where most objects I observed were white swans, and I went for days or years without seing anything else other than white swans, then seeing a green mini one day would indeed strengthen my belief that all swans are white.