Portal 2 Spoiler-Free Easter Egg

Posted by on Friday, 22nd April, 2011

As I made my way through Portal 2, I came across this amusing sign (click for full-size image):

I was especially excited by the last line, because it is a reference to Russell’s Paradox, discovered by the British mathematician and logician Bertrand Russell in 1901.

Think of it this way: Suppose someone gave you a catalogue about catalogues, called SuperMegaCatalogue, that contained every cataglogue that had ever been printed. Would SuperMegaCatalogue be featured in the pages of SuperMegaCatalogue?

As the Wikipedia page puts it:

Let R be the set of all sets that are not members of themselves. If R qualifies as a member of itself, it would contradict its own definition as a set containing all sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition.

Or, to use the terms of symbolic logic:

So now the question is: Who’s more nerdy? The Portal 2 team, for including Russell’s Paradox in the game — or me, for spotting it and pointing it out to everyone else?

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11 Comments

  1. skulduggerer says:

    Check out this L4D2 / Portal2 Mod. Awesome!

    http://www.youtube.com/watch?feature=player_embedded&v=0mE94ocfx9k

  2. DukeSkath says:

    FF: Yes, you’re correct that the P2 sign isn’t a technically accurate representation of the paradox.

    But as I said on Reddit: I think they just wanted to throw a fun reference to Russell into the game. I worry that some people are reading too much into this.

  3. FishFace says:

    Unfortunately, this is not Russell’s paradox, which says “Does the set of all sets *which do not contain themselves* contain itself”?

  4. woody says:

    Gonna look into this it looks quite interesting.

  5. DukeSkath says:

    Woody: I suck at maths, but I’m really interested in philosophy.

    I highly recommend the book Logicomix. It gives a superb overview of Russell’s life and work. (It goes a bit too far with the story-within-a-story-within-a-story thing, but it’s an excellent read.)

  6. Chrismjw says:

    I think theres plenty enough nerd there for both of you.

  7. TheDaddy says:

    Definately you ya geek lol, really though nice spot, and just goes to show how far Valve go to build a world, it’s a bit like the hidden stuff in the original Portal

  8. woody says:

    How’d you know about that Duke? I have a passing interest in theoretical physics but havent heard of that one that i can remember. I suppose thats maths And I have a black hole in my memory where A level maths used to be.

  9. thejcmyster says:

    Definately youre the nerdy one for spotting it! I bet the portal team where just adding in random technical sounding words and it was a coincidence!

  10. Hea7hen says:

    Nice spot Duke, Bertrand Russell – one of Britains great thinkers, some of his essays are downloadable on itunes and are a thought provoking read indeed.

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