Monday, 7 November 2016

Xavier and the Queen of Hearts

Xavier sits at a card table, across from Derren Brown.  Xavier has been asked to bring with him a brand new deck of cards, which has placed on the table.  Derren opens the pack, removes the jokers, and begins shuffling the deck.  Then he hands over the deck to Xavier and encourages him to inspect it to make sure that it's the same deck he brought and that it's a fair deck, with 52 different cards in it.

Xavier confirms that it's a fair deck.  Derren then asks Xavier to continue shuffling the pack, face down until he is happy that it's thoroughly blended.  Then Xavier is asked to cut the deck, and deal himself two cards, one face up and one face down.  Xavier is instructed to throw the rest of the deck behind him, away from the table, which he does.  Derren clarified that any card on the table or in Xavier's possession belongs to Xavier.

The card that is face up is the Queen of Hearts.  Call this Card A, and the face down card Card B.

Derren asks Xavier whether he believes that he owns the Queen of Hearts, to which Xavier says "yes".  When asked why, Xavier points to Card A and says "because I can see it right there - Card A is the Queen of Hearts".

Derren then asks Xavier to flip Card A over so it is face down, he points out that the cards on the table belong and asks whether he believes that he owns a Hearts card.  Xavier says "yes" and when asked why, says "because the Queen of Hearts is a Hearts card and Card A is the Queen of Hearts.  It's just there!"

Derren pulls his sleeves up, revealing his forearms, and asks Xavier to watch very carefully.  Then he takes a piece of wrapping paper, slips it carefully under Card B, making sure not to touch it with his fingers.  Then he gets some tape and asks Xavier to fold the wrapping paper over the card.  A few folds later and the card is securely wrapped.  Neither Darren nor Xavier has no idea what the face value of Card B is and the wrapping paper is thick enough to prevent either from seeing though it.

Derren now scoops up Card B, leans over and deposits it in Xavier's top pocket.  So, Card A is on the table and Card B is in Xavier's pocket.  Xavier owns both cards.

Now Derren asks whether Xavier believes that he owns a royal card.  Xavier says "yes" and when asked why, clarifies that the Queen of Hearts is a royal card and Card A (right there) is the Queen of Hearts.

At this point, Derren casually flips over Card A, revealing that it isn't the Queen of Hearts after all, but rather the Seven of Clubs.


This article is about a question of belief.

My position is that Xavier believed that he had the Queen of Hearts.  When prompted he assented to the notion that he believed that he owned a Hearts card, however, he didn't simply believe that he owned any old Hearts card, he believed that he owned the Queen of Hearts, which happens to be a Hearts card.  When asked about owning a royal card, he responded in the affirmative, but in reality he believed that he owned the Queen of Hearts, which happens to be a royal card.

Derren used the distraction, while putting Card B into Xavier's top pocket, to switch out the Queen of Hearts with the Four of Clubs which he had palmed earlier, during the initial shuffle.

The question revolves around Card B.  Nobody knows what that card is, not even Derren.  It could be a royal card.  If it is a royal card, noting that Xavier owns it, does this make his assent to the notion "Xavier owns a royal card" a true belief, if when asked he no longer owns the Queen of Hearts?

I don't think so, because I don't think that Xavier ever has a partially formed belief that he owns a royal card.  He very specifically believes that he owns the Queen of Hearts, which is a royal card.

Strangely enough, some people don't think this way.  They think that if Card B was, say, the Queen of Spades, then Xavier would have had a true belief that he owned a royal card, despite having a false belief that he owned the Queen of Hearts.

What do you believe?

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