Card paradox

Abstract: The logicians of the Middle Ages called paradoxes “insolubilia” — unsolvable problems for rational logicians —, and for some paradoxes they were right. If, for example, we define an egoist as being a non-altruist and an altruist as being a non-egoist, we run into a paradoxical situation when we have to explain how egoists (non-altruists) can behave altruistically. This is in nuce the paradox of the Prisoner’s Dilemma. But what happens if we repeat or ‘iterate’ such a paradoxical situation? Jourdain’s iterated card paradox is an illustrative example. “On the face side of a card there is written a true statement.” However, if you turn the card over there will appear the words: “On the other side of this card is written a false statement”. If we rely on common sense or on our logic and suppose that the statement on the front side is true, then the statement on the back side must be true, too; but, as a rational consequence of supposing the later statement to be true — which the logicians call proof by reductio ad absurdum —, the statement on the front must now be false! If we now assume that the statement on the front of the card is false, then the statement on the back must be false, too, and hence the statement on the front must now be true! Thus it is our logic which rationally connects the statements on both sides of the card and makes truth dependent on falsehood and falsehood on truth etc., ad infinitum. As Hofstadter (1978: 78) would say, we are trapped on a Moebius strip or an Escher staircase (Kreuzer, 1986).