Black and White Thinking: The burden of a binary brain in a complex world

by Professor Kevin Dutton

Warren Quinn brought Eubulides and Weber face to face in a fiendishly ingenious paradox every bit the equal to Sorites: the Paradox of the Self-Torturer. Imagine that I have a portable device that enables me to apply an electrical current to your body in increments so tiny that you are unable to feel them. The device has 1001 settings: 0, which is ‘off’, and then 1 to 1,000 (excruciating pain). Now suppose that I attach you to the device with the dial initially set at 0 and offer you the following deal. You may keep the device for as long as you wish on one condition: that you turn up the dial just one single notch each week. For each turn of the dial you will receive £10,000 but you can never undo a turn and revert to an earlier setting. Finally, here’s the kicker. If, eventually, you find the pain too much to endure, you are nevertheless unable to relinquish the fortune that you have accrued and must continue to suffer the anguish for the rest of your life. Would you take me up on the challenge? You can see how the problem arises. ‘Reality’ tells you you’d have to be barking mad; that it will end, quite literally, in tears. On the other hand, however, Sorites casts its spell. No matter how many notches you ratchet up the dial, those grains of pain will never make a heap.