and both each control a switch. There are wires going from an electricity A B source to these switches and then continuing on to must first decide whether C. A to flip his switch left or right, then must decide The B (knowing A’s choice). current flows, resulting in a bulb at turning on, iff both switches are in the same C position. wants to turn on the bulb, so flips her switch to the same position as B A does, and the bulb turns on. (100) Schematically: = = 1; C = 1 iff = B A A B Figure 3. Light Switch Halpern claims suggests that actions should not be viewed as a cause of the C bulb “intuition A’s being on, We cannot achieve this result with the modified HP whereas B’s should” (100). definition alone. If we hold B constant at its actual value (1) and intervene on A, we get A is a cause. Similarly for B. So we obtain both A and B as actual causes of the outcome. Looking to the original approach to normality, we get no to be the context where = 1, both u A help. “Taking [A = 0, 1, and [B 0, seem less normal than and there seems to be no reason to B = u] = u] u, prefer one to the other, so graded causality does not help in determining a The third cause” (101). approach also fails. for the alternative approach, both [[A = 0 ^ B = 1 ^ C = 0]] and “Similarly, [[B = 0 ^ C = 0]] are less normal than either [[A = 1 ^ C = 1]] or [[B = 1 ^ C = 1]]. Again, there is no reason to prefer B = 1 as a (101). So concludes that his previous cause.” Halpern’s approaches to incorporating normality offer no help in this scenario.
A and B both each control a switch. There are wires going from an electricity source to these switches and then continuing on to C. A must first decide whether to flip his switch left or right, then B must decide (knowing A’s choice). The current flows, resulting in a bulb at C turning on, iff both switches are in the same position. B wants to turn on the bulb, so flips her switch to the same position as A does, and the bulb turns on. (100) Schematically: B = A = 1; C = 1 iff A = B Figure 3. Light Switch Halpern claims “intuition suggests that A’s actions should not be viewed as a cause of the C bulb being on, whereas B’s should” (100). We cannot achieve this result with the modified HP definition alone. If we hold B constant at its actual value (1) and intervene on A, we get A is a cause. Similarly for B. So we obtain both A and B as actual causes of the outcome. Looking to the original approach to normality, we get no help. “Taking u to be the context where A = 1, both [A = 0, B = 1, u] and [B = 0, u] seem less normal than u, and there seems to be no reason to prefer one to the other, so graded causality does not help in determining a cause” (101). The third approach also fails. “Similarly, for the alternative approach, both [[A = 0 ^ B = 1 ^ C = 0]] and [[B = 0 ^ C = 0]] are less normal than either [[A = 1 ^ C = 1]] or [[B = 1 ^ C = 1]]. Again, there is no reason to prefer B = 1 as a cause.” (101). So Halpern’s concludes that his previous approaches to incorporating normality offer no help in this scenario.
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