## Thursday, September 3, 2015

### Thomson's lamp and two counterfactauls

Thomson's lamp toggles each time you press the button and nothing else affects its state. The lamp is on at noon, and then a supertask consisting of infinitely many button presses that completes by 1 pm, and the question is whether the light is on or off at 1 pm. There is no contradiction yet. But now add these two claims:

1. The state of the lamp at 1 pm would not be affected by shifting the times at which the button presses happen, if (a) all the button presses happen between noon and 1 pm, and (b) we ensure that no two button presses happen simultaneously.
2. If we removed one button press from the sequence of button presses between noon and 1 pm, the state of the lamp at 1 pm would not change.
Given this intuition, we do have a problem. Suppose that our sequence of supertask button presses occurs at 12:30, 12:45, 12:52.5, and so on. Then shift this sequence of button presses forward in time, so that now the sequence is at 12:45, 12:52.5, 12:45.25,and so on. By (1) this wouldn't affect the outcome, but by (2) it would as we will have gotten rid of the first button press. That's a contradiction.

So if we think Thomson's lamp is possible--which I do not--we need to deny at least one of the two counterfactuals. I think the best move would be simply to deny both (1) and (2), on the grounds that the connection between the state of the lamp at 1 pm and the button presses must be indeterministic.