Continuous choices

Suppose at at noon, Alice is relaxed in an armchair listening to music, but at any given time she is capable of choosing to get up, walk over to the kitchen and make herself a sandwich for lunch, which it’s time for. For fifteen minutes she continues listening to the music and then gets up at 12:15. It seems that she is continually responsible for her continuing to sit until 12:15, and then she is responsible for getting up.

Here is one realistic question about what happened between 12:00 and 12:15:

1. Did Alice make a vast number of choices, one at every moment until 12:15, to remain seated, and then at 12:15 a choice to get up?

In favor of a positive answer, it is difficult to see how she could be responsible for not getting up at a given time if she did not choose not to get up.

But a positive answer seems psychologically implausible. Indeed, it doesn’t seem like Alice would be enjoying the music if every moment she had to positively choose to stay.

Also, let’s think about what the reasons weighing in on each choice would be. On the one hand, there is a very weak reason to get up now. It’s a weak reason because getting up the next moment would be just as good hunger-wise. On the other hand, there is a very weak reason to keep sitting in order to enjoy music between this moment and the next. It’s a weak reason because the amount of music involved is very small. Choices on the basis of such very weak reasons are hard to make. These reasons would be hard to weigh. And when making choices between hard to weigh reasons, it seems that the chances of going for either option should be of the same order of magnitude. But if Alice were to make a vast number of choices between getting up and staying between, say, 12:00 and 12:10, with each choice having roughly the same order of magnitude of probability, then it was very unlikely that all these choices were choices to stay.

I find the responsibility argument pretty persuasive, though. Maybe, though, the right story that balances psychological plausibility with intuitions about responsibility is this: Alice made a small number of choices between 12:00 and 12:15. Most of these choices were a choice whether to think harder about whether to get up or just let the status quo continue “for a while”. Most of the time, she chose just to let the status quo roll on. At a time t during which the status quo was “just rolling on”, Alice’s responsibility for not getting up was derivative from her choice to stop thinking about the question. Sometimes, however, Alice decided to think harder about whether to get up. Finally, she thought harder, and got up.

Since the number of choices is smaller on this story, it doesn’t interfere as much with the enjoyment. There is some interference, but that’s realistic. And since the number of choices is smaller, the probabilities of each option can be of the same order of magnitude without this creating any problems.

Now, prescinding from the realism behind the discussion of (1), we can ask the also interesting question:

2. Could it be that both (a) time is continuous and (b) Alice literally makes a choice to remain seated at every single moment of time between 12:00 and 12:15?

The answer, I think, is negative. For consider a choice at t. Alice would be choosing between the good of slightly more music and the good of slightly earlier relief of hunger. But how long as the “slightly more” and “slightly earlier”? Zero temporal length! For if time is continuous, and Alice is choosing at every moment, zero length of time elapses between choices. Indeed, there is no sense to the idea of “between choices”. So Alice would be choosing between zero-value goods. And that doesn’t make rational sense.