Robotic persons?

If functionalism is true, a robot could be, or could constitute, a person. Suppose, then, a robot is or constitutes a person, Robby. Assume that the robot's memory state persists when he's turned off until the next time he's turned on, for instance because everything is stored in non-volatile memory or on a hard disk.

Question: Does Robby exist when turned off?

In favor of a yes:

1. If the robot is a person, rather than just constituting a person, then Robby exists when turned off, since robots, like vacuum cleaners and television sets, do exist when turned off.
2. If Mary Anne Warren in her defense of abortion piece is right that persons are beings with a developed capacity for agency, then the robot plainly has such a developed capacity even when off. Moreover, some pro-life opponents of Warren will agree that a developed capacity for agency is sufficient for personhood, though not necessary since an undeveloped capacity will also do.
3. Plainly, Robby exists when he is turned on, and when he is turned off and then on again, Robby will exist again. If it is impossible to have temporal gaps in one's existence, then Robby exists when turned off, too.
4. What does it mean to be "turned off"? When I turn my Palm PDA "off", it has a clock that keeps on ticking, and that will wake it up next time an alarm goes off, or a user pressed a key. Is it "off"? The official terminology for a state like that is "sleep" or "standby". (The only way to really turn off a Palm device is to remove or run out its battery.) We can imagine that Robby, to conserve power, can turn everything off but a timer that will turn him on in a second.[note 1] Surely, he still exists when he's turned off but the timer is running. But the distinction between what is and what is not a part of a robot is kind of arbitrary. Suppose we take a robot that doesn't have that ability, but we use rubber bands to attach to it a contraption involving a big analog alarm clock rigged to press the robot's power button after five minutes. We could set things up so the alarm clock attached to the robot is set up so that when we press the power button, it starts running, and then five minutes later it presses the power button. It seems that we should say that the person persists when turned off when there is such an alarm clock. (There is an alternate supposition, which is that there are two robot persons there: Robby and Robby-plus-alarm. But then we'll be multiplying persons absurdly--there is Robby, Robby-minus-foot, Robby-plus-alarm, Robby-plus-dust, etc.) But it shouldn't make a difference to whether Robby exists while off if we remove the rubber bands and just hold the alarm in place. And it also shouldn't matter whether we take the alarm away for a minute, and then bring it back in time to ring. And there is little difference between that and our just being resolved to turn Robby on. But surely whether Robby exists does not depend on what our plan is--on whether we are resolved to turn him on. So, Robby exists when turned off, even if there is no alarm or resolution.

In favor of a no:

1. It does not seem possible to draw any distinction between removing batteries and turning off. After all, turning off is disconnecting the batteries from the rest of the robot. It shouldn't matter for Robby's existence whether one is turning off the robot by removing the batteries physically from the battery holder, or disconnecting the contacts touching the batteries, or inducing a disconnection in the wires leading to these contacts. So Robby continues to exist even if his batteries are removed. But the story about the batteries can be modified further. It shouldn't make any difference vis-à-vis Robby's persistence status whether the power switch disconnects just the wires leading to the battery, or disconnects the wires elsewhere, e.g., around the CPU. We could imagine that the circuit is arranged in such a way that whenever the switch is pressed, the CPU is popped out, and this interrupts the circuit. Details of how turning off is implemented in the hardware surely should not matter, certainly not if one has the kind of functionalistic intuitions that are the main consideration in favor of thinking that there could be robot persons. But if so, we can imagine a radical case where the power switch disconnects all the major components of the robot. But again, there should be no difference between an electrical disconnect (especially on functionalist grounds) and an unplugging of a component. So, if Robby survives being turned off, he also survives all of his components being disconnected, as long as they could be put back together. It seems that the only functionalistically-acceptable constraint we can put on the taking apart is that the memory can be recovered. This leads to two absurdities. First, you can cut Robby up into small pieces and he will survive if the memory modules aren't destroyed. That doesn't seem right. (Certainly it isn't right if Robby is identical with the robot, but also doesn't seem right if Robby is constituted by the robot.) Second, if so, then we will survive as long as our memory modules aren't destroyed. But it is plausible that our brain's memory data persists a while after we're dead by any of the standard medical criteria--persists in the sense that future scientists will be able to recover it (after all, one can with sensitive instruments recover overwritten data from a hard drive). But at that time we're dead, and unless there is a soul (as I believe, but the functionalist likely denies), we don't exist when dead, so this is absurd.
2. If we didn't have souls, we wouldn't survive while not alive. But being turned on seems analogous to being alive. (If this is right, then people in cryogenic storage are dead.) And Robby doesn't have a soul. So, Robby doesn't survive being turned off.

Conclusion: If Robby were turned off, he would exist (by the first set of considerations) and not exist (by the second set). Hence, a robot can't be or constitute a person. Thus, functionalism is false.