Perfectly clear that you have stated nothing about 10:02. For all we know it turns into a pumpkin. — fishfry

Can't you see why I'm demanding that you write out, in one place, your entire description of the problem. That way you would be able to catch yourself making stuff up as you go. — fishfry

Quite so. But how does it help when we are thinking about an infinite sequence? As I understand it, the point is that the sequence cannot define it's own limit. — Ludwig V

And the phrase "completed sequence of tasks" is self-contradictory. — Ludwig V

So what do we need your argument for? — Ludwig V

You know perfectly well that's self-contradictory, so necessarily false. — Ludwig V

After I have completed the whole infinite sequence of jabs, i.e. at the end of the two minutes, is the lamp on or off? It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off. This is a contradiction.

You can think about us doing that, but you can't limit our thinking to that context. That's where the problems start. — Ludwig V

Us doing this is not an empirical possibility — Ludwig V

This is consistent with your premises:

The lamp is off at 11:00. The button is pushed at 12:00 and the lamp goes on. — TonesInDeepFreeze

C1 is a premise. — TonesInDeepFreeze

It seems to me that the premises don't preclude that the button can be pushed at 12:00 without there be an immediate predecessor state. — TonesInDeepFreeze

You are not including the premise "The lamp can only be on if immediately preceding it was off. And the lamp an be off only if immediately preceding it was on"? — TonesInDeepFreeze

You're reiterating a premise that we are free to reject. Just reiterating it like that is begging the question in this context. — TonesInDeepFreeze

So we can reject (1) and be left with a consistent set of two premises. — TonesInDeepFreeze

If we agree that (1) (2) (3) are together impossible, then we can infer anything from the assumption that they are possible. — TonesInDeepFreeze

Then, we may consider that the problem itself is impossible in the sense that it requires:

(1) a state requires an immediate predecessor state

(2) there is a state at 12:00

(3) there is no predecessor state to the state at 12:00 — TonesInDeepFreeze

But there is no immediate predecessor state to the state at 12:00, so I find it difficult to conceive also requiring that the state at 12:00 is determined by an immediate predecessor state that does not exist. — TonesInDeepFreeze

I'd find it helpful if you would write down a complete description of your version of the problem in one place, rather than pointing me to P1 here and C3 there. Just write down a complete description of the problem for my reference please. — fishfry

It's just that the rules don't apply at 12:00. — Ludwig V

Am I contradicting you? — Ludwig V

Benacerraf argues that neither outcome is inconsistent with the rules of the problem,
— fishfry

That seems to be true, so Benacerraf is right. — Ludwig V

So what are you arguing about? — Ludwig V

Is is not the case that "logically impossible" implies "metaphysically impossible"? — Ludwig V

So what are you arguing about? — Ludwig V

So we can agree that the consequent is false. — Ludwig V

Clearly not by you. Could've easily included it. So why didn't you? — Outlander

You missed out "The lamp is either on or off at all times." — Ludwig V

That seems to be true, so Benacerraf is right. — Ludwig V

I don't know if a button is pushed or not at the terminal time. Who says it's not? — fishfry

The terminal state is arbitrary. — fishfry

Why don't you just run the code and see? — Ludwig V

But since you've put the argument in a list, I'd make explicit all the premises. — TonesInDeepFreeze

var isLampOn = false

function pushButton()
{
  isLampOn = !isLampOn
}

var i = 120

while (true) {

  wait i *= 0.5 // seconds
  
  pushButton()

}

echo isLampOn

Lamps that switch state in arbitrarily small intervals of time? — fishfry

If "nothing other than pushing the button turns the lamp on or off," then at midnight, the button pusher pushes the button and turns the lamp on or off, per your premise. — fishfry

With the lamp, there is no possible way to assign a terminating value that makes any particular sense. Instead, absolutely any answer will do. On, Off, or as I facetiously said earlier, a plate of spaghetti; to emphasize the arbitrariness of the choice. — fishfry

var isLampOn = false

function pushButton()
{
  isLampOn = !isLampOn
}

var i = 120

while (true) {

  wait i *= 0.5
  
  pushButton()

}

echo isLampOn

Not just that it was off and then turned on, but rather that it was off at time t1 and on at time t2. That is, that it's not just a matter of the lamp having been off previously but rather that there is an off state that is an immediate predecessor of the on state and that that extends to 12:00 too so that for the lamp to be on at 12:00 there must be an immediate predecessor state in which the lamp was off, mutatis mutandis for the lamp being off at 12:00. Thomson mentions this. It's a premise that needs to be stated. — TonesInDeepFreeze

(1) The first task is impossible to be performed. The second task is impossible to be performed. The third task is impossible to be performed ...

Quantified:

For all tasks, there is not a performance of any of them.

I think that is not what you mean.

(2) It is not possible for there to be a single performance of all the tasks.

Quantified:

There is not a performance that performs all the tasks.

I surmise that is what you mean.

I wouldn't write "it is impossible for the first task to be performed at 11:00, the second at 11:30, the third at 11:45, and so on" because it can be understood in sense (1).

It is not possible for the first dancer to do a flip today, for the second dancer to do a flip tomorrow, and so on.

I would take that to mean that none of the dancers can do a flip on their appointed day. — TonesInDeepFreeze

As I mentioned, that is a premise that you don't include in your own argument. As I mentioned:

"his argument includes the premise that there is a state at 12:00 and that that state must be determined by an immediate predecessor state but that there is no immediate predecessor state."

I can't imagine anyone denying that there is no immediate predecessor state, but some partisans who don't accept the argument deny that the state at 12:00 must be determined by an immediate predecessor state. So you must include the premise that the state at 12:00 must be determined by an immediate predecessor state — TonesInDeepFreeze

It's not a matter of continuousness but rather of density. — TonesInDeepFreeze

If you don't mean "Therefore, it is impossible for the first task to be performed at 11:00, the second at 11:30, the third at 11:45, and so on" then it should be considered scratched. — TonesInDeepFreeze