Exactly on the mark with your cold example. Cold is not a separate thing from heat, it's just a place on the heat continuum from "Really Hot" to "Really Cold".
That is the basic everyday interpretation. But in fact it describes something that does not exist. There is no cold, there is just "no heat" to "lots of heat"
I claimed that inaction is a choice, and for it to be a choice you have to be aware of what your options are.
a simple google search on inaction gives me this: lack of action where some is expected or appropriate.
expected or appropriate would imply that awareness is required and that choosing that to not do anything is the same as inaction.
I'm not sure why choice matters. You're adding extra terms to the laws. Every time you rephrase the law you take if farther from its original meaning, even if you think you're using exact synonyms.
Now take an example of inaction. The AI controls the moving part still, but now its sensor is working. A hacker injects code that forces the machine part to close on someone tied to the floor. The AI has the ability to stop the process if it self-destructs in some way, such as locking a motor or overloading its power supply.
The action is self-destruction to prevent harm. The inaction is simply not doing that.
The option is between option 1: Self-destruct and option 2:Allow the part to move and injure human
That is a choice.
There is always a choice if there is awareness of a situation, even if that is to do nothing.
An industrial machine has safety sensors which stops the machine when interrupted, They are coded for an active signal so they basically send a continuous 'OK' and if they break, the machine stops.
That is the same as the first part of your first example.
First, you ignore the AI's ability to call for help which I specifically included. That means there are five theoretical outcomes: the AI does nothing (violating Law 1B (do not allow harm by inaction)), the AI shocks the hacker (violating Law 1A (do not harm)), the AI moves the part (violating Law 1A (do not harm)), the AI sacrifices itself to prevent moving the part. Separately the AI can call for help (which would be required by Law 1B because it's an action that could help prevent human harm and by not doing it the AI may be allowing human harm).
Again I don't think choice is a factor in this equation. The AI does not have the choice to do your #2 and hurt the human. It's simply incapable of doing that. The AI can choose from all of the options which are available to it, and #2 is not one of them. The AI has only one course it can take, which is to
alert security and self-destruct, and not shock and not move the part. There is no choice because there are no other options.
With AI, when a human manually inputs "OK, move that part" we would get 2 kinds of AI.
One AI would move the part because all available information tells it that it is okay to resume work.
The second type of AI is the kind of AI that goes mad in movies and wants to put humans in isolation cells with continuous supply of nutrients because the chance of harm is lowest that way.
That's hardly an AI at all. Compare two machines:
One does not think. When you press a button it moves the part.
Two thinks but has no sensors to gather its own information. When you press a button it knows it's ok to move the part. But it isn't allowed to move the part unless the button gets pressed, because that button press is the only way it knows that the area is clear. If it moved the part without a button press, it might harm a human.
Both machines behave identically. A human presses a button and the part moves.
Machine Two will hear the button press, move the part, end up killing a human eventually because a human was villainous or careless, and that action is totally fine with the Three Laws. The AI has to make a decision, based on its knowledge, and to the degree that knowledge is imperfect the decision may be imperfect.
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I think discussing it is cool, and we're not really arguing. It's mainly, as I said before, something like this:
You hand a copy of the rulebook to a dozen different people. They don't get to talk about the rules. The rules are pretty clear, but four of the people really want to get away with as much as they can so they think in circles and mark up their copies of the rules with marginalia until it's a travesty and nothing like the other copies. Of the other eight people, six interpret the rules in a commonsense way, one honestly misinterprets them, and the last is a troll who will do whatever he wants and point to parts of the rules out of context so they support whatever he was doing.
A conversation among these people is like a light illuminating all their shadowy misconceptions, like a fresh breeze blowing away all their iniquitous stinks. Talking now prevents yelling later.