There actually is a variant where you’re allowed to look into the boxes—Newcomb’s problem with transparent boxes.
And yes, it is undefined if you apply the same rules. However, there are two ways to re-define it.
1: Reduce the scope of the inputs. For example, Omega could operate on the following program: “If the contestant would take only one box when the million dollars is there, put the million dollars there.” Before, Omega was looking at both situations, and now it’s only looking at one.
2: Increase the scope of the program. There are two possible responses in two possible situations for a total of four inputs, so you just need to define Omega’s response for all four. It’s interesting that Omega now treats you differently depending on your thoughts, not just depending on which box you take, so this changes the genre of the problem.
There actually is a variant where you’re allowed to look into the boxes—Newcomb’s problem with transparent boxes.
And yes, it is undefined if you apply the same rules. However, there are two ways to re-define it.
1: Reduce the scope of the inputs. For example, Omega could operate on the following program: “If the contestant would take only one box when the million dollars is there, put the million dollars there.” Before, Omega was looking at both situations, and now it’s only looking at one.
2: Increase the scope of the program. There are two possible responses in two possible situations for a total of four inputs, so you just need to define Omega’s response for all four. It’s interesting that Omega now treats you differently depending on your thoughts, not just depending on which box you take, so this changes the genre of the problem.