You left out some steps in your argument. It appears you were going for a disjunction elimination, but if so I’m not convinced of one premise. Let me lay out more explicitly what I think your argument is supposed to be, then I’ll show where I think it’s gone wrong.
A = “The rational decision is to two-box”
B = “Omega has set me to one-box”
C = “The rational decision is to one-box”
D = “Omega has set me to two-box”
E = “I must not be deciding rationally”
1. (A∧B)→E
2. (C∧D)→E
3. (A∧B)∨(C∧D)
4. ∴ E
I’ll grant #1 and #2. This is a valid argument, but the dubious proposition is #3. It is entirely possible that (A∧D) or that (C∧B). And in those cases, E is not guaranteed.
In short, you might decide rationally in cases where you’re set to one-box and it’s rational to one-box.
It is possible that I will make the rational decision in one path of the scenario. But the scenario, by it’s very nature, contains both paths. In one of the two paths I must be deciding irrationally.
Given as it was stated that I will use my normal thought-processes in both paths, my normal thought-processes must, in order for this scenario to be possible, be irrational.
Proposition 3 is only required to be possible, not to be true, and is supported by the existence of both paths of the scenario: the scenario requires that both A and B are possible.
It is possible that I will make the rational decision in one path of the scenario. But the scenario contains both paths. In one of the two paths I must be deciding irrationally.
Given as it was stated that I will use my normal thought-processes in both paths, my normal thought-processes must, in order for this scenario to be possible, be irrational.
It is not the case that in order for this scenario to be possible, your normal thought-processes must be necessarily irrational. Rather, in order for this scenario to be possible, your normal thought-processes must be possibly irrational. And clearly that’s the case for normal non-supernatural decision-making.
If you did not know about the box, you’d experience your normal decision-making apparatus output a decision in the normal way. Either you’re the sort of person who generally decides rationally or not, and if you’re a particularly rational person the box might have to make you do some strange mental backflips to justify the decision in the case that it’s not rational to make the choice the box specifies.
It is isomorphic, in this sense, to the world determining your actions, except that you’ll get initial conditions that are very strange, in half the times you play this game (assuming a 50% chance of either outcome).
If you know about the box, then it becomes simpler, as you will indeed be able to use this reasoning and the box will probably just have to flip a bit here or there to get you to pick one or the other.
If you’re not the sort of person who usually decides rationally, then following your strategy should be easy. For me, I anticipate that I would decide rationally half the time, and go rather insane the other half (assuming there was a clear rational decision, as you implied above).
You left out some steps in your argument. It appears you were going for a disjunction elimination, but if so I’m not convinced of one premise. Let me lay out more explicitly what I think your argument is supposed to be, then I’ll show where I think it’s gone wrong.
A = “The rational decision is to two-box” B = “Omega has set me to one-box” C = “The rational decision is to one-box” D = “Omega has set me to two-box” E = “I must not be deciding rationally”
I’ll grant #1 and #2. This is a valid argument, but the dubious proposition is #3. It is entirely possible that (A∧D) or that (C∧B). And in those cases, E is not guaranteed.
In short, you might decide rationally in cases where you’re set to one-box and it’s rational to one-box.
It is possible that I will make the rational decision in one path of the scenario. But the scenario, by it’s very nature, contains both paths. In one of the two paths I must be deciding irrationally.
Given as it was stated that I will use my normal thought-processes in both paths, my normal thought-processes must, in order for this scenario to be possible, be irrational.
Proposition 3 is only required to be possible, not to be true, and is supported by the existence of both paths of the scenario: the scenario requires that both A and B are possible.
It is possible that I will make the rational decision in one path of the scenario. But the scenario contains both paths. In one of the two paths I must be deciding irrationally.
Given as it was stated that I will use my normal thought-processes in both paths, my normal thought-processes must, in order for this scenario to be possible, be irrational.
You’re mixing modes.
It is not the case that in order for this scenario to be possible, your normal thought-processes must be necessarily irrational. Rather, in order for this scenario to be possible, your normal thought-processes must be possibly irrational. And clearly that’s the case for normal non-supernatural decision-making.
ETA: Unknowns stated the conclusion better
Let’s try a different tack: Is it rational to decide rationally in Unknown’s scenario?
1.Thinking takes effort, and this effort is a disutility. (-c)
2.If I don’t think I will come to the answer the machine is set to. (of utility X)
3.If I do think I will come to the answer the machine is set to. (of utility X)
My outcome if I don’t think is “X” My outcome if I do think if “X-c” Which is less than “X” I shouldn’t waste my effort thinking this through.
If you did not know about the box, you’d experience your normal decision-making apparatus output a decision in the normal way. Either you’re the sort of person who generally decides rationally or not, and if you’re a particularly rational person the box might have to make you do some strange mental backflips to justify the decision in the case that it’s not rational to make the choice the box specifies.
It is isomorphic, in this sense, to the world determining your actions, except that you’ll get initial conditions that are very strange, in half the times you play this game (assuming a 50% chance of either outcome).
If you know about the box, then it becomes simpler, as you will indeed be able to use this reasoning and the box will probably just have to flip a bit here or there to get you to pick one or the other.
If you’re not the sort of person who usually decides rationally, then following your strategy should be easy. For me, I anticipate that I would decide rationally half the time, and go rather insane the other half (assuming there was a clear rational decision, as you implied above).