when it can’t logically influence whether there is money in the box.
That’s pretty much the heart of the issue, isn’t it? Clearly, by the omniscience of Omega’s prediction, your choice is extremely correlated with what’s in the box. So whether your choice determines the box contents, the box contents determines your choice, or some other thing determines both your choice and the box contents, there is a “logical influence” between your choice and the money in the box.
The assumption that your choice is independent of the state of the universe is flawed.
That’s pretty much the heart of the issue, isn’t it? Clearly, by the omniscience of Omega’s prediction, your choice is extremely correlated with what’s in the box. So whether your choice determines the box contents, the box contents determines your choice, or some other thing determines both your choice and the box contents, there is a “logical influence” between your choice and the money in the box.
The assumption that your choice is independent of the state of the universe is flawed.