I brought this argument from the Wikipedia entry on modal fallacy. They claim—and I do too—that the conclusion does not follow.
If you agree with me and with the Wikipedia article, I’d be happy to continue to the actually relevant question; if you don’t agree, I’d be glad to hear why you think they’re wrong.

https://en.m.wikipedia.org/wiki/Modal_fallacy

I haven’t read it, but I saw that this is about modal logic, and then of course it does not follow. The question is what the word “necessarily” means. Is the inference necessary? That it is. Or is the claim itself necessary? That it isn’t.
See this distinction in Column 301, in Judith Ronen’s formalization.
The problem here is in translating the everyday phrasing into formal phrasing. Everyday phrasing is not precise, and doesn’t have to be. So the “necessarily” here can be interpreted in those two senses.

Judith Ronen’s argument is exactly what I wanted to get to. If you accept that in the Wikipedia example we’re dealing with a modal fallacy and the conclusion does not follow, why don’t you accept Ronen’s argument that there is a modal fallacy in the argument against foreknowledge and free choice? What is the difference between the two arguments? (I read your discussion in the column; from what you wrote there it seems you didn’t understand Ronen. In another comment I’ll address what you wrote there if necessary).
I’ll present here the argument against foreknowledge and free choice so you can point out the difference:

– Necessarily, if God knows that you will choose x, you will choose x.
– God knows that you will choose x.
Therefore, you will necessarily choose x.
If you will necessarily choose x, you will not be able to choose otherwise—that is, there is no free choice.

What Ronen is saying, in simpler words, is the obvious point: our choices are contingent, not necessary. And the important point is that there is a contradiction between foreknowledge and free choice only if necessity is involved.

I explained this in Column 301. If she is right, that means there is a possible world in which God knows that I will choose X, but that will not actually happen. But that cannot be, because the implication between the two contingent claims is necessary. That is, if I have no possibility of choosing otherwise, then necessarily I choose X even if I imagine that I don’t. The opposing claim is that although I will always choose X (because there is no world in which God knows it and it does not occur), it still is not necessary. Philosophically, that is what necessity means: it is not possible that you choose otherwise.

Maybe I’m mistaken, but I think you didn’t notice the first response I wrote.
Either you don’t agree that there is a modal fallacy in the argument as I presented it, or you don’t agree that the contradiction exists only when necessity is involved.

It seems you didn’t fully grasp her point. If she is right, that does not mean there is a possible world in which God knows that you will choose x but it won’t actually happen. If she is right, it only means that your choice of x is not necessary.
In other words, necessarily, if God knows that you will choose x, you will choose x—but you will not necessarily choose x. There is a possible world in which you choose y, and in that world God’s knowledge would have been y.
Your choice determines God’s knowledge, not God’s knowledge determining your choice.

I understood all that exactly, and that is what I answered both in the column and here.
My claim is that if there is no possibility of choosing otherwise, then even if the choice is not necessary, de facto there is no choice. As for your claim that the relation goes in the opposite direction—that the choice determines the knowledge backward in time—I addressed that in the column itself (via Newcomb’s paradox and logical determinism). I explained there that you can say such a thing about the truth value of a proposition, but not about information that exists in someone’s possession (like God). That necessarily comes only after the events themselves.
You can also see it this way. Clearly there is no equivalence between the claim “It is necessary that if X then Y” and the claim “If X then Y is necessary.” I agree with that. But I argue that this distinction by itself does not solve the problem, because at least with respect to God the second claim is also true (certainly in the modal sense that I described). If in every possible world there is a choice that is not made otherwise, that is what necessity means for our purposes. What holds in every possible world is itself necessity. As for the backward-in-time relation from the act to the knowledge, see above.

Excellent, so basically you don’t agree that there is a contradiction only when necessity is involved. If so, the argument has to be phrased more like this:
God knows that you will choose x, therefore you will choose x.
If you will choose x and not y, then you do not have free choice.

From the fact that you chose x and not y, of course it does not follow that there is no free choice. You freely chose x and not y, and that is what God knew would happen. When the word “necessarily” is avoided, you can’t really get to the conclusion that there is no free will.

As for Newcomb, notice where the analogy breaks down. The player knows the prophet’s strategy, so he has access to the prophet’s knowledge, and that of course creates a paradox. That is almost equivalent to knowing what God knows you will choose; with that I absolutely agree there is a problem. It does not follow from that that there is no free choice; it follows that if God chooses to reveal His knowledge to you, He is effectively allowing you to make Him mistaken. Therefore, when God chooses to share His knowledge with you, He either prevents your free will regarding that choice that He knows, or He gives you the possibility of making Him wrong.

I explained why in my view this does mean there is no choice. We’re repeating ourselves.
As for Newcomb, I don’t see what connection there is to his revealing it to me. The paradox deals with a situation in which he does not reveal it to me. But in that column the paradox was brought only in order to rule out the possibility of backward causation in time (that the action causes the knowledge).

I don’t see that you demonstrated how the argument, without using necessity, entails that there is no choice. You only said it. I showed an attempt to construct the argument without using necessity, and from it it does not follow that there is no choice.

As for Newcomb, the point is that you can’t use it to demonstrate what you demonstrated in the column, because the cases are not equivalent. And they are not equivalent because the player is aware of the prophet’s strategy. I know that the paradox deals with a case where he does not reveal it to you, which is why I wrote that it is almost equivalent. I brought it as a simpler example to clarify that some kind of access to the information (or to the strategy) really does create an impossible situation.
In the same way, I could have said that it is equivalent to your having access to the “strategy,” or to the way God determines His prediction.

I take back what I said about Newcomb. The paradox is a paradox because it conflicts with two of our assumptions: the assumption that the prophet can predict, and our intuitive assumption that the future cannot determine the past. So if you used the paradox to show that the future cannot determine the past, then you basically assumed what you wanted to prove.
I don’t see any contradiction in accepting that the future actually can determine the past. You inferred from the paradox that the first assumption is wrong—that the prophet cannot predict, meaning the future cannot be known. And I inferred that the second assumption is wrong—that the future can determine the past. When a meteorologist gives a weather forecast, it is not the meteorologist who determines the weather; the weather determines the forecast.

So I take back the claim that knowledge of the prophet’s strategy poses a problem. If you do not accept the assumption that the future cannot determine the past, then there is no paradox here, and the player should choose the closed box, because only that choice will determine that there will be a million dollars in the box.