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The argument, as stated, is just confused. You have essentially tried to make a conditional proof that from "We are non-simulated" we can derive "We are probably simulated", which is evident nonsense.

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Thanks for your comment Dominik. I think there might be an important objection in the neighbourhood but I'm not totally sure. As I'm understanding it, this seems to be the idea:

We are actually uncertain whether or not this is the real world, if we were certain the argument would be pointless. Given that, what can we tell about the real world? Well, not much. There isn't much reason to think simulations need to be like the real world in any particular aspect (think of how movies or books distort reality), and it's pretty hard to learn from a single example.

So given our uncertainty, we might have a hard time reasoning about the ratio of simulated to non-simulated people.

So let's make an assumption that helps us reason about the real world. The assumption made in the paper is that this is in fact the real world. This seems like a good assumption to explore because:

1. If the conclusion is that we are simulated, this assumption doesn't seem to be helping push the argument towards the conclusion too much.

2. It really tells us a lot about how to think about the real world.

Now let's think about how we are actually uncertain to begin with. Well, given our uncertainty we know either: we are simulated and it's hard to reason about the real world. Or we are not simulated, in which case there is apparently overwhelming evidence that we are simulated.

This does seem suspicious given we wouldn't assume that we do not have lung cancer and then reason from there. But this is also a highly suspicious hypothesis, so perhaps it is more natural to assume it is false and see what evidence we have.

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