Our universe is most likely a computer simulation

[mathematic]

88. Logic most certainly breaks down when the implications are weird.

The history of the development of logic demonstrates that nicely. It might be best to think of logic as an empirically evaluated system of inference. How do we know that "logic" is "right"? Our bridges don't fall down.

A good example of changing logic is the law of the excluded middle. It states that either a proposition is true or the negation of the proposition is true. It's a rule of logic from antiquity that has been discarded by many modern systems of logic.

All that aside, your claim that your conclusion is a logical necessity is dubious:

Let's rephrase your question as a statement, "It is possible..." and call it A. Let's call "the universe is likely simulated" B. Your argument for our universe being a simulation is then

1) If A then B

Statements like 1) are logically true if A is true and B is true or if A is false. There are two issues here. Is 1) true? Is A true? From your argument, we can only conclude that B is true if both 1) and A are true.

Is A true?
Well I can certainly imagine it, if that's what you mean by "possible", but this sort of reasoning fell out of favor with philosophers when they realized people can imagine some pretty strange things. If "possible" actually means possible then we have no way of knowing. (And here, by complete coincidence, I'm invoking the flaw of the law of the excluded middle!)

Is 1) true?
For 1) to be true you need a lot more than logic. You also need to specify your form of statistical inference (probably bayesian) and the precise philosophical meanings you're ascribing to probability. You also have to justify your choice of probability distribution. These are the assumptions of your argument and do not rely on logic. It's also suspect how you can come to a reliable conclusion based on one observation (our universe).

In conclusion, based on a lack of logical necessity, a premise with unknown veracity, the reliance on a boatload of probability assumptions, and the inapplicability of statistical inference using one data point, I find no compelling reason to believe that we are living in a simulated universe. But it is fun to think about.