Why must our universe being dominated by Boltzmann Brains necessarily mean we must be them?

Simply because the number of Boltzmann brains to ever exist (infinite because they keep spawning eternally in a given large enough finite volume) would dwarf the number of "ordinary observers" (finite for a given finite volume, because they eventually stop spawning).

And since you can't really tell whether you are a Boltzman brain or "ordinary", it is an unobservable, a random variable. Which overwhelmingly favors you being a Boltzmann brain.

According to the thought experiment of course, please don't believe you are one. The struggle is how do you fix the theory to get rid of Boltzmann brains.

The idea of an infinite number of Boltzmann brains is not intended to be taken seriously, but simply to illustrate improbabilities. The logic that suggests infinitely many brains also suggests infinitely many of everything else you care to mention. You might consider, for example, that infinitely many extermination machines- programmed to detect and destroy brains- might spontaneously appear first, in which case the brain problem will be neatly nipped in the bud.

I think the argument that we are probably Boltzmann brains is completely invalid.

1. Assume you are a Boltzmann brain

2. The above implies that everything that you know, including the laws of physics, could be lies. The laws in your hallucination probably do not correspond to the laws in the outside universe

3. But you used the laws of physics in the first place to arrive at the possibility of Boltzmann brains.

4. Therefore, the assumption that you are a Boltzmann brain is self defeating.

Regarding the statistical question as opposed to the general plausibility or cognitive stability of such objects as Boltzmann brains:

Statistical arguments that start with the assumption that we are in a randomly selected index beg the question unless we have a strong argument that some person or process actually did select randomly. It's one of the all time most attractive statistical fallacies because it seems to let us extract useful information from insufficient data. But all the information we seem to be able to extract is the information that we put in ourselves by making the assumption.

I'm going to take the premise, "There's a major chance that we're Boltzmann objects," at face value in the following, while throwing in a horrible solution.

But first, then: by "major chance" I mean a probability greater than 50%, however little or large the difference over 50% is. An interchangeable phrase would be "majority probability."

Now, per unitarity, it's to be said that if there's e.g. a 75% chance of something being the case, there's a 25% chance of something else being the case instead. But why, in physical reality, can't there be a 75% chance of A and a 75% chance of ~A? Might we not adopt a paraconsistent logic of probability and advance such a claim? Or suppose we deny unitarity. The solution offered, as such, to the fear of being a Boltzmann object, is: yes, there's an almost 100% chance that we're such objects, but there's also an almost 100% chance that we're not (the basis for the alternative being e.g. epistemic justification, a default justified belief that we're not Boltzmann objects).

Some papers on paraconsistent probability theory (not necessarily directly relevant to the above):

1. Goertzel[21], "Paraconsistent Foundations for Quantum Probability"

2. Carnielli and Testa[20], "Paraconsistent Logics for Knowledge Representation and Reasoning: advances and perspectives"

3. Brandom and Rescher's book on inconsistency logic, viz. this passage:

To accept the prospect of P and ~P conjointly is to give weight to the {P} = + + case in a distribution of probabilities across the whole gamut of alternative cases. And so if a probability distribution is to divide a total weight of 1 across all the standard cases (with only non-negative values), then, over-all, we are driven to a non-standard probability theory with positive probabilities for some non-standard cases—and so with certain outcomes taking on a probability greater than 1 (and conceivably also assigning some outcomes a negative prob￾ability value—certainly so if the over-all sum is to remain at 1). [bold emphasis added]

The seeming possibility of more-than-unitary probabilities tout court seems mostly to come up, or even only come up ever, in the analysis of quantum physics. But stipulative definitions aside, is there any "proof" that probability theories "ought to" be unitarity-compliant?