Against Boltzmann Brain
"Cognitive Instability" is a term coined by Sean Carroll for a type of argument against Boltzmann brain. Simply put: if you believe you are a disembodied brain that came into existence due to random fluctuation as the theory suggests, then you have no logical basis in believing said theory. Because the supporting evidence: your perceptions and memories, your very thought that the theory is correct, are the result of said fluctuation. You can't expect them to reflect true physics. It is unstable because it cannot be true and justifiably believed at the same time.
This counter doesn't completely rule out you being a Boltzmann brain as a logical possibility. No argument can do that. Yet it convincingly shows why we shouldn't put our faith in it: it's unlikely a fluctuation just happens to produce the brain, i.e. yourself, with the correct physical theory of the universe in its mind. Claiming the contrary would be arrogant and teleological. Like many ingenious arguments, "cognitive instability" has an element of self-reference in it.
What About Free Will?
Sean Carroll is probably not going to like this. But the same argument can be used against physicalism and in particular the denial of free will.
For this discussion, let's say something's behaviour is "free" as in it cannot be fully explained by physics. In another word, it's not physically causally closed. Here it's not about if we currently have the technical ability to analyze it, or if the world is ultimately deterministic or stochastic. Free will means it fundamentally cannot be physically reduced, not even in principle. Most people, physicalists for certain, would say this kind of free will cannot be real. Otherwise, it would be a direct violation of physical laws.
This view would regard your thoughts and actions as the outcome of the underlying physical processes. There is no other contributing factor. Our sense of free conscious choices can be seen as an illusion, or "what it feels like from the inside" of the actual processes, or maybe something else. But no matter how we choose to interpret that, it has no causal power.
But this means your belief is merely a product of this physical system called a person, by its internal dynamics and interactions with the environment. The feeling of thinking based on reasoning and rationality has no bearing on the outcome. Then how can you be certain that, this particular physical system happens to believe in the correct theories about the universe? Including theories like "I have no free will"?
Reviewing your own reasoning can't justify it, even if it seems impeccable. Because all evaluation supervenes on some underlying physical process. We can write a program to return "1+1=3". Say it can double-check to see whether the code has been correctly executed. It would still hold that "1+1=3" is the right answer. Consider your body as a machine running an algorithm. What reason there is to say: my algorithm must be nothing like that program. It ought to produce the correct metaphysical theories. Isn't that just as arrogant and teleological?
It has the same instability. That can't be true and justifiably believed at the same time.
One can argue this changes nothing. Because unlike in Boltzmann brain's case, the alternative here is so outlandishly absurd. I can't be seriously suggesting that I have the supernatural power of altering physical reality with my mind. That's even more arrogant and arguably inconsistent. It must be false. "Once eliminate the impossible, whatever remains, however improbable, must be the truth". And "cognitive instability" only says it's improbable. It does not rule "no free will" out.
That is certainly a reasonable position. But it still makes me uncomfortable. That means it just so happens I really am a physical system producing the correct metaphysical theory. That's a suspicious coincidence. It might have settled on the improbable too soon instead of looking harder for other alternatives.
Personally, I think we shouldn't view physics as an objective description of the world from the uniquely privileged view from nowhere. This cognitive instability comes down to the dilemma of thinking theories ought to be judged from this transcendental viewpoint yet they are produced and reviewed by worldly things, like you and me. Instead, maybe we should treat physics as inherently perspective-dependent. Among other benefits, it would not have this conflict and be stable.