As an explanation for our observations, yes. — wonderer1

How so? There will be Boltzmann brains that have the same observations as ordinary observers; and in fact, there will be significantly (infinitely?) more Boltzmann brains that have those same observations as ordinary observers.

or if folk prefer simple language, there are no observations that settle the issue, and hence it remains mere speculation — Banno

The same with us not being Boltzmann brains.

That is not nearly as self defeating as a scientific hypothesis. — wonderer1

You think a quantum fluctuation universe is more likely than quantum fluctuation brains with false, consistent memories?

Any method for calculating probabilities ought come to the conclusion that the most likely observer is the one we know exists - us. — Banno

If we are Boltzmann brains then a calculation that shows a Boltzmann brain to be more likely than a regular observer has satisfied the above.

Your reasoning (or Vilenkin's) seems to beg the question.

Perhaps a different line of reasoning:

Borrowing from Tryon and Vilenkin, assume that any universe is itself a quantum fluctuation. Which is more likely; that we are a decades old Boltzmann brain or that we are an ordinary brain in a 14 billion year old Boltzmann universe?

I suppose the answer to that depends on what "surrounds" this universe. If it's an infinite and eternal vacuum then presumably there are an infinite number of Boltzmann universes and an infinite number of Boltzmann brains and so it is meaningless to say that one is more likely than the other.

We're just either a Boltzmann brain or an ordinary brain in a Boltzmann universe, with no evidence or reasoning to prefer either.

Somewhat of a coincidence, but that scientist wrote a paper that continues the work of the article I posted above.

Adding to the above, there's also Is the Universe a Vacuum Fluctuation?:

The author proposes a big bang model in which our Universe is a fluctuation of the vacuum, in the sense of quantum field theory. The model predicts a Universe which is homogeneous, isotropic and closed, and consists equally of matter and anti-matter. All these predictions are supported by, or consistent with, present observations.

Although it doesn't specifically refer to Boltzmann brains, the above is analogous to a Boltzmann universe, and as quantum fluctuations giving rise to a 14 billion year old universe is exponentially less likely than a quantum fluctuation giving rise to a several decades old brain, it stands to reason that evidence of the former is also evidence of the latter.

What you put in quotes there was something that someone wrote on Wikipedia. Can you quote a physicist making such a claim? — wonderer1

Brian Greene

I am confident that I am not a Boltzmann brain. However, we want our theories to similarly concur that we are not Boltzmann brains, but so far it has proved surprisingly difficult for them to do so. So, I see Boltzmann brains as a mathematical problem that we need to solve, as opposed to an existential affront. I believe it is a problem that we will one day overcome.

Sean Carroll

Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang.

...

The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed.

Sean Carroll (again)

We're not arguing that Boltzmann Brains exist — we're trying to avoid them.

Those are people who have considered the possibility that we are Boltzmann brains. Not people who claim what you attribute to them. I already quoted Sean Carroll on the topic and it seemed pretty clear to me that Carroll doesn't make the claim that you are attributing to him. — wonderer1

"The consensus amongst cosmologists is that some yet to be revealed error is hinted at by the surprising calculation that Boltzmann brains should vastly outnumber normal human brains."

They accept that the science entails that we are most likely Boltzmann brains. They consider this proof that something is wrong with the science.

This is consistent with what I've been saying.

Either we are most likely Boltzmann brains or our science is inaccurate.

And I want to know what justifies the assertion that we are not Boltzmann brains given that the science suggests otherwise.

As for Carroll specifically, see Why Boltzmann Brains Are Bad:

Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang.

...

The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed.

The science says one thing; he then suggests that it's irrational to believe it, i.e. that it's rational to reject the science.

On ChatGPT, here is an example of it contradicting itself three times in a row.
https://chat.openai.com/share/96378835-0a94-43ce-a25b-f05e5646ec40
And don't ever ask it to do any engineering https://chat.openai.com/share/b5241b53-e4d8-4cab-9a81-87fa73d740ad — Lionino

Yeah, ChatGPT doesn't reason. It basically just repeats what it's read elsewhere. Sometimes it makes stuff up. I tried using it for programming once and it fabricated a function that doesn't exist.

What scientist makes the claim that we have scientific evidence that we are most likely Boltzmann brains? — wonderer1

Several are mentioned in the Wikipedia article, e.g. Boltzmann, Eddington, Feynman, Sean Carroll, and Brian Greene.

3 is a contradiction, hard to disagree with that. My point was more that you seemed to agree with Sean Caroll, because his argument was the opposite of the premise that you refuted by probability in the original argument. Sean's point is about justification. — Lionino

Carroll pointed out the paradoxical nature of this:

1. Assume that we are most likely Boltzmann brains
2. Most Boltzmann brains do not have accurate scientific knowledge
3. Therefore, we most likely do not have accurate scientific knowledge
4. Our scientific knowledge entails that we are most likely Boltzmann brains
5. Therefore, our scientific knowledge that entails that we are most likely Boltzmann brains is most likely inaccurate
6. Therefore, we are most likely not Boltzmann brains

He then uses this to reject (1).

I then simply offered an inverse of the argument:

1. Assume that we are most likely ordinary humans
2. Assume that we have accurate scientific knowledge
3. Our scientific knowledge entails that we are most likely Boltzmann brains
4. Therefore, our scientific knowledge that entails that we are most likely Boltzmann brains is most likely accurate
5. Therefore, we are most likely not ordinary humans

I then use this to reject either (1) or (2).

The "cognitive instability" applies to both sides of the issue.

That's a false dichotomy, and things aren't nearly that black or white. — wonderer1

Then to be more accurate: either we are most likely Boltzmann brains or we cannot trust the scientific evidence that entails that we are most likely Boltzmann brains.

There are areas in which I can and do trust my scientific knowledge with my life (and the lives of other people) depending on it. There are other areas of scientific knowledge in which I can't trust my knowledge to nearly the same extent. — wonderer1

Which is why I asked the question: given that we have scientific evidence that entails that we are most likely Boltzmann brains, what justifies our claim that we are not most likely Boltzmann brains?

Sorry, me no understand. — Lionino

Consider this strengthened argument:

1. If we are not Boltzmann brains then our scientific theories are true
2. One of our scientific theories is that we are most likely Boltzmann brains
3. Therefore, if we are not Boltzmann brains then the scientific theory that we are most likely Boltzmann brains is true

Do you see the problem with (3)?

But in that case, your hard-won scientific knowledge just randomly fluctuated into existence as well; you have no reason to actually think that it represents an accurate view of reality.

Also on this, the same argument I made to Banno earlier can be used.

Each of these is true (if our current theories are correct):

1. Most Boltzmann brains have inaccurate scientific knowledge
2. Most observers with accurate scientific knowledge are Boltzmann brains

His argument is if P, not Q (if we are Boltzmann brains, we cannot trust our scientific knowledge); you showed how {if not P, Q} (if we are not Boltzmann brains, we can trust our scientific knowledge) entails a contradiction. How does that show his position has the same issue? — Lionino

It's right there in that post you first responded to:

1. If we are not Boltzmann brains then we can trust our scientific knowledge
2. Our scientific knowledge strongly suggests that we are most likely Boltzmann brains
3. Therefore, if we are not Boltzmann brains then we are most likely Boltzmann brains

Obviously (3) is problematic. Therefore we must reject either (1) or (2). As I said in my above post, many prominent physicists accept that (2) is true (even if they want to avoid the implication), and so I defer to their expertise.

So, as I said earlier, either we are most likely Boltzmann brains or we cannot trust our scientific knowledge.

That just begs the question by assuming that our scientific theories show that we are most likely Boltzmann brains — Janus

I'm not assuming it. It's what physicists like Boltzmann, Eddington, Feynman, Sean Carroll, Brian Greene, and others say. I'm deferring to their expertise.

I think number 1 is upside down, what Sean Carroll seems to suggest is that: — Lionino

I was presenting the inverse of his argument to show that his position suffers from that same cognitive instability.

How about a Boltzmann universe?

Is it possible that you and your surrounding environment, including all of your purported knowledge of the past and the outside world, randomly fluctuated into existence out of a chaotic soup of particles? Sure, it’s possible. But you should never attach very high credence to the possibility. Such a scenario is cognitively unstable, in the words of David Albert. You use your hard-won scientific knowledge to put together a picture of the world, and you realize that in that picture, it is overwhelmingly likely that you have just randomly fluctuated into existence. But in that case, your hard-won scientific knowledge just randomly fluctuated into existence as well; you have no reason to actually think that it represents an accurate view of reality. It is impossible for a scenario like this to be true and at the same time for us to have good reasons to believe in it. The best response is to assign it a very low credence and move on with our lives. — Sean Carroll

1. If we are not Boltzmann brains then we can trust our scientific knowledge
2. Our scientific knowledge strongly suggests that we are most likely Boltzmann brains
3. Therefore, if we are not Boltzmann brains then we are most likely Boltzmann brains

There's certainly some "cognitive instability" in his position, too.

So it's back to what I said here. Either we are most likely Boltzmann brains or we cannot trust our scientific knowledge.

There are lots of theories outside of physics that have a lot of evidentiary support as well. — wonderer1

So which theories outside physics are evidence against the eventual heat death of the universe and/or the fluctuations/nucleations that will give rise to Boltzmann brains? And how do we determine which evidence is stronger?

Of course, one solution to all of this is to abandon scientific realism and favour instrumentalism instead.

To play chess you must accept the reality of the pieces as objects in order to move them, therefore you must accept "chess reality" to play chess. Since it may not be stated in the rules that the pieces are "objects" the acceptance is only implicit, unlike set theory in which case the rule is explicit, therefore acceptance is explicit. — Metaphysician Undercover

You can play chess without a physical board and physical pieces. You can play it with pen and paper if you like; much like we do with maths. Or, if you're very smart, you can play it in your head; again, much like we do with maths.

When playing chess in your head you're not committed to being a realist about the queen you're playing with. When using set theory you're not committed to being a realist about the mathematical objects you're using.

You just follow the rules.

p) In A, A is a member of itself/A.
q) In U, A is not a member of itself/A.

p and q are true by definition. — Philosopher19

No, it's nonsense. That's not how set theory works.

1 is a member of N and R.
A is a member of A and B.

That's it.

Just take a few actual lessons in set theory.

I don't see the relevance. You do not need to accept the premise of "mathematical objects" to play chess. You do need to accept the premise of "mathematical objects" to follow the rules of set theory. — Metaphysician Undercover

You need to accept the premise of queens and kings and pawns to play chess, but accepting this premise doesn't commit you to "chess realism".

You need to accept the premise of a murderer and a victim when playing Cluedo, but accepting this premise doesn't commit you to "Cluedo realism".

And so accepting the premise of mathematical objects when using set theory doesn't commit you to mathematical realism.

When using set theory, mathematical objects "exist" only in the sense that queens "exist" in chess and a murderer "exists" in Cluedo, i.e. not in any realist sense.

And how would you justify that claim? — Metaphysician Undercover

I already did above. The axioms of some given set theory are just rules that you must follow when using that set theory. Different set theories have different axioms and so different rules. Given that there's no connection between using some set theory and believing in the mind-independent existence of abstract mathematical objects, there's no hypocrisy in using some set theory and being a mathematical antirealist.

Your position is like arguing that it's hypocritical to play chess if I do not believe that the rules of chess correspond to some mind-independent fact about the world.

However, it's hypocrisy to say "I'm a mathematical antirealist" and then go ahead and use set theory. — Metaphysician Undercover

No it's not.

Set theory begins with the assumption of mathematical objects, hence it is based in Platonic realism. — Metaphysician Undercover

You don't need to believe in Platonic realism to use set theory. Its axioms are just rules to follow when "doing" maths. There's no need to think of them as statements that correspond to some mind-independent fact about the world.

In some set theories, sets can contain themselves. In others, they can't. As a mathematical antirealist I wouldn't claim that one of them must be "wrong". They're just following different rules.

If you are "mathematical antirealist" you ought to reject set theory on the basis of the axioms it employs. — Metaphysician Undercover

Why?

BB speculations are scientifically self defeating. — wonderer1

Why? They're entailed by our best scientific theories.

Given the bigger picture, resulting from empirical observations considered more broadly, the evidence points towards us being the result of biological evolution. Do you think the majority of physicists would disagree? — wonderer1

See modern reactions to the Boltzmann brain problem:

The consensus amongst cosmologists is that some yet to be revealed error is hinted at by the surprising calculation that Boltzmann brains should vastly outnumber normal human brains. Sean Carroll states "We're not arguing that Boltzmann Brains exist—we're trying to avoid them." Carroll has stated that the hypothesis of being a Boltzmann brain results in "cognitive instability". Because, he argues, it would take longer than the current age of the universe for a brain to form, and yet it thinks that it observes that it exists in a younger universe, this shows that memories and reasoning processes would be untrustworthy if it were indeed a Boltzmann brain. Seth Lloyd has stated, "They fail the Monty Python test: Stop that! That's too silly!" A New Scientist journalist summarizes that "The starting point for our understanding of the universe and its behavior is that humans, not disembodied brains, are typical observers."

Some argue that brains produced via quantum fluctuation, and maybe even brains produced via nucleation in the de Sitter vacuum, do not count as observers. Quantum fluctuations are easier to exclude than nucleated brains, as quantum fluctuations can more easily be targeted by straightforward criteria (such as their lack of interaction with the environment at infinity).

Carroll believes that a better understanding of the measurement problem in quantum mechanics would show that some vacuum states have no dynamical evolution and cannot support nucleated brains, nor any other type of observer. Some cosmologists believe that a better understanding of the degrees of freedom in the quantum vacuum of holographic string theory can solve the Boltzmann brain problem.

Brian Greene states: "I am confident that I am not a Boltzmann brain. However, we want our theories to similarly concur that we are not Boltzmann brains, but so far it has proved surprisingly difficult for them to do so."

The general gist seems to be:

1. our scientific theories suggest that we are most likely Boltzmann brains
2. we are not most likely Boltzmann brains
3. therefore, our scientific theories are mistaken

The point I am making is that, by this very argument, (2) is not supported by the scientific evidence. Rather it's something like "common sense" or "intuition" or "faith".

I'm then asking if it's reasonable to favour common sense, intuition, or faith over scientific evidence.

Of course, if you admit that we can sometimes be justified in believing that the scientific evidence is mistaken then you open yourself up to arguments for idealism or theism, as it would certainly be hypocritical, or special pleading, to argue that we must believe in an external material world because there is scientific evidence for it but that we must not believe that we are Boltzmann brains even though there is scientific evidence for it.

It's my first look at anything in set theory so I don't have background. — Mark Nyquist

Then you really shouldn't comment, because by your own admission you don't understand the problem.

Finally, yes — Mark Nyquist

This was explained in the very first comment of this discussion by fishfry.

If the Russell set doesn't exist there is no contradiction. — Mark Nyquist

This is what you're failing to understand.

According to naive set theory, the Russell set "exists".

The Russell set doesn't "exist", because the Russell set is a contradiction.

Therefore, naive set theory is inconsistent.

The solution is to fix the inconsistencies with naive set theory, which was done in ZFC (and others).

I'll copy from the Wikipedia article:

The term "naive set theory" is used in various ways. In one usage, naive set theory is a formal theory, that is formulated in a first-order language with a binary non-logical predicate $\in$, and that includes the axiom of extensionality:

$\forall x \, \forall y \, ( \forall z \, (z \in x \iff z \in y) \implies x = y)$

and the axiom schema of unrestricted comprehension:

$\exists y \forall x (x \in y \iff \varphi(x))$

for any formula $\varphi$ with the variable $x$ as a free variable inside $\varphi$. Substitute $x \notin x$ for $\varphi(x)$ to get:

$\exists y \forall x (x \in y \iff x \notin x)$

Then by existential instantiation (reusing the symbol $y$) and universal instantiation we have:

$y \in y \iff y \notin y ,$

a contradiction. Therefore, this naive set theory is inconsistent.

Didn't we go over this here?

but it does depend on assumptions such as that the universe is eternal — wonderer1

This isn't just an assumption. Rather:

The preponderance of evidence to date, based on measurements of the rate of expansion and the mass density, favors a universe that will continue to expand indefinitely, resulting in the "Big Freeze" scenario below.

The heat death of the universe, also known as the Big Freeze (or Big Chill), is a scenario under which continued expansion results in a universe that asymptotically approaches absolute zero temperature. Under this scenario, the universe eventually reaches a state of maximum entropy in which everything is evenly distributed and there are no energy gradients—which are needed to sustain information processing, one form of which is life. This scenario has gained ground as the most likely fate.

In this scenario, stars are expected to form normally for 10¹² to 10¹⁴ (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker. Eventually black holes will dominate the universe, which themselves will disappear over time as they emit Hawking radiation. Over infinite time, there could be a spontaneous entropy decrease by the Poincaré recurrence theorem, thermal fluctuations, and the fluctuation theorem.

That final sentence is what entails Boltzmann brains.

I wonder if mathematical realists and mathematical antirealists have different views about mathematical infinity. I'm a mathematical antirealist. I have no problem with mathematical infinity. The "existence" of infinite sets does not entail the existence of infinities in nature (whether material or Platonic).

Boltzmann brains are a matter of speculation and not observation. — wonderer1

You're right that it's not a matter of observation (and perhaps that my binary distinction is imprecise), but it's wrong to suggest that it's as simple as speculation. Rather it's a consequence of our best understandings of quantum mechanics and thermodynamics.

So either we are most likely Boltzmann brains or our best understandings of quantum mechanics and thermodynamics is mistaken.

Given that the scientific evidence supports our best understandings of quantum mechanics and thermodynamics, the scientific evidence doesn't support the claim that we are not likely to be Boltzmann brains.

So what justifies your claim that we are not likely to be Boltzmann brains? Is it just "common sense" or "intuition"? Are "common sense" and "intuition" more reasonable than scientific evidence?

Are not all theories interpretations? Are our memories of what we have learned of science and mathematics also illusions? If so, then how can we justifiably use them to support any conclusions at all? — Janus

See here.

It pays to remember that scientific theories, and science generally, only tell us how to make sense of how things appear to be to ordinary humans. — Janus

They tell us how to make sense of how things appear to us. Whether or not we are ordinary humans or Boltzmann brains is the very question being considered.

it is a fact that some interpretations of our current scientific theories entail that we are more likely to be Boltzmann brains than ordinary humans. — Janus

Not just some, but the leading theories.

And given that there is a brain, the longer it persists the less likely it is to be merely a quantum fluctuation. — Banno

But still more likely than not being a Boltzmann brain.

It's odd to me when one exclaims that they are more likely to be a philosophical tool of thinking than a human. — creativesoul

It is a fact that our current scientific theories entail that we are more likely to be Boltzmann brains than ordinary humans.

It's certainly counter-intuitive, but then so is much of science. I won't claim that my intuitions ought take precedence over scientific evidence.

It is impossible for a human to not be a human. — creativesoul

And it's impossible for a Boltzmann brain to not be a Boltzmann brain, or for a horse to not be a horse.

What of it?

As if basing one's beliefs on empirical evidence were not an act of faith... If you are a Boltzmann brain, what are the chances of your having just happened to have imagined into being a world that exactly corresponds to the actual world? You happened to drop into existence in a way that allows you to realise you are a Boltzmann brain... — Banno

There are, broadly speaking, four possibilities:

1. We are Boltzmann brains and our scientific theories are mostly correct
2. We are Boltzmann brains and our scientific theories are mostly incorrect
3. We are not Boltzmann brains and our scientific theories are mostly correct
4. We are not Boltzmann brains and our scientific theories are mostly incorrect

If our scientific theories are mostly correct then either (1) or (3) is the case, with (1) being most likely (as per those very scientific theories).

So one of these is true:

a. We are most likely Boltzmann brains (1 or 3)
b. Our scientific theories are mostly incorrect (2 or 4)