Michael

The symbol "=" is defined in ZFC by saying that "A = B" is true if and only if A is B. They could have used the symbol "#" instead, but they decided o...

Yes, there are 4 major predictions: Big Freeze, Big Rip, Big Crunch, and vacuum instability. With Big Freeze being considered to have the most evident...

Then I'll make it clear: I'm not saying that therefore all science is completely wrong and that all the facts may be utterly different than what we be...

Yes. How is that relevant?

Yes. I defer to what physicists say about what the scientific evidence entails, as is proper. I don’t want them to be saying anything. I’m simply repo...

In fact I'll set out the above in a more structured format: 1. The universe will succumb to the Big Freeze 2. The time between the Big Bang and the Bi...

The general principle is that the time between the Big Bang and the Big Freeze is finite. Therefore the number of normal observers is finite. The time...

But still more likely than not being one.

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

The same with us not being Boltzmann brains.

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

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 rea...

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?: Although it doesn't specifically refer to Boltzmann brains, the above is anal...

Brian Greene Sean Carroll Sean Carroll (again)

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

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 a...

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

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 s...

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 B...

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...

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 br...

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 k...

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 exper...

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

How about a Boltzmann universe?

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 Bol...

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 yo...

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 s...

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...

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 d...

No it's not.

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 t...

Why?

Why? They're entailed by our best scientific theories. See modern reactions to the Boltzmann brain problem: The general gist seems to be: 1. our scien...

Then you really shouldn't comment, because by your own admission you don't understand the problem. This was explained in the very first comment of thi...

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 Russe...

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 ...

Didn't we go over this here?

This isn't just an assumption. Rather: 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 ha...

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 simpl...

See here.

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 consid...

But still more likely than not being a Boltzmann brain.

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-i...

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?

There are, broadly speaking, four possibilities: 1. We are Boltzmann brains and our scientific theories are mostly correct 2. We are Boltzmann brains ...

I'm arguing that Philosopher19 doesn't understand set theory, and that his attempted "solution" to the Russell paradox makes no sense. The Russell par...

And you're welcome to do so. But it's a faith, not something supported by empirical evidence.