1.No, because their belief doesn't make any sense. It even has logical contradictions, which makes it "super impossible", meaning there's no possible world where it could be true (the omnipotence paradox proves that omnipotence is logically inconsistent; a god which is nearly omnipotent, nearly omniscient and nearly omnibenevolent wouldn't allow suffering, which, undoubtably, exists; "God wants to allow free will" isn't a valid defence, since there's a lot of suffering that isn't caused by other humans, like illness and natural catastrophes) (note: I'm adding "nearly" to avoid paradoxes like the omnipotence paradox)
2. belief isn't a choice, for example, you can't "chose" to believe that the continent Australia doesn't actually exist. Therefore, I wouldn't be able to hold religious believes even if I'd acknowledge that this would bring greater happiness without negative side effects.
However, if we make the hypothetical world even less convenient by adding that, actually, I would be able to effectivly self-deceive, and there would be absolutly no negative side effects, then Yes, I would chose to believe.
3. I'm already highly sympathetic towards the "Effective altruism" movement and donate a lot of money to their causes. The reason I'm not donating literally everything I don't need for survival is that I'm not morally perfect; I admit that.
(EDIT just to correct spelling)
There would actually be several changes:
I would stop being vegan.
I would stop donating money (note: I currently donate quite a lot of money for projects of "Effective altruism").
I would stop caring about Fairtrade.
I would stop feeling guilty about anything I did, and stop making any moral considerations about my future behaviour.
If others are overly friendly, I would fully abuse this for my advantage.
I might insult or punch strangers "for fun" if I'm pretty sure I will never see them again (and they don't seem like the kind of person who seeks retribution).
I would become less willing to help others.
I would care very little about politics, and might not go voting.
I wouldn't be angry at anyone unless they're action influences me personally (note: If they hurt a person with which I have a relationship, this would influence me. If they hurt a stranger, this wouldn't influence me)
And there would probably be quite a few more changes I haven't thought of yet.
I would still continue my current hobbies, and do things if I have a "feeling "that I "want" to do them. These "feelings" would only be stopped by fear for personal costs, not by moral consideration (And not making moral considerations would indeed make a change see above)
More acuratly, "absence of evidence you would expect to see if the statement is true" is evidence of absence.
If there's no evidence you'd expect if the statement is true, absence of evidence is not evidence of absence.
For example, if I tell you I've eaten cornflakes for breakfast, no matter whether or not the statement is true, you won't have any evidence in either direction (except for the statement itself) unless you're willing to investigate the matter (like, asking my roommates). In this case, absence of evidence is not evidence of absence.
Now, suppose we meet in person and I tell you I've eaten garlic just an hour before. You'd expect evidence if that statement is true (bad breath), in this case, absence of evidence is evidence of absence.
I've actually noticed this long before I've read the post. For me, the thought "I'm having many old thoughts" is itself an old thought now.
The same is true for the thought "the thought "I'm having many old thoughts" is itself an old thought now" and so on
I see another way to show that 1/5 is the correct solution:
P(2 Aces | Ace of Spades revealed)= P(2 Aces AND Ace of Spades revealed)/P(Ace of Spades revealed)
(note: for further calculations, I'm assuming that there are 5 possible hands and the probability for each hand is 1/5, since it already has been revealed that there is at least one Ace. The end result would be the same if you would also set aside a random card in case you have no Ace,but the probabilities in the steps before the end results would have to change accordingly)
P(2 Aces AND Ace of Spades reveled)=P(2 Aces)*1/2 = 1/5 * 1/2 =1/10
P(Ace of Spades revealed)= 2/5 * 1 + 1/5 * 1/2 = 5/10
Assigning Bayes-probabilities <1 to mathematical statements (that have been definitly proven) seems absurd and logically contradictory, because you need mathematics to even asign probabilities.
If you assign any Bayes probability to the statement that Bayes probabilities even work, you already assume that they do work.
And, arguably, 2+2=4 is much simpler than the concept of Bayes-probability
(To be fair, the same might not be true for my most complex statement that Pi is irrational)
This article actually made me question „Wait, is this even true?“ when I read an article with weird claims; then I research whether the source is trustworthy and sometimes, it turns out that it isn‘t
I agree that you can never be „infinitly certain“ about the way the physical world is (because there‘s always a very tiny possibility that things might suddenly change, or everything is just a simulation, or a dream, or […] ), but you should assign probability 1 to mathematical statements for which there isn‘t just evidence, but actual, solid proof.
Suppose you have the choice beetween the following options:
A You get a lottery with a 1-Epsilon chance of winning.
B You win if 2+2=4 and 53 is a prime number and Pi is an irrational number.
Is there any Epsilon>0 for which you would chose option A? What if something really bad happens if you lose (like, all of humanity being tortured for [insert large number] years)?
I would chose option B for any Epsilon>0, which means assigning Bayes-probability 1 to option B.
I don‘t understand the meaning of the sentence „And since inferences can propagate backward and forward through causal networks, epistemic entanglements can easily cross the borders of light cones. “