There is not outcome-I-could-have-expected-to-observe that is the negation of existence. There are outcomes I could have expected to observe that are alternative characters of existence, to the one I experience. For example, “I was born in Connecticut” is not the outcome I actually observed, and yet I don’t see how we can say that it’s not a logically coherent counterfactual, if logically coherent counterfactuals can be said to exist at all.
I think that you are interpreting negation too narrowly here, in that the negation operator also includes this scenario, because the complement of being born in a specific time and place is being born in any other place and time, no matter which other place and time (other than the exact same one), so it is valid information to infer that you were born in a specific time and place, but remember to be careful of independence assumptions, and check if there was a non-independent event that happened to cause your birth.
Remember, the negation of something is often less directly informative than the thing itself, because you rarely only specify 1 thing with a negation operator on something else, while directly specifying the thing perfectly points to only 1 thing.
The key value of this quote below is to remember that if you could never observe a different outcome, than no new information was gotten, and this is why general theories tend to be uninformative.
It is also a check on the generality of theories, because if a theory predicts everything, then it is worthless for inferring anything that depends on specific outcomes.
If you couldn’t have possibly expected to observe the outcome not A, you do not get any new information by observing outcome A and there is nothing to update on.
To answer the question
Light+Red: God keeps the lights in all the rooms on. You wake up and see that you have a red jacket. What should your credence be on heads?
Given that you always have a red jacket in the situation, the answer is that you have a 1⁄2 chance that the coin was heads, assuming it’s a fair coin, because the red jacket is already known and cannot contribute to the probability further.
Darkness: God keeps the lights in all the rooms off. You wake up in darkness and can’t see your jacket. What should your credence be on heads?
Given that the implicit sampling method is random and independent (due to the fair coin), the credence in tails is a million to 1, thus you very likely are in the tails world.
If the sampling method was different, the procedure would be more complicated, and I can’t calculate the probabilities for that situation yet.
The reason it works is because the sampling was independent of your existence, and if it wasn’t, the answer would no longer be valid and the problem gets harder. This is why a lot of anthropic reasoning tends to be so terrible, in that they incorrectly assume random/independent sampling applies universally when in fact the reason that the anthropic approach worked is because we knew a-priori that the sampling was independent and random, thus we always get new information, so if this doesn’t work (say because we know that certain outcomes are impossible or improbable), then a lot of the anthropic reasoning becomes invalid too.
Heads: Two people with red jackets, one with blue.
Tails: Two people with red jackets, nine hundred and ninety nine thousand, nine hundred and
ninety-seven people with blue jackets.
Lights off.
Guess your jacket color. Guess what the coin came up. Write down your credences.
Light on.
Your jacket is red. What did the coin come up?
[ Also, re
Given that the implicit sampling method is random and independent (due to the fair coin), the credence in heads is a million to 1, thus you very likely are in the head’s world.
I think that you are interpreting negation too narrowly here, in that the negation operator also includes this scenario, because the complement of being born in a specific time and place is being born in any other place and time, no matter which other place and time (other than the exact same one), so it is valid information to infer that you were born in a specific time and place, but remember to be careful of independence assumptions, and check if there was a non-independent event that happened to cause your birth.
Remember, the negation of something is often less directly informative than the thing itself, because you rarely only specify 1 thing with a negation operator on something else, while directly specifying the thing perfectly points to only 1 thing.
The key value of this quote below is to remember that if you could never observe a different outcome, than no new information was gotten, and this is why general theories tend to be uninformative.
It is also a check on the generality of theories, because if a theory predicts everything, then it is worthless for inferring anything that depends on specific outcomes.
To answer the question
Given that you always have a red jacket in the situation, the answer is that you have a 1⁄2 chance that the coin was heads, assuming it’s a fair coin, because the red jacket is already known and cannot contribute to the probability further.
Given that the implicit sampling method is random and independent (due to the fair coin), the credence in tails is a million to 1, thus you very likely are in the tails world.
If the sampling method was different, the procedure would be more complicated, and I can’t calculate the probabilities for that situation yet.
The reason it works is because the sampling was independent of your existence, and if it wasn’t, the answer would no longer be valid and the problem gets harder. This is why a lot of anthropic reasoning tends to be so terrible, in that they incorrectly assume random/independent sampling applies universally when in fact the reason that the anthropic approach worked is because we knew a-priori that the sampling was independent and random, thus we always get new information, so if this doesn’t work (say because we know that certain outcomes are impossible or improbable), then a lot of the anthropic reasoning becomes invalid too.
You are confused.
How about this:
Lights off.
Guess your jacket color. Guess what the coin came up. Write down your credences.
Light on.
Your jacket is red. What did the coin come up?
[ Also, re
Did you mean ‘tails’? ]