Random vs nonrandom is not a Boolean question. “Random” is the null value we can give as an answer to the question “What is our prior?” When we are asking ourselves “What is our prior?”, we cannot sensibly give the answer “Yes, we have a prior”. If we want to give a more detailed answer to the question “What is our prior?” than “random”/”nothing”/”null”/”I don’t know”, it must have particular contents; otherwise it is meaningless.
I was anthropically sampled out of some space, having some shape; that I can say definite things about what this space must be, such as “it had to be able to support conscious processes”, does not obviate that, for many purposes, I was sampled out of a space having higher cardinality than the empty set.
As I learn more and more about the logical structure by which my anthropic position was sampled, it will look less and less “random”. For example, my answer to “How were you were sampled from the space of all possible universes?” is basically, “Well, I know I had to be in a universe that can support conscious processes”. But ask me “Okay, how were you sampled from the space of conscious processes?”, and I’ll say “I don’t know”. It looks random.
“Random” is the null value we can give as an answer to the question “What is our prior?”
I think the word you are looking for here is “equiprobable”.
It’s propper to have equiprobable prior between outcomes of a probability experiment, if you do not have any reason to expect that one is more likely than the other.
It’s ridiculous to have equiprobable prior between states that are not even possible outcomes of the experiment, to the best of your knowledge.
You are not an incorporeal ghost that could’ve inhabited any body throughout human history. You are your parents child. You couldn’t have been born before them or after they are already dead. Thinking otherwise is as silly as throwing a 6 sided die and then expecting to receive any outcome from a 20 sided die.
I was anthropically sampled out of some space
You were not anthropically sampled. You were born as a result of a physical process in a real world that you are trying to approximate as a probability experiment. This process had nothing to do with selecting universes that support conscious processes. This process has already been instantiated in a specific universe and has very limited time frame for your existence.
You will have to ignore all this knowledge and pretend that the process is completely different, without any evidence to back it up, to satisfy the conditions of Doomsday argument.
You can’t say “equiprobable” if you have no known set of possible outcomes to begin with.
Genuine question: what are your opinions on the breakfast hypothetical? [The idea that being able to give an answer to “how would you feel if you hadn’t eaten breakfast today?” is a good intelligence test, because only idiots are resistant to “evaluating counterfactuals”.]
This isn’t just a gotcha; I have my own opinions and they’re not exactly the conventional ones.
You can’t say “equiprobable” if you have no known set of possible outcomes to begin with.
Not really. Nothing prevents us from reasoning about a set with unknown number of elements and saying that measure is spreaded equally among them, no matter how many of them there is. But this is irrelevant to the question at hand.
We know very well the size of set of possible outcomes for “In which ten billion interval your birth rank could’ve been”. This size is 1. No amount of pregnancy complications could postpone or hurry your birth so that you managed to be in a different 10 billion group.
Genuine question: what are your opinions on the breakfast hypothetical?
I think it’s prudent to be careful about counterfactual reasoning on general principles. And among other reasons for it, to prevent the kind of mistake that you seem to be making: confusing
A) I’ve thrown a six sided die, even though I could’ve thrown a 20 sided one, what is the probability to observe 6?
and
B) I’ve thrown a six sided die, what would be the probability to observe 6, if I’ve thrown a 20 sided die instead?
The fact that question B has an answer doesn’t mean that question A has the same answer as well.
As for whether breakfast hypothetical is a good intelligence test, I doubt it. I can’t remember a single person whom I’ve seen have problems with intuitive understanding of counterfactual reasoning. On the other hand I’ve seen a bunch of principled hard determinists who didn’t know how to formalize “couldness” in a compatibilist way and threfore were not sure that counterfactuals are coherent on philosophical grounds. At best the distribution of the intelligence is going to be bi-modal.
And after you bothered to overcome your ignorance, naturally you can’t keep treating the setting as random sampling.
With Doomsday argument, we did bother—to the best of our knowledge we are not a random sample throught all the humans history. So case closed.
Random vs nonrandom is not a Boolean question. “Random” is the null value we can give as an answer to the question “What is our prior?” When we are asking ourselves “What is our prior?”, we cannot sensibly give the answer “Yes, we have a prior”. If we want to give a more detailed answer to the question “What is our prior?” than “random”/”nothing”/”null”/”I don’t know”, it must have particular contents; otherwise it is meaningless.
I was anthropically sampled out of some space, having some shape; that I can say definite things about what this space must be, such as “it had to be able to support conscious processes”, does not obviate that, for many purposes, I was sampled out of a space having higher cardinality than the empty set.
As I learn more and more about the logical structure by which my anthropic position was sampled, it will look less and less “random”. For example, my answer to “How were you were sampled from the space of all possible universes?” is basically, “Well, I know I had to be in a universe that can support conscious processes”. But ask me “Okay, how were you sampled from the space of conscious processes?”, and I’ll say “I don’t know”. It looks random.
I think the word you are looking for here is “equiprobable”.
It’s propper to have equiprobable prior between outcomes of a probability experiment, if you do not have any reason to expect that one is more likely than the other.
It’s ridiculous to have equiprobable prior between states that are not even possible outcomes of the experiment, to the best of your knowledge.
You are not an incorporeal ghost that could’ve inhabited any body throughout human history. You are your parents child. You couldn’t have been born before them or after they are already dead. Thinking otherwise is as silly as throwing a 6 sided die and then expecting to receive any outcome from a 20 sided die.
You were not anthropically sampled. You were born as a result of a physical process in a real world that you are trying to approximate as a probability experiment. This process had nothing to do with selecting universes that support conscious processes. This process has already been instantiated in a specific universe and has very limited time frame for your existence.
You will have to ignore all this knowledge and pretend that the process is completely different, without any evidence to back it up, to satisfy the conditions of Doomsday argument.
You can’t say “equiprobable” if you have no known set of possible outcomes to begin with.
Genuine question: what are your opinions on the breakfast hypothetical? [The idea that being able to give an answer to “how would you feel if you hadn’t eaten breakfast today?” is a good intelligence test, because only idiots are resistant to “evaluating counterfactuals”.]
This isn’t just a gotcha; I have my own opinions and they’re not exactly the conventional ones.
Not really. Nothing prevents us from reasoning about a set with unknown number of elements and saying that measure is spreaded equally among them, no matter how many of them there is. But this is irrelevant to the question at hand.
We know very well the size of set of possible outcomes for “In which ten billion interval your birth rank could’ve been”. This size is 1. No amount of pregnancy complications could postpone or hurry your birth so that you managed to be in a different 10 billion group.
I think it’s prudent to be careful about counterfactual reasoning on general principles. And among other reasons for it, to prevent the kind of mistake that you seem to be making: confusing
A) I’ve thrown a six sided die, even though I could’ve thrown a 20 sided one, what is the probability to observe 6?
and
B) I’ve thrown a six sided die, what would be the probability to observe 6, if I’ve thrown a 20 sided die instead?
The fact that question B has an answer doesn’t mean that question A has the same answer as well.
As for whether breakfast hypothetical is a good intelligence test, I doubt it. I can’t remember a single person whom I’ve seen have problems with intuitive understanding of counterfactual reasoning. On the other hand I’ve seen a bunch of principled hard determinists who didn’t know how to formalize “couldness” in a compatibilist way and threfore were not sure that counterfactuals are coherent on philosophical grounds. At best the distribution of the intelligence is going to be bi-modal.