Yovanni tells Zenia, “The winner of the lottery was Xavier Williams of California.”
When evaluating the veracity of this statement, Zenia is not evaluating the odds of someone with that name winning a lottery. Someone won the lottery and their name has been made publicly available. What she is evaluating is Yovanni’s general trustworthiness in this kind of situations. Does Yovanni like to make stuff up? To play pranks? Has reading comprehension issues? The odds of the lottery have zero to do with this. They would only matter if Yovanni could have some useful additional information, such as if it was a raffle at a party, and you knew that no one named Xavier Williams was invited.
Scenario 1: A friend who you know to generally be fairly trustworthy tells you that there is a snowstorm in New York City.
Scenario 2: A friend who you know to generally be fairly trustworthy tells you that there is a snowstorm in Ecuador.
Scenario 3: A friend who you know to generally be fairly trustworthy tells you that there is a snowstorm on the surface of Venus, which they spotted by looking up into the sky with their keen vision after Batman showed up and used his power ring to grant them super senses.
As I understand your comment above, it sounds like you’re saying you will evaluate the veracity of the three scenarios above the same way, caring only about the friend’s trustworthiness and not at all about how implausible the story sounds. This seems very strange—am I misunderstanding?
The ‘paradox’ being mentioned in the post is that Xavier Williams winning the lottery seems like it should be a plausible-sounding story (a la Scenario A), but a naive mathematical analysis (missing Phil’s point above) makes it seem like a very implausible-sounding one.
No, these are completely different. NYC and Equador are not random samples of places where a snowstorm is equally likely. A more charitable comparison would be “It’s winter in the Northern Hemisphere, and there was a snowstorm in one of the major cities. Yovanni checks the weather app and says that it’s in NYC.”
When evaluating the veracity of this statement, Zenia is not evaluating the odds of someone with that name winning a lottery. Someone won the lottery and their name has been made publicly available. What she is evaluating is Yovanni’s general trustworthiness in this kind of situations. Does Yovanni like to make stuff up? To play pranks? Has reading comprehension issues? The odds of the lottery have zero to do with this. They would only matter if Yovanni could have some useful additional information, such as if it was a raffle at a party, and you knew that no one named Xavier Williams was invited.
Scenario 1: A friend who you know to generally be fairly trustworthy tells you that there is a snowstorm in New York City.
Scenario 2: A friend who you know to generally be fairly trustworthy tells you that there is a snowstorm in Ecuador.
Scenario 3: A friend who you know to generally be fairly trustworthy tells you that there is a snowstorm on the surface of Venus, which they spotted by looking up into the sky with their keen vision after Batman showed up and used his power ring to grant them super senses.
As I understand your comment above, it sounds like you’re saying you will evaluate the veracity of the three scenarios above the same way, caring only about the friend’s trustworthiness and not at all about how implausible the story sounds. This seems very strange—am I misunderstanding?
The ‘paradox’ being mentioned in the post is that Xavier Williams winning the lottery seems like it should be a plausible-sounding story (a la Scenario A), but a naive mathematical analysis (missing Phil’s point above) makes it seem like a very implausible-sounding one.
No, these are completely different. NYC and Equador are not random samples of places where a snowstorm is equally likely. A more charitable comparison would be “It’s winter in the Northern Hemisphere, and there was a snowstorm in one of the major cities. Yovanni checks the weather app and says that it’s in NYC.”