Thank you, Mr. Kasper, for your thorough reply. Because all of this is new to me, I feel rather as I did the time I spent an hour on a tennis court with a friend who had won a tennis scholarship to college. Having no real tennis ability myself, I felt I was wasting his time; I appreciated that he’d agreed to play with me for that hour.
As I began to grasp the reasoning, I decided that each time you state the chance that the coin is heads, you are stating a fact. I asked myself what that means. I imagined the following:
I encounter you after you’ve spent two months traveling the world. You address me as follows:
“During my first month, I happened upon one hundred men who told me—each of them—that he had just flipped a coin twice. In each case, I asked, ‘Was at least one of the results heads?’ Each man said yes, and I knew that, in each case, the probability was 1⁄3 that both flips had been heads.
“In my second month, I again happened upon one hundred men who told me—each of them—that he had just flipped a coin twice. Each added, ‘One of the results was heads; I don’t remember what the other was.’ I knew that, in each case, the probability was 1⁄2 that both flips had been heads.
“Just as I was about to return home, I was approached by a man who had video recordings of the coin flips that those two hundred men had mentioned. In watching the recordings, I learned that both flips had been heads in fifty of the first one hundred cases and that, likewise, both flips had been heads in fifty of the second one hundred cases.”
In considering that, Mr. Kasper, I imagined the following exchange, which you may imagine as taking place between you and me. I speak first.
“My dog is in that box.”
“Is that a fact?”
“Yes.”
“In saying it’s a fact, you mean what?”
“I mean I regard it as true.”
“Which means what?”
“Which means I can imagine events that culminate in my saying, ‘I seem to have been mistaken; my dog wasn’t in that box.’”
“For example.”
“You walk over to the box and remove its lid, and I see my dog is not in it.”
“Maybe the dog disappeared—vanished into thin air—while I was walking over to the box.”
“That’s a possibility I wouldn’t be able to rule out; but because it would seem to me unlikely, I would say, ‘I seem to have been mistaken; my dog wasn’t in the box.’”
“How much is 189 plus 76?”
“To tell you that, I would have to get a pencil and paper and add them.”
“Please get a pencil and paper and add them; then tell me the result.”
“I’ve just done as you requested. Using a pencil and paper, I’ve added those two numbers. The result is 265.”
“189 + 76 = 265.”
“Correct.”
“Is that a fact?”
“Yes.”
“Please add them again.”
“I’ve just done as you requested. Using my pencil and paper, I’ve added those numbers a second time. I seem to have been mistaken. The result is 255.”
“Are you sure?”
“Well—”
“Please add them again.”
“I’ve just done as you requested. With my pencil and paper, I’ve added the numbers a third time.”
“And?”
“I was right the first time. The sum is 265.”
“Is that a fact?”
“That the sum is 265?”
“Yes.”
“I would say yes. It’s a fact.”
“How much is two plus two?”
“Four.”
“Did you use your pencil and paper to determine that?”
“No.”
“You used your pencil and paper to add 189 and 76 but not to add two and two.”
“That’s right.”
“Is there any sequence of events that could culminate in your saying, ‘I seem to have been mistaken; two plus two is not four.’”
Here are two links to classic posts by Eliezer Yudkowsky that you may find pertinent to the second dialog from your last comment. I hope you enjoy them.
Thank you for those links, Mr. Kasper. In taking a quick first look at the two pieces, I’ve noticed passages with which I’m familiar, so I must have encountered those posts as I made my initial reconnaissance, so to speak, of this very-interesting website. Now that you’ve directed my attention to those posts in particular, I’ll be able to read them with real attention.
Thank you, Mr. Kasper, for your thorough reply. Because all of this is new to me, I feel rather as I did the time I spent an hour on a tennis court with a friend who had won a tennis scholarship to college. Having no real tennis ability myself, I felt I was wasting his time; I appreciated that he’d agreed to play with me for that hour.
As I began to grasp the reasoning, I decided that each time you state the chance that the coin is heads, you are stating a fact. I asked myself what that means. I imagined the following:
I encounter you after you’ve spent two months traveling the world. You address me as follows:
“During my first month, I happened upon one hundred men who told me—each of them—that he had just flipped a coin twice. In each case, I asked, ‘Was at least one of the results heads?’ Each man said yes, and I knew that, in each case, the probability was 1⁄3 that both flips had been heads.
“In my second month, I again happened upon one hundred men who told me—each of them—that he had just flipped a coin twice. Each added, ‘One of the results was heads; I don’t remember what the other was.’ I knew that, in each case, the probability was 1⁄2 that both flips had been heads.
“Just as I was about to return home, I was approached by a man who had video recordings of the coin flips that those two hundred men had mentioned. In watching the recordings, I learned that both flips had been heads in fifty of the first one hundred cases and that, likewise, both flips had been heads in fifty of the second one hundred cases.”
In considering that, Mr. Kasper, I imagined the following exchange, which you may imagine as taking place between you and me. I speak first.
“My dog is in that box.”
“Is that a fact?”
“Yes.”
“In saying it’s a fact, you mean what?”
“I mean I regard it as true.”
“Which means what?”
“Which means I can imagine events that culminate in my saying, ‘I seem to have been mistaken; my dog wasn’t in that box.’”
“For example.”
“You walk over to the box and remove its lid, and I see my dog is not in it.”
“Maybe the dog disappeared—vanished into thin air—while I was walking over to the box.”
“That’s a possibility I wouldn’t be able to rule out; but because it would seem to me unlikely, I would say, ‘I seem to have been mistaken; my dog wasn’t in the box.’”
“How much is 189 plus 76?”
“To tell you that, I would have to get a pencil and paper and add them.”
“Please get a pencil and paper and add them; then tell me the result.”
“I’ve just done as you requested. Using a pencil and paper, I’ve added those two numbers. The result is 265.”
“189 + 76 = 265.”
“Correct.”
“Is that a fact?”
“Yes.”
“Please add them again.”
“I’ve just done as you requested. Using my pencil and paper, I’ve added those numbers a second time. I seem to have been mistaken. The result is 255.”
“Are you sure?”
“Well—”
“Please add them again.”
“I’ve just done as you requested. With my pencil and paper, I’ve added the numbers a third time.”
“And?”
“I was right the first time. The sum is 265.”
“Is that a fact?”
“That the sum is 265?”
“Yes.”
“I would say yes. It’s a fact.”
“How much is two plus two?”
“Four.”
“Did you use your pencil and paper to determine that?”
“No.”
“You used your pencil and paper to add 189 and 76 but not to add two and two.”
“That’s right.”
“Is there any sequence of events that could culminate in your saying, ‘I seem to have been mistaken; two plus two is not four.’”
“No.”
“Is it a fact?”
“That two plus two is four?”
“Yes.”
“Yes. It’s a fact.”
“In saying that, you mean what?”
“—I don’t know.”
Thank you again.
Mr. Bonaccorsi:
Here are two links to classic posts by Eliezer Yudkowsky that you may find pertinent to the second dialog from your last comment. I hope you enjoy them.
How to Convince Me That 2 + 2 = 3
The Simple Truth
Thank you for those links, Mr. Kasper. In taking a quick first look at the two pieces, I’ve noticed passages with which I’m familiar, so I must have encountered those posts as I made my initial reconnaissance, so to speak, of this very-interesting website. Now that you’ve directed my attention to those posts in particular, I’ll be able to read them with real attention.