Ironically, this is mathematically true. (Assuming Eliezer hasn’t forsaken epistemic rationality, that is.) It’s just that if Eliezer changes what he wants to believe, the color of snow won’t change to reflect it.
In mathematics, an “if and only if” statement is defined as being true whenever its arguments are both true, or both false. “Snow is white” and “that’s what Eliezer Yudkowsky wants to believe” are both true, so the statement is true.
Statements containing “if” often (usually?) have an implied “for all” in them, though. The implication here is something like “For all possible values of what-Eliezer-Yudkowsky-wants-to-believe, snow is white if and only if that’s what Eliezer Yudkowsky wants to believe.”
Hm. Yeah, that’s how I read it. I’d say it this way, when I see an “if and only if”, I see a statement about the whole truth table, not just the particular values of p and q that happen to hold. This is a mistake?
I wouldn’t call it a mistake. Your interpretation is probably the intended interpretation of the statement, and a more natural one. My interpretation is what you get when you translate the statement naively into formal logic.
Snow is white if and only if that’s what Eliezer Yudkowsky wants to believe.
Ironically, this is mathematically true. (Assuming Eliezer hasn’t forsaken epistemic rationality, that is.) It’s just that if Eliezer changes what he wants to believe, the color of snow won’t change to reflect it.
What?! Blasphemy!
No, it’s also mathematically true. He won’t change what he wants to believe.
Hm. Isn’t that what “and only if” would be about?
In mathematics, an “if and only if” statement is defined as being true whenever its arguments are both true, or both false. “Snow is white” and “that’s what Eliezer Yudkowsky wants to believe” are both true, so the statement is true.
Statements containing “if” often (usually?) have an implied “for all” in them, though. The implication here is something like “For all possible values of what-Eliezer-Yudkowsky-wants-to-believe, snow is white if and only if that’s what Eliezer Yudkowsky wants to believe.”
Hm. Yeah, that’s how I read it. I’d say it this way, when I see an “if and only if”, I see a statement about the whole truth table, not just the particular values of p and q that happen to hold. This is a mistake?
I wouldn’t call it a mistake. Your interpretation is probably the intended interpretation of the statement, and a more natural one. My interpretation is what you get when you translate the statement naively into formal logic.
Gotcha. Thanks for the replies.