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I thought of a simpler way to say it.
If Hillary Clinton was a man, she wouldn't be Bill Clinton's wife. She'd be his husband.
Similarly, if PA proved that 6 was prime, it wouldn't be PA. It would be Bill Clinton's husband. And so ZF would not imply that 6 is actually prime.
<p>Larry, you have not proven that 6 would be a prime number if PA proved 6 was a prime number, because PA does not prove that 6 is a prime number.</p>
<p>The theorem is only true for the phi that it's true for.</p>
<p>The claim that phi must be true because if it's true then it's true, and if it'...(read more)
Caledonian, it's possible to care deeply about choices that were made in a seemingly-arbitrary way. For example, a college graduate who takes a job in one of eight cities where he got job offers, might within the year care deeply about that city's baseball team. But if he had taken a different job i...(read more)
I haven't read Roko's blog, but from the reflection in Eliezer's opposition I find I somewhat agree.
To the extent that morality is about what you *do*, the more you can do the higher the stakes.
If you can drive a car, your driving amplifies your ability to do good. And it amplifies your ability ...(read more)
"You should care about the moral code you have arbitrarily chosen."
<i>No, I shouldn't. Which seems to be the focal point of this endless 'debate'.</i>
Well, you might choose to care about a moral code you have arbitrarily chosen. And it could be argued that if you don't care about it then you hav...(read more)
<i>We are born with some theorems of right (in analogy to PA).</i>
Kenny, I'd be fascinated to learn more about that. I didn't notice it in my children, but then I wouldn't necessarily notice.
When I was a small child people claimed that babies are born with only a fear of falling and a startle re...(read more)
<p>Larry, one of them is counterfactual.</p>
<p>If you draw implications on a false asumption then the result is useful only to show that an assumption is false.</p>
<p>So if PA -> 1=2 then PA -> 1<>2. How is that useful?</p>
<p>If PA -> 6 is prime then PA also -> 6 is not prime...(read more)
<i>Honestly I do not understand how you can continue calling Eliezer a relativist when he has persistently claimed that what is right doesn't depend on who's asking and doesn't depend on what anyone thinks is right.</i>
Before I say anything else I want you to know that I am not a Communist.
Marx ...(read more)
But Larry, PA does not actually say that 6 is prime, and 6 is not prime.
You could say that if PA proved that every theorem is false then every theorem would be false.
Or what would it mean if PA proved that Lob's theorem was false?
It's customary to say that any conclusion from a false premise i...(read more)
Let me try to say that clearer.
Suppose that A is false.
How the hell are you going to show that if PA proves A true then A will be true, when A is actually false?
If you can't prove what would happen if PA proved A true when A is actually false, then if you can prove that if PA proves A is true ...(read more)