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.
The theorem is only true for the phi that it's true for.
The claim that phi must be true because if it's true then it's true, and if it's false then "if PA |- phi then phi" has an officially true conclusion whenever PA does not imply phi, is bogus.
It's simply and obviously bogus, and I don't understand why there was any difficulty about seeing it.
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 it would be a completely different baseball team.
You might care about the result of arbitrary choices. I don't say you necessarily will.
It sounds like you're saying it's wrong to care about morals unless they're somehow provably correct? I'm not sure I get your o...
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 to do bad. If you have a morality that leaves you doing more good than bad, and driving increases the good and the bad you do proportionately, then your driving is a good thing.
True human beings have an insatiable curiousity, and they naturally want to find out about ...
"You should care about the moral code you have arbitrarily chosen."
No, I shouldn't. Which seems to be the focal point of this endless 'debate'.
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 haven't "really" chosen it.
I agree with you that there needn't be any platonic absolute morality that says you ought choose a moral code arbitrarily and care about it, or that if you do happen to choose a moral code arbitrarily that you should then care about it.
We are born with some theorems of right (in analogy to PA).
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 reflex for loud noises. I was pretty sure that was wrong, but it wasn't clear to me what we're born with. It takes time to learn to see. I remember when I invented the inverse square law for vision, and understood why things get smaller when they go farther away. It takes time to notice that parents have their own desires that need to be taken into account.
What is it that we're born with? Do you have a quick link maybe?
Larry, one of them is counterfactual.
If you draw implications on a false asumption then the result is useful only to show that an assumption is false.
So if PA -> 1=2 then PA -> 1<>2. How is that useful?
If PA -> 6 is prime then PA also -> 6 is not prime.
Once you assume that PA implies something that PA actually implies is false, you get a logical contradiction. Either PA is inconsistent or PA does not imply the false thing.
How can it be useful to reason about what we could prove from false premises? What good is it to pretend that PA is inconsistent?
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.
Before I say anything else I want you to know that I am not a Communist.
Marx was right about everything he wrote about, but he didn't know everything, I wouldn't say that Marx had all the answers. When the time is ripe the proletariat will inevitably rise up and create a government that will organize the people, it will put everybody to work accord...
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 is true. If 6 is prime then God's in his heaven, everything's right with the world and we are all muppets. Also God's in hell, everything's wrong with the world, and we are all mutant ninja turtles. It doesn't really matter what conclusions you draw from a false premis...
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 then A has to be true, it must be that A is true in the first place.
If this reasoning is correct then there isn't much mystery involved here.
One more time. If PA proves you are a werewolf, then you're really-and-truly a werewolf. PA never proves anything that isn't ac...
I went to the carnival and I met a fortune-teller. Everything she says comes true. Not only that, she told me that everything she says always comes true.
I said, "George Washington is my mother" and she said it wasn't true.
I said, "Well, if George Washington was my mother would you tell me so?" and she refused to say she would. She said she won't talk about what would be true if George Washingto was my mother, because George Washington is not my mother.
She says that everything she says comes true. She looked outside her little tent, and ...
The same boy who rationalized a way into believing there was a chocolate cake in the asteroid belt, should know better than to rationalize himself into believing it is right to prefer joy over sorrow.
Obviously, he does know. So the next question is, why does he present material that he knows is wrong?
Professional mathematicians and scientists try not to do that because it makes them look bad. If you present a proof that's wrong then other mathematicians might embarrass you at parties. But maybe Eliezer is immune to that kind of embarrassment. Socrates pres...
When you try to predict what will happen it works pretty well to assume that it's all deterministic and get what results you can. When you want to negotiate with somebody it works best to suppose they have free will and they might do whatever-the-hell they want.
When you can predict what inanimate objects will do with fair precision, that's a sign they don't have free will. And if you don't know how to negotiate with them, you haven't got a lot of incentive to assume they have free will. But particularly when they're actually predictable.
The more predictabl...
People keep using the term "moral relativism". I did a Google search of the site and got a variety of topics with the term dating from 2007 and 2008. Here's what it means to me.
Relative moral relativism means you affirm that to the best of your knowledge nobody has demonstrated any sort of absolute morality. That people differ in moralities, and if there's anything objective to say one is right and another is wrong that you haven't seen it. That very likely these different moralities are good for different purposes and different circumstances, an...
We have quick muscles, so we do computation to decide how to organise those muscles.
Trees do not have quick muscles, so they don't need that kind of computation.
Trees need to decide which directions to grow, and which directions to send their roots. Pee on the ground near a tree and it will grow rootlets in your direction, to collect the minerals you give it.
Trees need to decide which poisons to produce and where to pump them. When they get chewed on by bugs that tend to stay on the same leaf the trees tend to send their poisons to that leaf. When it's bug...
If you've ever taken a mathematics course in school, you yourself may have been introduced to a situation where it was believed that there were right and wrong ways to factor a number into primes. Unless you were an exceptionally good student, you may have disagreed with your teacher over the details of which way was right, and been punished for doing it wrong.
My experience with math classes was much different from yours. When we had a disagreement, the teacher said, "How would we tell who's right? Do you have a proof? Do you have a counter-example?&q...
Nominull, don't the primalists have a morality about heaps of stones?
They believe there are right ways and wrong ways to do it. They sometimes disagree about the details of which ways are right and they punish each other for doing it wrong.
How is that different from morality?
I think there is an important distinction between "kill or die" and "kill or be killed." The wolf's life may be at stake, but the rabbit clearly isn't attacking the wolf. If I need a heart transplant, I would still not be justified in killing someone to obtain the organ.
Mario, you are making a subtler distinction than I was. There is no end to the number of subtle distinctions that can be made.
In warfare we can distinguish between infantrymen who are shooting directly at each other, versus infantry and artillery or airstrikes that dump ...
This series of Potemkin essays makes me increasingly suspicious that someone's trying to pull a fast one on the Empress.
Agreed. I've suspected for some time that -- after laying out descriptions of how bias works -- Eliezer is now presenting us with a series of arguments that are all bias, all the time, and noticing how we buy into it.
It's not only the most charitable explanation, it's also the most consistent explanation.
If you were to stipulate that the rabbit is the only source of nourishment available to the fox, this still in no way justifies murder. The fox would have a moral obligation to starve to death.
How different is it when soldiers are at war? They must kill or be killed. If the fact that enemy soldiers will kill them if they don't kill the enemy first isn't enough justification, what is?
Should the soldiers on each side sit down and argue out the moral justification for the war first, and the side that is unjustified should surrender?
But somehow it seems like they hardly ever do that....
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.