Are you saying that you would not be even a little suspicious and inclined to back off if someone said they’d give you $6.50 in exchange for $3+$3? Not because your belief in arithmetic is shaky, but because your trust that people will give you fifty cents for no obvious reason is nonexistent and there is probably something going on?
I’m not denying that in a thought experiment, agents that are wrong about arithmetic can be money-pumped. I’m skeptical that in reality, human beings that are wrong about arithmetic can be money-pumped on an interesting scale.
Are you saying that you would not be even a little suspicious and inclined to back off if someone said they’d give you $6.50 in exchange for $3+$3? Not because your belief in arithmetic is shaky, but because your trust that people will give you fifty cents for no obvious reason is nonexistent and there is probably something going on?
In my hypothetical, we can suppose that they are perfectly aware of the existence of the other group. That is, the people who think that 3+4=7 are aware of the people who think that 3+4=6, and vice versa. This will provide them with all the explanation they need for the offer. They will think, “this person is one of those people who think that 3+4=7”, and that will explain to them the deal. They will see that the others are trying to profit off them, but they will believe that the attempt will fail, because after all, 3+4=6.
As a matter of fact, in my hypothetical the people who believe that 3+4=6 would be just as likely to offer those who believe that 3+4=7 a deal in an attempt to money-pump them. Since they believe that 3+4=6, and are aware of the belief of the others, they might offer the others the following deal: “give us $6.50, and then the next day we will give you $3 and the day after $4.” Since they believe that 3+4=6, they will think they are ripping the others off.
I’m not denying that in a thought experiment, agents that are wrong about arithmetic can be money-pumped. I’m skeptical that in reality, human beings that are wrong about arithmetic can be money-pumped on an interesting scale.
The thought experiment wasn’t intended to be applied to humans as they really are. It was intended to explain humans as they really are by imagining a competition between two kinds of humans—a group that is like us, and a group that is not like us. In the hypothetical scenario, the group like us wins.
And I think you completely missed my point, by the way. My point was that arithmetic is not merely a matter of agreement. The truth of a sum is not merely a matter of the majority of humanity agreeing on it. If more than half of humans believed that 3+4=6, this would not make 3+4=6 be true. Arithmetic truth is independent of majority opinion (call the view that arithmetic truth is a matter of consensus within a human group “arithmetic relativism” or “the consensus theory of arithmetic truth”). I argued for this as follows: suppose that half of humanity—nay, more than half—believed that 3+4=6, and a minority believed that 3+4=7. I argued that the minority with the latter belief would have the advantage. But if consensus defined arithmetic truth, that should not be the case. Therefore consensus does not define arithmetic truth.
My point is this: that arithmetic relativism is false. In your response, you actually assumed this point, because you’ve been assuming all along that 3+4=6 is false, even though in my hypothetical scenario a majority of humanity believed it is true.
So you’ve actually assumed my conclusion but questioned the argument that I used to argue for the conclusion.
And this, in turn, was to illustrate a more general point about consensus theories and relativism. The context was a discussion of morality. I had been interpreted as advocating what amounts to a consensus theory of morality, and I was trying to explain why may specific claims do not entail a consensus theory of morality, but are also compatible with a theory of morality as independent of consensus.
Are you saying that you would not be even a little suspicious and inclined to back off if someone said they’d give you $6.50 in exchange for $3+$3? Not because your belief in arithmetic is shaky, but because your trust that people will give you fifty cents for no obvious reason is nonexistent and there is probably something going on?
I’m not denying that in a thought experiment, agents that are wrong about arithmetic can be money-pumped. I’m skeptical that in reality, human beings that are wrong about arithmetic can be money-pumped on an interesting scale.
In my hypothetical, we can suppose that they are perfectly aware of the existence of the other group. That is, the people who think that 3+4=7 are aware of the people who think that 3+4=6, and vice versa. This will provide them with all the explanation they need for the offer. They will think, “this person is one of those people who think that 3+4=7”, and that will explain to them the deal. They will see that the others are trying to profit off them, but they will believe that the attempt will fail, because after all, 3+4=6.
As a matter of fact, in my hypothetical the people who believe that 3+4=6 would be just as likely to offer those who believe that 3+4=7 a deal in an attempt to money-pump them. Since they believe that 3+4=6, and are aware of the belief of the others, they might offer the others the following deal: “give us $6.50, and then the next day we will give you $3 and the day after $4.” Since they believe that 3+4=6, they will think they are ripping the others off.
The thought experiment wasn’t intended to be applied to humans as they really are. It was intended to explain humans as they really are by imagining a competition between two kinds of humans—a group that is like us, and a group that is not like us. In the hypothetical scenario, the group like us wins.
And I think you completely missed my point, by the way. My point was that arithmetic is not merely a matter of agreement. The truth of a sum is not merely a matter of the majority of humanity agreeing on it. If more than half of humans believed that 3+4=6, this would not make 3+4=6 be true. Arithmetic truth is independent of majority opinion (call the view that arithmetic truth is a matter of consensus within a human group “arithmetic relativism” or “the consensus theory of arithmetic truth”). I argued for this as follows: suppose that half of humanity—nay, more than half—believed that 3+4=6, and a minority believed that 3+4=7. I argued that the minority with the latter belief would have the advantage. But if consensus defined arithmetic truth, that should not be the case. Therefore consensus does not define arithmetic truth.
My point is this: that arithmetic relativism is false. In your response, you actually assumed this point, because you’ve been assuming all along that 3+4=6 is false, even though in my hypothetical scenario a majority of humanity believed it is true.
So you’ve actually assumed my conclusion but questioned the argument that I used to argue for the conclusion.
And this, in turn, was to illustrate a more general point about consensus theories and relativism. The context was a discussion of morality. I had been interpreted as advocating what amounts to a consensus theory of morality, and I was trying to explain why may specific claims do not entail a consensus theory of morality, but are also compatible with a theory of morality as independent of consensus.